de Méritens. Disk winding was also successfully introduced for
alternators, as in the magneto-machines of Nollet (1849) and the
alternators of Wilde (1866) and Siemens (1878), and its use was
continued in the machines of W.M. Mordey and S.Z. Ferranti. But although
the ring, discoidal-ring and disk methods of winding deserve mention
from their historical importance, experience has shown that drum winding
possesses a marked superiority for both electrical and manufacturing
reasons; the three former methods have in fact been practically
discarded in its favour, so that the drum method will hereafter alone be
considered.

The drum coil, composed of several loops wound side by side, may
therefore be regarded as the constituent active element out of which the
armature winding of the modern dynamo is developed. Its application to
the multipolar machine is easily followed from fig. 9, which illustrates
the heteropolar type of dynamo. The span of the loops, which is nearly
180° or across the diameter of the two-pole machine, is reduced
approximately to 90° in the four-pole or to 60° in the six-pole machine
and so on, the curvature of the coil becoming gradually less as the
number of poles is increased. The passage of a coil through two magnetic
fields of opposite direction yields a complete wave of E.M.F., such as
is shown in fig. 6, and the time in seconds taken to pass through such a
complete cycle is the "period" of the alternating E.M.F. The number of
complete periods through which the E.M.F. of the coil passes per second
is called the "periodicity" or "frequency" of the machine. In the
bipolar machine this is equal to the number of revolutions per second,
and in the multipolar machine it is equal to the number of pairs of
fields through which the coil passes in one second; hence in general the
periodicity is pN/60, where N = the number of revolutions per minute and
p = the number of pairs of poles, and this holds true of the E.M.F. and
current round the coil, even though the E.M.F. and current furnished to
the external circuit may be rendered unidirectional or continuous. The
only difference on this point is that in the continuous-current machine
the poles are usually fewer than in the alternator, and the periodicity
is correspondingly lower. Thus in the former case the number of poles
ranges from 2 to 12 and the usual frequencies from 5 to 20; but with
alternators the frequencies in commercial use range from 25 to 120, and
in large machines driven by slow-speed engines the number of poles may
even be as high as 96.

[Illustration: FIG. 9.

I. Smooth. II. Toothed.]

[Illustration: FIG. 10.]

The drum coil may be applied either to the external surface of a
rotating armature, the field-magnet being external and stationary (fig.
9), or to the internal surface of a stationary armature (fig. 10), the
field-magnet being internal and rotating. While the former combination
is universally adopted in the continuous-current dynamo, the latter is
more usual in the modern alternator. In either case the iron armature
core must be "laminated"; the passage of the lines of the field across
its surface sets up E.M.F.'s which are in opposite directions under
poles of opposite sign, so that if the core were a solid mass a
current-sheet would flow along its surface opposite to a pole, and
complete its circuit by passing through the deeper layers of metal or by
returning in a sheet under a pole of opposite sign. Such "eddy-currents"
can be practically avoided by dividing the metal core into laminations
at right angles to the length of the active wires which are themselves
arranged to secure the greatest rate of line-cutting and maximum E.M.F.
The production of the eddy-current E.M.F. is not thereby prevented, but
the paths of the eddy-currents are so broken up that the comparatively
high resistance with which they meet reduces their amount very greatly.
The laminae must be lightly insulated from one another, right up to
their edges, so that the E.M.F.'s which still act across their thickness
will not be added up along the length of the core, but will only produce
extremely small currents circulating through the interior of the
separate laminations. Each thin iron plate is either coated with an
insulating varnish or has one of its sides covered with a sheet of very
thin paper; the thickness of the laminae is usually about one-fortieth
of an inch, and if this is not exceeded the rate at which energy is
dissipated by eddy-currents in the core is so far reduced that it does
not seriously impair the efficiency of the machine.

Lastly, the drum coils may be either attached to the surface of a smooth
armature core (fig. 9, I.), or may be wound through holes formed close
to the periphery of the core, or may be embedded in the slots between
projecting iron teeth (figs. 9 [II.] and 10). Originally employed by
Antonio Pacinotti in connexion with ring winding, the toothed armature
was after some considerable use largely discarded in favour of the
smooth core; it has, however, been reintroduced with a fuller
understanding of the special precautions necessitated in its design, and
it is now so commonly used that it may be said to have superseded the
smooth-surface armature.

  Not only does the toothed armature reduce the length of the air-gap to
  the minimum permitted by mechanical and magnetic considerations, and
  furnish better mechanical protection to the armature coils, but it
  also ensures the positive holding of the active wires against the
  mechanical drag which they experience as they pass through the
  magnetic field. Further, the active wires in the toothed armature are
  relieved of a large proportion of this mechanical drag, which is
  transferred to the iron teeth. The lines of the field, after passing
  through the air-gap proper, divide between the teeth and the slots in
  proportion to their relative permeances. Hence at any moment the
  active wires are situated in a weak field, and for a given armature
  current the force on them is only proportional to this weak field.
  This important result is connected with the fact that when the
  armature is giving current the distribution of the lines over the face
  of each tooth is distorted, so that they become denser on the
  "trailing" side than on the "leading" side;[13] the effect of the
  non-uniform distribution acting on all the teeth is to produce a
  magnetic drag on the armature core proportional to the current passing
  through the wires, so that the total resisting force remains the same
  as if the armature had a smooth core. The amount by which the stress
  on the active wires is reduced entirely depends upon the degree to
  which the teeth are saturated, but, since the relative permeability of
  iron even at a flux density of 20,000 lines per sq. cm. is to that of
  air approximately as 33:1, the embedded wires are very largely
  relieved of the driving stress. An additional gain is that solid bars
  of much greater width can be used in the toothed armature than on a
  smooth core without appreciable loss from eddy-currents within their
  mass.

  A disadvantage of the slotted core is, however, that it usually
  necessitates the lamination of the pole-pieces. If the top of the slot
  is open, and its width of opening is considerably greater than the
  length of the air-gap from the iron of the pole-face to the surface of
  the teeth, the lines become unequally distributed not only at the
  surface of the teeth, but also at the face of the pole-pieces; and
  this massing of the lines into bands causes the density at the
  pole-face to be rhythmically varied as the teeth pass under it. No
  such variation can take place in a solid mass of metal without the
  production of eddy-currents within it; hence if the width of the
  slot-opening is equal to or exceeds twice the length of the single
  air-gap, lamination of the pole-pieces in the same plane as that of
  the armature core becomes advisable.

  If the wires are threaded through holes or tunnels pierced close to
  the periphery of the core, the same advantages are gained as with open
  slots, and lamination of the pole-pieces is rendered unnecessary. But
  on the other hand, the process of winding becomes laborious and
  expensive, while the increase in the inductance of the coils owing to
  their being surrounded by a closed iron circuit is prejudicial to
  sparkless commutation in the continuous-current dynamo and to the
  regulation of the voltage of the alternator. A compromise is found in
  the half-closed slot, which is not uncommon in alternators, although
  the open slot is more usual in continuous-current dynamos.

With the addition of more turns to the elementary drum loop or of
several complete coils, new questions arise, and in connexion therewith
the two great classes of machines, viz. alternators and
continuous-current dynamos, which have above been treated side by side,
diverge considerably, so that they are best considered separately. The
electromotive-force equation of the alternator will be first deduced,
and subsequently that of the continuous-current machine.

[Illustration: FIG. 11.]

Corresponding to the number of pairs of poles in the multipolar
alternator, it is evident that there may also be an equal number of
coils as shown diagrammatically in fig. 11. The additional coils, being
similarly situated in respect to other pairs of poles, will exactly
reproduce the E.M.F. of the original coil in phase and magnitude, so
that when they are connected in series the total E.M.F. will be
proportional to the number of coils in series; or if they are connected
in parallel, while not adding to the E.M.F., they will proportionately
increase the current-carrying capacity of the combination. But within
each coil the addition of more loops will not cause an equal increase in
the total E.M.F., unless the phases of the component E.M.F.'s due to the
several turns are identical, and on this account it becomes necessary to
consider the effect of the width of the coil-side.

[Illustration: FIG. 12.]

If the additional loops are wound within the same slots as the original
loop, the winding is "concentrated," and each turn will then add the
same E.M.F. But if the coil-side is divided between two or more slots,
the phase of the E.M.F. yielded by the wires in one slot being different
from that of the wires in another neighbouring slot, the sum of all the
E.M.F.'s will be less than the E.M.F. of one component loop multiplied
by the number of loops or turns in the coil. The percentage reduction in
the E.M.F. will depend upon the number of the slots in a coil-side and
their distance apart, i.e. on the virtual width of the coil-side
expressed as a fraction of the "pole-pitch" or the distance measured
along the pitch-line from the centre of one pole to the centre of a
neighbouring pole of opposite sign (fig. 12). The winding is now to be
regarded as "grouped," since a small number of distinct phases
corresponding to the groups within the two, three or four slots have to
be compounded together. As the number of slots per coil-side is
increased, an approach is gradually made to the case of "uniform
distribution," such as would obtain in a smooth-core armature in which
the turns of the coil are wound closely side by side. Thus in the
six-turn coil of fig. 12 A, which represents the development of a
two-pole armature when the core is cut down to the shaft and opened out
flat, there are in effect six phases compounded together, each of which
differs but little from that of its next neighbour. With numerous wires
lying still closer together a large number of phases are compounded
until the distribution becomes practically uniform; the decrease in the
E.M.F., as compared with that of a single turn multiplied by the number
in series, is then immediately dependent upon the width of the coil-side
relatively to the pole-pitch.

[Illustration: FIG. 13.]

If the width of the inner loop of fig. 12 A is less than that of the
pole-face, its two sides will for some portion of each period be moving
under the same pole, and "differential action" results, the net E.M.F.
being only that due to the difference between the E.M.F.'s of the two
sides. The loop of smallest width must therefore exceed the width of
pole-face, if direct differential action is to be avoided. The same
consideration also determines the width of the outer loop; if this be
deducted from twice the pole-pitch, the difference should not be less
than the width of the pole-face, so that, e.g., in a bipolar machine the
outer loop may stand to the S. pole exactly as the inner loop stands to
the N. pole (fig. 13). In other words, the width of the coil-side must
not exceed the width of the interpolar gap between two fields. Evidently
then if the ratio of the pole-width to the pole-pitch approaches unity,
the width of the coil-side must be very small, and vice versa. A
compromise between these conflicting considerations is found if the pole
is made not much more than half the pole-pitch, and the width of the
coil-side is similarly about half the pole-pitch and therefore equal in
width to the pole (fig. 13). A single large coil, such as that of fig.
12 A, can, however, equally well be divided into two halves by taking
the end-connexions of one half of the turns round the opposite side of
the shaft (fig. 12 B), as indeed has already been done in fig. 13. Each
sheaf or band of active wires corresponding to a pole is thereby
unaffected, but the advantages are gained that the axial length of the
end-connexions is halved, and that they have less inductance. Thus if in
fig. 11 there are four turns per coil, fig. 14 is electrically
equivalent to it (save that the coils are here shown divided into two
parallel paths, each carrying half the total current). When the large
coils are divided as above described, it results that there are as many
coils as there are poles, the outer loop of the small coil having a
width equal to the pole-pitch, and the inner a width equal to the
pole-face.

[Illustration: FIG. 14.]

Such is the form which the "single-phase alternator" takes, but since
only one-half of the armature core is now covered with winding, an
entirely distinct but similar set of coils may be wound to form a second
armature circuit between the coils of the first circuit. The phase of
this second circuit will differ by 90° or a quarter of a period from
that of the first, and it may either be used to feed an entirely
separate external circuit possibly at a different pressure or, if it be
composed of the same number of turns and therefore gives the same
voltage, it may be interconnected with the first circuit to form a
"quarter-phase alternator," as will be more fully described later. By an
extension of the same process, if the width of each side of a coil is
reduced to one-sixth of the pole-pitch, three armature circuits can be
wound on the same core, and a "three-phase alternator," giving waves of
E.M.F. differing in phase by 120°, is obtained.

  The fundamental "electromotive-force equation" of the heteropolar
  alternator can now be given a more definite form. Let Z_a be the
  number of C. G. S. lines or the total flux, which issuing from any
  one pole flows through the armature core, to leave it by another pole
  of opposite sign. Since each active wire cuts these lines, first as
  they enter the armature core and then as they emerge from it to enter
  another pole, the total number of lines cut in one revolution by any
  one active wire is 2pZ_a. The time in seconds taken by one revolution
  is 60/N. The average E.M.F. induced in each active wire in one
  revolution being proportional to the number of lines cut divided by
  the time taken to cut them is therefore 2Z_a(pN/60) × 10^(-8) volts.
  The active wires which are in series and form one distinct phase may
  be divided into as many bands as there are poles; let each such band
  contain t active wires, which as before explained may either form one
  side of a single large coil or the adjacent sides of two coils when
  the large coil is divided into two halves. Since the wires are joined
  up into loops, two bands are best considered together, which with
  either arrangement yield in effect a single coil of t turns. The
  average E.M.F.'s of all the wires in the two bands when added together
  will therefore be 4Z_a(pN/60)t × 10^(-8). But unless each band is
  concentrated within a single slot, there must be some differential
  action as they cross the neutral line between the poles, so that the
  last expression is virtually the _gross_ average E.M.F. of the loops
  on the assumption that the component E.M.F.'s always act in agreement
  round the coil and do not at times partially neutralize one another.
  The _net_ average E.M.F. of the coil as a whole, or the arithmetical
  mean of all the instantaneous values of a half-wave of the actual
  E.M.F. curve, is therefore reduced to an extent depending upon the
  amount of differential action and so upon the width of the coil-side
  when this is not concentrated. Let k' = the coefficient by which the
  gross average E.M.F. must be multiplied to give the net average
  E.M.F.; then k' may be called the "width-factor," and will have some
  value less than unity when the wires of each band are spread over a
  number of slots. The net average E.M.F. of the two bands corresponding
  to a pair of poles is thus e_(av) = 4k'Z_a(pN/60)t × 10^(-8).

  The shape of the curve of instantaneous E.M.F. of the coil must
  further be taken into account. The "effective" value of an alternating
  E.M.F. is equal to the square root of the mean square of its
  instantaneous values, since this is the value of the equivalent
  unidirectional and unvarying E.M.F., which when applied to a given
  resistance develops energy at the same rate as the alternating E.M.F.,
  when the effect of the latter is averaged over one or any whole number
  of periods. Let k" = the ratio of the square root of the mean square
  to the average E.M.F. of the coil, i.e. = effective E.M.F./average
  E.M.F. Since it depends upon the shape of the E.M.F. curve, k" is also
  known as the "form-factor"; thus if the length of gap between
  pole-face and armature core and the spacing of the wires were so
  graduated as to give a curve of E.M.F. varying after a sine law, the
  form-factor would have the particular value of [pi]/2[root]2 = 1.11,
  and to this condition practical alternators more or less conform. The
  effective E.M.F. of the two bands corresponding to a pair of poles is
  thus e_(eff) = 4k'k"Z_a(pN/60)t × 10^(-8).

  In any one phase there are p pairs of bands, and these may be divided
  into q parallel paths, where q is one or any whole number of which p
  is a multiple. The effective E.M.F. of a complete phase is therefore
  pe{eff}/q. Lastly, if m = the number of phases into which the armature
  winding is divided, and [tau] = the total number of active wires on
  the armature counted all round its periphery, t = [tau]/2pm, and the
  effective E.M.F. per phase is E_a = 2k'k"Z_a(pN[tau]/60mq) × 10^(-8).

  The two factors k' and k" may be united into one coefficient, and the
  equation then takes its final form

    E_a = 2KZ_a(pN[tau]/60mq) × 10^(-8) volts  (1a)

  In the alternator q is most commonly 1, and there is only one circuit
  per phase; finally the value of K or the product of the width-factor
  and the form-factor usually falls between the limits of 1 and 1.25.

We have next to consider the effect of the addition of more armature
loops in the case of dynamos which give a unidirectional E.M.F. in
virtue of their split-ring collecting device, i.e. of the type shown in
fig. 7 with drum armature or its equivalent ring form. As before, if the
additional loops are wound in continuation of the first as one coil
connected to a single split-ring, this coil must be more or less
concentrated into a narrow band; since if the width becomes nearly equal
to or exceeds the width of the interpolar gap, the two edges of the
coil-side will just as in the alternator act differentially against one
another during part of each revolution. The drum winding with a single
coil thus gives an armature of the H- or "shuttle" form invented by Dr
Werner von Siemens. Although the E.M.F. of such an arrangement may have
a much higher maximum value than that of the curve of fig. 7 for a
single loop, yet it still periodically varies during each revolution and
so gives a pulsating current, which is for most practical uses
unsuitable. But such pulsation might be largely reduced if, for example,
a second coil were placed at right angles to the original coil and the
two were connected in series; the crests of the wave of E.M.F. of the
second coil will then coincide with the hollows of the first wave,
and although the maximum of the resultant curve of E.M.F. may be no
higher its fluctuations will be greatly decreased. A spacial
displacement of the new coils along the pole-pitch, somewhat as in a
polyphase machine, thus suggests itself, and the process may be carried
still further by increasing the number of equally spaced coils, provided
that they can be connected in series and yet can have their connexion
with the external circuit reversed as they pass the neutral line between
the poles.

[Illustration: FIG. 15.]

[Illustration: FIG. 16.]

Given two coils at right angles and with their split-rings displaced
through a corresponding angle of 90°, they may be connected in series by
joining one brush to the opposite brush of the second coil, the external
circuit being applied to the two remaining brushes.[14] The same
arrangement may again be repeated with another pair of coils in parallel
with the first, and we thus obtain fig. 15 with four split-rings, their
connexions to the loops being marked by corresponding numerals; the four
coils will give the same E.M.F. as the two, but they will be jointly
capable of carrying twice the current, owing to their division into two
parallel circuits. Now in place of the four split-rings may be employed
the greatly simplified four-segment structure shown in fig. 16, which
serves precisely the same purpose as the four split-rings but only
requires two instead of eight brushes. The effect of joining brush 2 in
fig. 15 across to brush 3, brush 4 to brush 5, 5 to 6, &c., has
virtually been to connect the end of coil A with the beginning of coil
B, and the end of coil B with the beginning of coil A', and so on, until
they form a continuous closed helix. Each sector of fig. 16 will
therefore replace two halves of a pair of adjacent split-rings, if the
end and beginning of a pair of adjacent coils are connected to it in a
regular order of sequence. The four sectors are insulated from one
another and from the shaft, and the whole structure is known as the
"commutator,"[15] its function being not simply to collect the current
but also to commute its direction in any coil as it passes the
interpolar gap. The principle of the "closed-coil continuous-current
armature" is thus reached, in which there are at least two parallel
circuits from brush to brush, and from which a practically steady
current can be obtained. Each coil is successively short-circuited, as a
brush bridges over the insulation between the two sectors which
terminate it; and the brushes must be so set that the period of
short-circuit takes place when the coil is generating little or no
E.M.F., i.e. when it is moving through the zone between the pole-tips.
The effect of the four coils in reducing the percentage fluctuation of
the E.M.F. is very marked, as shown at the foot of fig. 15 (where the
upper curve is the resultant obtained by adding together the separate
curves of coils A and B), and the levelling process may evidently be
carried still further by the insertion of more coils and more
corresponding sectors in the commutator, until the whole armature is
covered with winding. For example, figs. 17 and 18 show a ring and a
drum armature, each with eight coils and eight commutator sectors; their
resultant curve, on the assumption that a single active wire gives the
flat-topped curve of fig. 4, will be the upper wavy line of E.M.F.
obtained by adding together two of the resultant curves of fig. 15, with
a relative displacement of 45°. The amount of fluctuation for a given
number of commutator sectors depends upon the shape of the curve of
E.M.F. yielded by the separate small sections of the armature winding;
the greater the polar arc, the less the fluctuation. In practice, with a
polar arc equal to about 0.75 of the pitch, any number of sectors over
32 per pair of poles yields an E.M.F. which is sensibly constant
throughout one or any number of revolutions.

[Illustration: FIG. 17.]

[Illustration: FIG. 18.]

  The fundamental electro-motive-force equation of the
  continuous-current heteropolar machine is easily obtained by analogy
  from that of the alternator. The gross average E.W.F. from the two
  sides of a drum loop without reference to its direction is as before
  4Z_a(pN/60) × 10^(-8) volts. But for two reasons its net average
  E.M.F. may be less; the span of the loop may be less than the
  pole-pitch, so that even when the brushes are so set that the position
  of short-circuit falls on the line where the field changes its
  direction, the two sides of the loop for some little time act against
  each other; or, secondly, even if the span of the loop be equal to the
  pole-pitch, the brushes may be so set that the reversal of the
  direction of its induced E.M.F. does not coincide with reversal of the
  current by the passage of the coil under the brushes. The net average
  E.M.F. of the loop is therefore proportional to the algebraic sum of
  the lines which it cuts in passing from one brush to another, and this
  is equal to the net amount of the flux which is included within the
  loop when situated in the position of short-circuit under a brush. The
  amount of this flux may be expressed as k'Z_a where k' is some
  coefficient, less than unity if the span of the coil be less than the
  pole-pitch, and also varying with the position of the brushes. The net
  average E.M.F. of the loop is therefore

    4k'Z_a(pN/60) × 10^(-8).

  In practice the number of sections of the armature winding is so large
  and their distribution round the armature periphery is so uniform,
  that the sum total of the instantaneous E.M.F.'s of the several
  sections which are in series becomes at any moment equal to the net
  average E.M.F. of one loop multiplied by the number which are in
  series. If the winding is divided into q parallel circuits, the number
  of loops in series is [tau]/2q, so that the total E.M.F. is E_a =
  2(k'/q)Z_a(pN/60)[tau] × 10^(-8) volts. Thus as compared with the
  alternator not only is there no division of the winding into separate
  phases, but the form-factor k' disappears, since the effective and
  average E.M.F.'s are the same. Further whereas in the alternator q may
  = 1, in the continuous-current closed-coil armature there can never be
  less than two circuits in parallel from brush to brush, and if more,
  their number must always be a multiple of two, so that q can never be
  less than two and must always be an even number. Lastly, the factor k'
  is usually so closely equal to 1, that the simplified equation may in
  practice be adopted, viz.

    E_a = (2/q)(ZpN/60)[tau] × 10^(-8) volts  (1b)

  The fundamental equation of the electromotive force of the dynamo in
  its fully developed forms (1 a) (and 1 b) may be compared with its
  previous simple statement (1.). The three variable terms still find
  their equivalents, but are differently expressed, the density B_g
  being replaced by the total flux of one field Z_a, the length L of the
  single active wire by the total number of such wires [tau], and the
  velocity of movement V by the number of revolutions per second. Even
  when the speed is fixed, an endless number of changes may be rung by
  altering the relative values of the remaining two factors; and in
  successful practice these may be varied between fairly wide limits
  without detriment to the working or economy of the machine. While it
  may be said that the equation of the E.M.F. was implicitly known from
  Faraday's time onwards, the difficulty under which designers laboured
  in early days was the problem of choosing the correct relation of Z_a
  or [tau] for the required output; this, again, was due chiefly to the
  difficulty of predetermining the total flux before the machine was
  constructed. The general error lay in employing too weak a field and
  too many turns on the armature, and credit must here be given to the
  American inventors, E. Weston and T.A. Edison, for their early
  appreciation of the superiority in practical working of the drum
  armature, with comparatively few active wires rotating in a strong
  field.

  The armature core.

_Continuous-current Dynamos._--On passing to the separate consideration
of alternators and continuous-current dynamos, the chief constructive
features of the latter will first be taken in greater detail. As already
stated in the continuous-current dynamo the armature is usually the
rotating portion, and the necessity of laminating its core has been
generally described. The thin iron stampings employed to build up the
core take the form of circular washers or "disks," which in small
machines are strung directly on the shaft; in larger multipolar
machines, in which the required radial depth of iron is small relatively
to the diameter, a central cast iron hub supports the disks. Since the
driving force is transmitted through the shaft to the disks, they must
in the former case be securely fixed by keys sunk into the shaft; when a
central hub is employed (fig. 19) it is keyed to the shaft, and its
projecting arms engage in notches stamped on the inner circumference of
the disks, or the latter have dovetailed projections fitting into the
arms. The disks are then tightly compressed and clamped between stout
end-plates so as to form a nearly solid iron cylinder of axial length
slightly exceeding the corresponding dimension of the poles. If the
armature is more than 4 ft. in diameter, the disks become too large to
be conveniently handled in one piece, and are therefore made in
segments, which are built up so as to break joint alternately. Prior to
assemblage, the external circumference of each disk is notched in a
stamping machine with the required number of slots to receive the
armature coils, and the longitudinal grooves thereby formed in the
finished core only require to have their sharp edges smoothed off so
that there may be no risk of injury to the insulation of the coils.

[Illustration: FIG. 19.]

  Armature winding.

With open slots either the armature coils may be encased with wrappings
of oiled linen, varnished paper and thin flexible micanite sheeting in
order to insulate them electrically from the iron slots in which they
are afterwards embedded; or the slots may be themselves lined with
moulded troughs of micanite, &c., for the reception of the armature
coils, the latter method being necessary with half-closed slots.
According to the nature of the coils armatures may be divided into the
two classes of coil-wound and bar-wound. In the former class, round
copper wire, double-cotton covered, is employed, and the coils are
either wound by hand directly on to the armature core, or are shaped on
formers prior to being inserted in the armature slots. Hand-winding is
now only employed in very small bipolar machines, the process being
expensive and accompanied by the disadvantage that if one section
requires to be repaired, the whole armature usually has to be dismantled
and re-wound. Former-wound coils are, on the other hand, economical in
labour, perfectly symmetrical and interchangeable, and can be thoroughly
insulated before they are placed in the slots. The shapers employed in
the forming process are very various, but are usually arranged to give
to the finished coil a lozenge shape, the two straight active sides
which fit into the straight slots being joined by V-shaped ends; at each
apex of the coil the wire is given a twist, so that the two sides fall
into different levels, an upper and a lower, corresponding to the two
layers which the coil-sides form on the finished armature. Rectangular
wire of comparatively small section may be similarly treated, and if
only one loop is required per section, wide and thin strip can be bent
into a complete loop, so that the only soldered joints are those at the
commutator end where the loops are interconnected. But finally with
massive rectangular conductors, the transition must be made to
bar-winding, in which each bar is a half-loop, insulated by being taped
after it has been bent to the required shape; the separate bars are
arranged on the armature in two layers, and their ends are soldered
together subsequently to form loops. As a general rule, whether bars or
former-wound coils are employed, the armature is barrel-wound, i.e. the
end-connexions project outwards from the slots with but little change of
level, so that they form a cylindrical mass supported on projections
from the end-plates of the core (fig. 19); but, in certain cases, the
end-connexions are bent downwards at right angles to the shaft, and they
may then consist of separate strips of copper bent to a so-called
butterfly or evolute shape.

After the coils or loops have been assembled in the slots on the
armature core, and the commutator has been fixed in place on the shaft,
the soldering of the ends of the coils proceeds, by which at once the
union of the end of one coil with the beginning of the next, and also
their connexion to the commutator sectors, is effected, and in this lies
the essential part of armature winding.

[Illustration: FIG. 20.

Lap-loops]

    Lap-winding.

  The development of the modern drum armature, with its numerous coils
  connected in orderly sequence into a symmetrical winding, as
  contrasted with the earlier Siemens armatures, was initiated by F. von
  Hefner Alteneck (1871), and the laws governing the interconnexion of
  the coils have now been elaborated into a definite system of winding
  formulae. Whatever the number of wires or bars in each side of a coil,
  i.e. whether it consist of a single loop or of many turns, the final
  connexions of its free ends are not thereby affected, and it may be
  mentally replaced by a single loop with two active inducing sides. The
  coil-sides in their final position are thus to be regarded as separate
  primary elements, even in number, and distributed uniformly round the
  armature periphery or divided into small, equally spaced groups by
  being located within the slots of a toothed armature. Attention must
  then be directed simply to the span of the back connexion between the
  elements at the end of the armature further from the commutator, and
  to the span of the front connexion by which the last turn of a coil is
  finally connected to the first turn of the next in sequence, precisely
  as if each coil of many turns were reduced to a single loop. In order
  to avoid direct differential action, the span of the back connexion
  which fixes the width of the coil must exceed the width of the
  pole-face, and should not be far different from the pole-pitch; it is
  usually a little less than the pole-pitch. Taking any one element as
  No. 1 in fig. 20, where for simplicity a smooth-core bipolar armature
  is shown, the number of winding-spaces, each to be occupied by an
  element, which must be counted off in order to find the position of
  the next element in series, is called the "pitch" of the
  end-connexion, front or back, as the case may be. Thus the back pitch
  of the winding as marked by the dotted line in fig. 20 is 7, the
  second side of the first loop being the element numbered 1 + 7 = 8. In
  forming the front end-connexion which completes the loop and joins it
  to the next in succession, two possible cases present themselves. By
  the first, or "lap-winding," the front end-connexion is brought
  backwards, and passing on its way to a junction with a commutator
  sector is led to a third element lying within the two sides of the
  first loop, i.e. the second loop starts with the element, No. 3, lying
  next but one to the starting-point of the first loop. The winding
  therefore returns backwards on itself to form each front end, but as a
  whole it works continually forwards round the armature, until it
  finally "re-enters," after every element has been traversed. The
  development of the completed winding on a flat surface shows that it
  takes the form of a number of partially overlapping loops, whence its
  name originates. The firm-line portion of fig. 21 gives the
  development of an armature similar to that of fig. 18 when cut through
  at the point marked X and opened out; two of the overlapping loops are
  marked thereon in heavy lines. The multipolar lap-wound armature is
  obtained by simply repeating the bipolar winding p times, as indicated
  by the dotted additions of fig. 21 which convert it from a two-pole to
  a four-pole machine. The characteristic feature of the lap-wound
  armature is that there are as many parallel paths from brush to brush,
  and as many points at which the current must be collected, as there
  are poles. As the bipolar closed-coil continuous-current armature has
  been shown to consist in reality of two circuits in parallel, each
  giving the same E.M.F. and carrying half the total current, so the
  multipolar lap-wound drum consists of p pairs of parallel paths, each
  giving the same E.M.F. and carrying 1/2p of the total current. Thus in
  equation 1.b we have q = 2p, and the special form which the _E.M.F.
  equation of the lap-wound armature_ takes is E_[alpha] = Z_a
  (N/60)[tau] × 10^(-8) volts. All the brushes which are of the same
  sign must be connected together in order to collect the total armature
  current. The several brush-sets of the multipolar lap-wound machine
  may again be reduced to two by "cross-connexion" of sectors situated
  360°/p apart, but this is seldom done, since the commutator must then
  be lengthened p times in order to obtain the necessary brush
  contact-surface for the collection of the entire current.

  [Illustration: FIG. 21.]

  [Illustration: FIG. 22.

  Wave-loops]

  [Illustration: FIG. 23.]

    Wave-winding.

  But for many purposes, especially where the voltage is high and the
  current small, it is advantageous to add together the inductive effect
  of the several poles of the multipolar machine by throwing the E.M.F's
  of half the total number of elements into series, the number of
  parallel circuits being conversely again reduced to two. This is
  effected by the second method of winding the closed-coil continuous
  current drum, which is known as "wave-winding." The front pitch is now
  in the same direction round the armature as the back pitch (fig. 22),
  so that the beginning of the second loop, i.e. element No. 15, lies
  outside the first loop. After p loops have been formed and as many
  elements have been traversed as there are poles, the distance covered
  either falls short of or exceeds a complete tour of the armature by
  two winding-spaces, or the width of two elements. A second and third
  tour are then made, and so on, until finally the winding again closes
  upon itself. When the completed winding is developed as in fig. 23, it
  is seen to work continuously forwards round the armature in zigzag
  waves, one of which is marked in heavy lines, and the number of
  complete tours is equal to the average of the back and front pitches.
  Since the number of parallel circuits from brush to brush is q = 2,
  the _E.M.F. equation of the wave-wound drum_ is E_a = pZ_a (N/60)[tau]
  × 10^(-8) volts. Only two sets of brushes are necessary, but in order
  to shorten the length of the commutator, other sets may also be added
  at the point of highest and lowest potential up to as many in number
  as there are poles. Thus the advantage of the wave-wound armature is
  that for a given voltage and number of poles the number of active
  wires is only 1/p of that in the lap-wound drum, each being of larger
  cross-section in order to carry p times as much current; hence the
  ratio of the room occupied by the insulation to the copper area is
  less, and the available space is better utilized. A further advantage
  is that the two circuits from brush to brush consist of elements
  influenced by all the poles, so that if for any reason, such as
  eccentricity of the armature within the bore of the pole-pieces, or
  want of uniformity in the magnetic qualities of the poles, the flux of
  each field is not equal to that of every other, the equality of the
  voltage produced by the two halves of the winding is not affected
  thereby.

  In appearance the two classes of armatures, lap and wave, may be
  distinguished in the barrel type of winding by the slope of the upper
  layer of back end-connexions, and that of the front connexions at the
  commutator end being parallel to one another in the latter, and
  oppositely directed in the former.

[Illustration: FIG. 24.]

After completion of the winding, the end-connexions are firmly bound
down by bands of steel or phosphor bronze binding wire, so as to resist
the stress of centrifugal force. In the case of smooth-surface
armatures, such bands are also placed at intervals along the length of
the armature core, but in toothed armatures, although the coils are
often in small machines secured in the slots by similar bands of a
non-magnetic high-resistance wire, the use of hard-wood wedges driven
into notches at the sides of the slots becomes preferable, and in very
large machines indispensable. The external appearance of a typical
armature with lap-winding is shown in fig. 24.

  The commutator.

A sound mechanical construction of the commutator is of vital importance
to the good working of the continuous-current dynamo. The narrow,
wedge-shaped sectors of hard-drawn copper, with their insulating strips
of thin mica, are built up into a cylinder, tightly clamped together,
and turned in the lathe; at each end a V-shaped groove is turned, and
into these are fitted rings of micanite of corresponding section (fig.
19); the whole is then slipped over a cast iron sleeve, and at either
end strong rings are forced into the V-shaped grooves under great
pressure and fixed by a number of closely-pitched tightening bolts. In
dynamos driven by steam-turbines in which the peripheral speed of the
commutator is very high, rings of steel are frequently shrunk on the
surface of the commutator at either end and at its centre. But in every
case the copper must be entirely insulated from the supporting body of
metal by the interposition of mica or micanite and the prevention of any
movement of the sectors under frequent and long-continued heating and
cooling calls for the greatest care in both the design and the
manufacture.

  Forms of field-magnet.

On passing to the second fundamental part of the dynamo, namely, the
field-magnet, its functions may be briefly recalled as follows:--It has
to supply the magnetic flux; to provide for it an iron path as nearly
closed as possible upon the armature, save for the air-gaps which must
exist between the pole-system and the armature core, the one stationary
and the other rotating; and, lastly, it has to give the lines such
direction and intensity within the air-gaps that they may be cut by the
armature wires to the best advantage. Roughly corresponding to the three
functions above summarized are the three portions which are more or less
differentiated in the complete structure. These are: (1) the magnet
"cores" or "_limbs_," carrying the exciting coils whereby the inert iron
is converted into an electro-magnet; (2) the _yoke_, which joins the
limbs together and conducts the flux between them; and (3) the
_pole-pieces_, which face the armature and transmit the lines from the
limbs through the air-gap to the armature core, or vice versa.

  [Illustration: FIG. 25.]

  Of the countless shapes which the field-magnet may take, it may be
  said, without much exaggeration, that almost all have been tried; yet
  those which have proved economical and successful, and hence have met
  with general adoption, may be classed under a comparatively small
  number of types. For bipolar machines the _single horse-shoe_ (fig.
  25), which is the lineal successor of the permanent magnet employed in
  the first magneto-electric machines, was formerly very largely used.
  It takes two principal forms, according as the pole-pieces and
  armature are above or beneath the magnet limbs and yoke. The
  "over-type" form is best suited to small belt-driven dynamos, while
  the "under-type" is admirably adapted to be directly driven by the
  steam-engine, the armature shaft being immediately coupled to the
  crank-shaft of the engine. In the latter case the magnet must be
  mounted on non-magnetic supports of gun-metal or zinc, so as to hold
  it at some distance away from the iron bedplate which carries both
  engine and dynamo; otherwise a large proportion of the flux which
  passes through the magnet limbs would leak through the bedplate across
  from pole to pole without passing through the armature core, and so
  would not be cut by the armature wires.

  [Illustration: FIG. 26.]

  Next may be placed the "Manchester" field (fig. 26)--the type of a
  divided magnetic circuit in which the flux forming one field or pole
  is divided between two magnets. An exciting coil is placed on each
  half of the double horse-shoe magnet, the pair being so wound that
  consequent poles are formed above and below the armature. Each magnet
  thus carries one-half of the total flux, the lines of the two halves
  uniting to form a common field where they issue forth into or leave
  the air-gaps. The pole-pieces may be lighter than in the single
  horse-shoe type, and the field is much more symmetrical, whence it is
  well suited to ring armatures of large diameter. Yet these advantages
  are greatly discounted by the excessive magnetic leakage, and by the
  increased weight of copper in the exciting coils. Even if the greater
  percentage which the leakage lines bear to the useful flux is
  neglected, and the cross sectional area of each magnet core is but
  half that of the equivalent single horse-shoe, the weight of wire in
  the double magnet for the same rise of temperature in the coils must
  be some 40% more than in the single horse-shoe, and the rate at which
  energy is expended in heating the coils will exceed that of the single
  horse-shoe in the same proportion.

  Thirdly comes the two-pole _ironclad_ type, so called from the
  exciting coil being more or less encased by the iron yoke; this latter
  is divided into two halves, which pass on either side of the armature.
  Unless the yoke be kept well away from the polar edges and armature,
  the leakage across the air into the yoke becomes considerable,
  especially if only one exciting coil is used, as in fig. 27 A; it is
  better, therefore, to divide the excitation between two coils, as in
  fig. 27 B, when the field also becomes symmetrical.

  From this form is easily derived the _multipolar_ type of fig. 28 or
  fig. 29, which is by far the most usual for any number of poles from
  four upwards; its leakage coefficient is but small, and it is
  economical in weight both of iron and copper.

    Materials of magnets.

  As regards the materials of which magnets are made, generally speaking
  there is little difference in the permeability of "wrought iron" or
  "mild steel forgings" and good "cast steel"; typical (B, H) curves
  connecting the magnetizing force required with different
  flux-densities for these materials are given under ELECTROMAGNETISM.
  On the other hand there is a marked inferiority in the case of "cast
  iron," which for a flux-density of B = 8000 C.G.S. lines per sq. cm.
  requires practically the same number of ampere-turns per centimetre
  length as steel requires for B = 16,000. Whatever the material, if the
  flux-density be pressed to a high value the ampere-turns are very
  largely increased owing to its approaching saturation, and this
  implies either a large amount of copper in the field coils or an undue
  expenditure of electrical energy in their excitation. Hence there is a
  limit imposed by practical considerations to the density at which the
  magnet should be worked, and this limit may be placed at about B =
  16,000 for wrought iron or steel, and at half this value for cast
  iron. For a given flux, therefore, the cast iron magnet must have
  twice the sectional area and be twice as heavy, although this
  disadvantage is partly compensated by its greater cheapness. If,
  however, cast iron be used for the portion of the magnetic circuit
  which is covered with the exciting coils, the further disadvantage
  must be added that the weight of copper on the field-magnet is much
  increased, so that it is usual to employ forgings or cast steel for
  the magnet cores on which the coils are wound. If weight is not a
  disadvantage, a cast iron yoke may be combined with the wrought iron
  or cast steel magnet cores. An absence of joints in the magnetic
  circuit is only desirable from the point of view of economy of expense
  in machining the component parts during manufacture; when the surfaces
  which abut against each other are drawn firmly together by screws, the
  want of homogeneity at the joint, which virtually amounts to the
  presence of a very thin film of air, produces little or no effect on
  the total reluctance by comparison with the very much longer air-gaps
  surrounding the armature. In order to reduce the eddy-currents in the
  pole-pieces, due to the use of toothed armatures with relatively wide
  slots, the poles themselves must be laminated, or must have fixed to
  them laminated pole-shoes, built up of thin strips of mild steel
  riveted together (as shown in fig. 29).

  [Illustration: FIG. 27.]

  [Illustration: FIG. 28.]

  However it be built up, the mechanical strength of the magnet system
  must be carefully considered. Any two surfaces between which there
  exists a field of density B_g experience a force tending to draw them
  together proportional to the square of the density, and having a value
  of B_g²/(1.735 × 10^6) lb. per sq. in. of surface, over which the
  density may be regarded as having the uniform value B_g. Hence, quite
  apart from the torque with which the stationary part of the dynamo
  tends to turn with the rotating part as soon as current is taken out
  of the armature, there exists a force tending to make the pole-pieces
  close on the armature as soon as the field is excited. Since both
  armature and magnet must be capable of resisting this force, they
  require to be rigidly held; although the one or the other must be
  capable of rotation, there should otherwise be no possibility of one
  part of the magnetic circuit shifting relatively to any other part. An
  important conclusion may be drawn from this circumstance. If the
  armature be placed exactly concentric within the bore of the poles,
  and the two or more magnetic fields be symmetrical about a line
  joining their centres, there is no tendency for the armature core to
  be drawn in one direction more than in another; but if there is any
  difference between the densities of the several fields, it will cause
  an unbalanced stress on the armature and its shaft, under which it
  will bend, and as this bending is continually reversed relatively to
  the fibres of the shaft, they will eventually become weakened and give
  way. Especially is this likely to take place in dynamos with short
  air-gaps, wherein any difference in the lengths of the air-gaps
  produces a much greater percentage difference in the flux-density than
  in dynamos with long air-gaps. In toothed armatures with short
  air-gaps the shaft must on this account be sufficiently strong to
  withstand the stress without appreciable bending.

  The magnetic circuit.

Reference has already been made to the importance in dynamo design of
the _predetermination of the flux_ due to a given number of ampere-turns
wound on the field-magnet, or, conversely, of the number of ampere-turns
which must be furnished by the exciting coils in order that a certain
flux corresponding to one field may flow through the armature core from
each pole. An equally important problem is the correct proportioning of
the field-magnet, so that the useful flux Z_a may be obtained with the
greatest economy in materials and exciting energy. The key to the two
problems is to be found in the concept of a magnetic circuit as
originated by H.A. Rowland and R.H.M. Bosanquet;[16] and the full
solution of both may be especially connected with the name of Dr J.
Hopkinson, from his practical application of the concept in his design
of the Edison-Hopkinson machine, and in his paper on "Dynamo-Electric
Machinery."[17] The publication of this paper in 1886 begins the second
era in the history of the dynamo; it at once raised its design from the
level of empirical rules-of-thumb to a science, and is thus worthy to be
ranked as the necessary supplement of the original discoveries of
Faraday. The process of predetermining the necessary ampere-turns is
described in a simple case under ELECTROMAGNETISM. In its extension to
the complete dynamo, it consists merely in the division of the magnetic
circuit into such portions as have the same sectional area and
permeability and carry approximately the same total flux; the difference
of magnetic potential that must exist between the ends of each section
of the magnet in order that the flux may pass through it is then
calculated _seriatim_ for the several portions into which the magnetic
circuit is divided, and the separate items are summed up into one
magnetomotive force that must be furnished by the exciting coils.

[Illustration: FIG. 29.]

  The chief sections of the magnetic circuit are (1) the air-gaps, (2)
  the armature core, and (3) the iron magnet.

  The _air-gap_ of a dynamo with smooth-core armature is partly filled
  with copper and partly with the cotton, mica, or other materials used
  to insulate the core and wires; all these substances are, however,
  sensibly non-magnetic, so that the whole interferric gap between the
  iron of the pole-pieces and the iron of the armature may be treated as
  an air-space, of which the permeability is constant for all values of
  the flux density, and in the C.G.S. system is unity. Hence if l_g and
  A_g be the length and area of the single air-gap in cm. and sq. cm.,
  the reluctance of the double air-gap is 2l_g/A_g, and the difference
  of magnetic potential required to pass Z_a lines over this reluctance
  is Z_a·2l_g/A_g = B_g·2l_g; or, since one ampere-turn gives 1.257
  C.G.S. units of magnetomotive force, the exciting power in
  ampere-turns required over the two air-gaps is X_g = B_g·2l_g/1.257 =
  0.8 B_g·2l_g. In the determination of the area A_g small allowance
  must be made for the fringe of lines which extend beyond the actual
  polar face. In the toothed armature with open slots, the lines are no
  longer uniformly distributed over the air-gap area, but are graduated
  into alternate bands of dense and weak induction corresponding to the
  teeth and slots. Further, the lines curve round into the sides of the
  teeth, so that their average length of path in the air and the air-gap
  reluctance is not so easily calculated. Allowance must be made for
  this by taking an increased length of air-gap = ml_g, where m is the
  ratio _maximum density/mean density_, of which the value is chiefly
  determined by the ratios of the width of tooth to width of slot and of
  the width of slot to the air-gap between pole-face and surface of the
  armature core.

  The _armature core_ must be divided into the teeth and the core proper
  below the teeth. Owing to the tapering section of the teeth, the
  density rises towards their root, and when this reaches a high value,
  such as 18,000 or more lines per sq. cm., the saturation of the iron
  again forces an increasing proportion of the lines outwards into the
  slot. A distinction must then be drawn between the "apparent"
  induction which would hold if all the lines were concentrated in the
  teeth, and the "real" induction. The area of the iron is obtained by
  multiplying the number of teeth under the pole-face by their width and
  by the net length of the iron core parallel to the axis of rotation.
  The latter is the gross length of the armature less the space lost
  through the insulating varnish or paper between the disks or through
  the presence of ventilating ducts, which are introduced at intervals
  along the length of the core. The former deduction averages about 7 to
  10% of the gross length, while the latter, especially in large
  multipolar machines, is an even more important item. Alter calculating
  the density at different sections of the teeth, reference has now to
  be made to a (B, H) or flux-density curve, from which may be found the
  number of ampere-turns required per cm. length of path. This number
  may be expressed as a function of the density in the teeth, and f(B_t)
  be its average value over the length of a tooth, the ampere-turns of
  excitation required over the teeth on either side of the core as the
  lines of one field enter or leave the armature is X_t = f(B_t)·2l_t,
  where l_t is the length of a single tooth in cm.

  In the core proper below the teeth the length of path continually
  shortens as we pass from the middle of the pole towards the centre
  line of symmetry. On the other hand, as the lines gradually accumulate
  in the core, their density increases from zero midway under the poles
  until it reaches a maximum on the line of symmetry. The two effects
  partially counteract one another, and tend to equalize the difference
  of magnetic potential required over the paths of varying lengths; but
  since the reluctivity of the iron increases more rapidly than the
  density of the lines, we may approximately take for the length of path
  (l_a) the minimum peripheral distance between the edges of adjacent
  pole-faces, and then assume the maximum value of the density of the
  lines as holding throughout this entire path. In ring and drum
  machines the flux issuing from one pole divides into two halves in the
  armature core, so that the maximum density of lines in the armature is
  B_a = Z_a/2ab, where a = the radial depth of the disks in centimetres
  and b = the net length of iron core. The total exciting power required
  between the pole-pieces is therefore, at no load, X_p = X_g + X_t +
  X_a, where X_a = f(B_a)·l_a; in order, however, to allow for the
  effect of the armature current, which increases with the load, a
  further term X_b, must be added.

  [Illustration: Fig. 30.]

  In the continuous-current dynamo it may be, and usually is, necessary
  to move the brushes forward from the interpolar line of symmetry
  through a small angle in the direction of rotation, in order to avoid
  sparking between the brushes and the commutator (_vide infra_). When
  the dynamo is giving current, the wires on either side of the diameter
  of commutation form a current-sheet flowing along the surface of the
  armature from end to end, and whatever the actual end-connexions of
  the wires, the wires may be imagined to be joined together into a
  system of loops such that the two sides of each loop are carrying
  current in opposite directions. Thus a number of armature ampere-turns
  are formed, and their effect on the entire system of magnet and
  armature must be taken into account. So long as the diameter of
  commutation coincides with the line of symmetry, the armature may be
  regarded as a cylindrical electromagnet producing a flux of lines, as
  shown in fig. 30. The direction of the self-induced flux in the
  air-gaps is the same as that of the lines of the external field in one
  quadrant on one side of DC, but opposed to it in the other quadrant on
  the same side of DC; hence in the resultant field due to the combined
  action of the field-magnet and armature ampere-turns, the flux is as
  much strengthened over the one half of each polar face as it is
  weakened over the other, and the total number of lines is unaffected,
  although their distribution is altered. The armature ampere-turns are
  then called _cross-turns_, since they produce a cross-field, which,
  when combined with the symmetrical field, causes the leading
  pole-corners ll to be weakened and the trailing pole-corners tt to be
  strengthened, the neutral line of zero field being thus twisted
  forwards in the direction of rotation. But when the brushes and
  diameter of commutation are shifted forward, as shown in fig. 31, it
  will be seen that a number of ampere-turns, forming a zone between the
  lines Dn and mC, are in effect wound immediately on the magnetic
  circuit proper, and this belt of ampere-turns is in direct opposition
  to the ampere-turns of the field, as shown by the dotted and crossed
  wires on the pole-pieces. The armature ampere-turns are then divisible
  into the two bands, the _back-turns_, included within twice the angle
  of lead [lambda], weakening the field, and the cross-turns, bounded by
  the lines Dm, nC, again producing distortion of the weakened
  symmetrical field. If, therefore, a certain flux is to be passed
  through the armature core in opposition to the demagnetizing turns,
  the difference of magnetic potential between the pole-faces must
  include not only X_a, X_t, and X_g, but also an item X_b, in order to
  balance the "back" ampere-turns of the armature. The amount by which
  the brushes must be shifted forward increases with the armature
  current, and in corresponding proportion the back ampere-turns are
  also increased, their value being c[tau]2[lambda]/360°, where c = the
  current carried by each of the [tau] active wires. Thus the term X_b,
  takes into account the effect of the armature reaction on the total
  flux; it varies as the armature current and angle of lead required to
  avoid sparking are increased; and the reason for its introduction in
  the fourth place (X_p = X_g + X_t + X_a + X_b), is that it increases
  the magnetic difference of potential which must exist between the
  poles of the dynamo, and to which the greater part of the leakage is
  due. The leakage paths which are in parallel with the armature across
  the poles must now be estimated, and so a new value be derived for the
  flux at the commencement of the _iron-magnet_ path. If P = their joint
  permeance, the leakage flux due to the difference of potential at the
  poles is z_l = 1.257X_p × P, and this must be added to the useful flux
  Z_a, or Z_p = Z_a + Z_l. There are also certain leakage paths in
  parallel with the magnet cores, and upon the permeance of these a
  varying number of ampere-turns is acting as we proceed along the
  magnet coils; the magnet flux therefore increases by the addition of
  leakage along the length of the limbs, and finally reaches a maximum
  near the yoke. Either, then, the density in the magnet B_m = Z_m/A_m
  will vary if the same sectional area be retained throughout, or the
  sectional area of the magnet must itself be progressively increased.
  In general, sufficient accuracy will be obtained by assuming a certain
  number of additional leakage lines z_n as traversing the entire length
  of magnet limbs and yoke (= l_m), so that the density in the magnet
  has the uniform value B_m = (Z_p + z_n)/A_m. The leakage flux added on
  actually within the length of the magnet core or z_n will be
  approximately equal to half the total M.M.F. of the coils multiplied
  by the permeance of the leakage paths around one coil. The
  corresponding value of H can then be obtained from the (B, H) curve of
  the material of which the magnet is composed, and the ampere-turns
  thus determined must be added to X_p, or X = X_p + X_m, where X_m =
  f(B_m)l_m. The final equation for the exciting power required on a
  magnetic circuit as a whole will therefore take the form

    X = A[Tau] = 0.8B_g·2l_g + f(B_t)2l_t + f(B_a)l_a + X_b + f(B_m)l_m. (3)

  If the magnet cores are of wrought iron or cast steel, and the yoke is
  of cast iron, the last term must be divided into two portions
  corresponding to the different materials, i.e. into f(B_m)l_m +
  f(B_y)l_y. In the ordinary multipolar machine with as many
  magnet-coils as there are poles, each coil must furnish half the above
  number of ampere-turns.

  [Illustration: FIG. 31.]

    Magnetic leakage.

  Since no substance is impermeable to the passage of magnetic flux, the
  only form of magnetic circuit free from leakage is one uniformly wound
  with ampere-turns over its whole length. The reduction of the
  _magnetic leakage_ to a minimum in any given type is therefore
  primarily a question of distributing the winding as far as possible
  uniformly upon the circuit, and as the winding must be more or less
  concentrated into coils, it resolves itself into the necessity of
  introducing as long air-paths as possible between any surfaces which
  are at different magnetic potentials. No iron should be brought near
  the machine which does not form part of the magnetic circuit proper,
  and especially no iron should be brought near the poles, between which
  the difference of magnetic potential practically reaches its maximum
  value. In default of a machine of the same size or similar type on
  which to experiment, the probable direction of the leakage flux must
  be assumed from the drawing, and the air surrounding the machine must
  be mapped out into areas, between which the permeances are calculated
  as closely as possible by means of such approximate formulae as those
  devised by Professor G. Forbes.

    Excitation of field-magnet.

  In the earliest "magneto-electric" machines permanent steel magnets,
  either simple or compound, were employed, and for many years these
  were retained in certain alternators, some of which are still in use
  for arc lighting in lighthouses. But since the field they furnish is
  very weak, a great advance was made when they were replaced by soft
  iron electromagnets, which could be made to yield a much more intense
  flux. As early as 1831 Faraday[18] experimented with electromagnets,
  and after 1850 they gradually superseded the permanent magnet. When
  the total ampere-turns required to excite the electromagnet have been
  determined, it remains to decide how the excitation shall be obtained;
  and, according to the method adopted, continuous-current machines may
  be divided into four well-defined classes.

  [Illustration: FIG. 32.]

  The simplest method, and that which was first used, is _separate
  excitation_ from some other source of direct current, which may be
  either a primary or a secondary battery or another dynamo (fig. 32).
  But since the armature yields a continuous current, it was early
  suggested (by J. Brett in 1848 and F. Sinsteden in 1851) that this
  current might be utilized to increase the flux; combinations of
  permanent and electromagnets were therefore next employed, acting
  either on the main armature or on separate armatures, until in 1867 Dr
  Werner von Siemens and Sir C. Wheatstone almost simultaneously
  discovered that the dynamo could be made _self-exciting_ through the
  residual magnetism retained in the soft iron cores of the
  electromagnet. The former proposed to take the whole of the current
  round the magnet coils which were in series with the armature and
  external circuit, while the latter proposed to utilize only a portion
  derived by a shunt from the main circuit; we thus arrive at the second
  and third classes, namely, _series_ and _shunt_ machines. The starting
  of the process of excitation in either case is the same; when the
  brushes are touching the commutator and the armature is rotated, the
  small amount of flux left in the magnet is cut by the wires, and a
  very small current begins to flow round the closed circuit; this
  increases the flux, which in turn further increases the E.M.F. and
  current, until, finally, the cumulative effect stops through the
  increasing saturation of the iron cores. Fig. 33, illustrating the
  _series_ machine, shows the winding of the exciting coils to be
  composed of a few turns of thick wire. Since the current is undivided
  throughout the whole circuit, the resistance of both the armature and
  field-magnet winding must be low as compared with that of the external
  circuit, if the useful power available at the terminals of the machine
  is to form a large percentage of the total electrical power--in other
  words, if the efficiency is to be high. Fig. 34 shows the third
  method, in which the winding of the field-magnets is a _shunt_ or
  fine-wire circuit of many turns applied to the terminals of the
  machine; in this ease the resistance of the shunt must be high as
  compared with that of the external circuit, in order that only a small
  proportion of the total energy may be absorbed in the field.

  [Illustration: FIG. 33.]

  [Illustration: FIG. 34.]

  Since the whole of the armature current passes round the field-magnet
  of the series machine, any alteration in the resistance of the
  external circuit will affect the excitation and also the voltage. A
  curve connecting together corresponding values of external current and
  terminal voltage for a given speed of rotation is known as the
  _external-characteristic_ of the machine; in its main features it has
  the same appearance as a curve of magnetic flux, but when the current
  exceeds a certain amount it begins to bend downwards and the voltage
  decreases. The reason for this will be found in the armature reaction
  at large loads, which gradually produces a more and more powerful
  demagnetizing effect, as the brushes are shifted forwards to avoid
  sparking; eventually the back ampere-turns overpower any addition to
  the field that would otherwise be due to the increased current flowing
  round the magnet. The "external characteristic" for a shunt machine
  has an entirely different shape. The field-magnet circuit being
  connected in parallel with the external circuit, the exciting current,
  if the applied voltage remains the same, is in no way affected by
  alterations in the resistance of the latter. As, however, an increase
  in the external current causes a greater loss of volts in the armature
  and a greater armature reaction, the terminal voltage, which is also
  the exciting voltage, is highest at no load and then diminishes. The
  fall is at first gradual, but after a certain critical value of the
  armature current is reached, the machine is rapidly demagnetized and
  loses its voltage entirely.

  [Illustration: FIG. 35.]

  The last method of excitation, namely, _compound-winding_ (fig. 35),
  is a combination of the two preceding, and was first used by S.A.
  Varley and by C.F. Brush. If a machine is in the first instance
  shunt-wound, and a certain number of series-turns are added, the
  latter, since they carry the external current, can be made to
  counteract the effect which the increased external current would have
  in lowering the voltage of the simple shunt machine. The ampere-turns
  of the series winding must be such that they not only balance the
  increase of the demagnetizing back ampere-turns on the armature, but
  further increase the useful flux, and compensate for the loss of volts
  over their own resistance and that of the armature. The machine will
  then give for a constant speed a nearly constant voltage at its
  terminals, and the curve of the external characteristic becomes a
  straight line for all loads within its capacity. Since with most prime
  movers an increase of the load is accompanied by a drop in speed, this
  effect may also be counteracted; while, lastly, if the series-turns
  are still further increased, the voltage may be made to rise with an
  increasing load, and the machine is "over-compounded."

  Commutation and sparking at the brushes.

At the initial moment when an armature coil is first short-circuited by
the passage of the two sectors forming its ends under the contact
surface of a brush, a certain amount of electromagnetic energy is stored
up in its magnetic field as linked with the ampere-turns of the coil
when carrying its full share of the total armature current. During the
period of short-circuit this quantity of energy has to be dissipated as
the current falls to zero, and has again to be re-stored as the current
is reversed and raised to the same value, but in the opposite direction.
The period of short-circuit as fixed by the widths of the brush and of
the mica insulation between the sectors, and by the peripheral speed of
the commutator is extremely brief, and only lasts on an average from
(1/200)th to (1/1000)th of a second. The problem of sparkless
commutation is therefore primarily a question of our ability to
dissipate and to re-store the required amount of energy with sufficient
rapidity.

An important aid towards the solution of this problem is found in the
effect of the varying contact-resistance between the brush and the
surfaces of the leading and trailing sectors which it covers. As the
commutator moves under the brush, the area of contact which the brush
makes with the leading sector diminishes, and the resistance between the
two rises; conversely, the area of contact between the brush and the
trailing sector increases and the resistance falls. This action tends
automatically to bring the current through each sector into strict
proportionality to the amount of its surface which is covered by the
brush, and so to keep the current-density and the loss of volts over the
contacts uniform and constant. As soon as the current-density in the two
portions of the brush becomes unequal, a greater amount of heat is
developed at the commutator surface, and this in the first place affords
an additional outlet for the dissipation of the stored energy of the
coil, while after reversal of the current it is the accompaniment of a
re-storage of the required energy. This energy, as well as that which is
spent in heating the coil, can in fact, in default of other sources, be
derived through the action of the unequal current-density from the
electrical output of the rest of the armature winding, and so only
indirectly from the prime mover.

In practice, when the normal contact-resistance of the brushes is low
relatively to the resistance of the coil, as is the case with metal
brushes of copper or brass gauze, but little benefit can be obtained
from the action of the varying contact-resistance. It exerts no
appreciable effect until close towards the end of the period of
short-circuit, and then only with such a high-current-density at the
trailing edge of the leaving sector that at the moment of parting the
brush-tip is fused, or its metal volatilized, and sparking has in fact
set in. With such brushes, then, it becomes necessary to call in the aid
of a reversing E.M.F. impressed upon the coil by the magnetic field
through which it is moving. If such a reversing field comes into action
while the current is still unreversed, its E.M.F. is opposed to the
direction of the current, and the coil is therefore driving the armature
forward as in a motor; it thus affords a ready means of rapidly
dissipating part of the initial energy in the form of mechanical work
instead of as heat. After the current has been reversed, the converse
process sets in, and the prime mover directly expends mechanical energy
not only in heating the coil, but also in storing up electromagnetic
energy with a rapidity dependent upon the strength of the reversing
field. The required direction of external field can be obtained in the
dynamo by shifting the brushes forward, so that the short-circuited coil
enters into the fringe of lines issuing from the leading pole-tip, i.e.
by giving the brushes an "angle of lead." An objection to this process
is that the main flux is thereby weakened owing to the belt of back
ampere-turns which arises (_v. supra_). A still greater objection is
that the amount of the angle of lead must be suited to the value of the
load, the corrective power of copper brushes being very small if the
reversing E.M.F. is not closely adjusted in proportion to the armature
current.

On this account metal brushes have been almost entirely superseded by
carbon moulded into hard blocks. With these, owing to their higher
specific contact-resistance, a very considerable reversing effect can be
obtained through the action of unequal current-density, and indeed in
favourable cases complete sparklessness can be obtained throughout the
entire range of load of the machine with a fixed position of the
brushes. Yet if the work which they are called upon to perform exceeds
certain limits, they tend to become overheated with consequent glowing
or sparking at their tips, so that, wherever possible, it is advisable
to reinforce their action by a certain amount of reversing field, the
brushes being set so that its strength is roughly correct for, say, half
load.

In the case of dynamos driven by steam-turbines, sparkless commutation
is especially difficult to obtain owing to the high speed of rotation
and the very short space of time in which the current has to be
reversed. Special "reversing poles" then become necessary; these are
wound with magnetizing coils in series with the main armature current,
so that the strength of field which they yield is roughly proportional
to the current which has to be reversed. These again may be combined
with a "compensating winding" embedded in the pole-faces and carrying
current in the opposite direction to the armature ampere-turns, so as to
neutralize the cross effect of the latter and prevent distortion of the
resultant field.

    Heating effects.

  From the moment that a dynamo begins to run with excited field, heat
  is continuously generated by the passage of the current through the
  windings of the field-magnet coils and the armature, as well as by the
  action of hysteresis and eddy currents in the armature and
  pole-pieces. Whether the source of the heat be in the field-magnet or
  in the armature, the mass in which it originates will continue to rise
  in temperature until such a difference of temperature is established
  between itself and the surrounding air that the rate at which the heat
  is carried off by radiation, convection and conduction is equal to the
  rate at which it is being generated. Evidently, then, the temperature
  which any part of the machine attains after a prolonged run must
  depend on the extent and effectiveness of the cooling surface from
  which radiation takes place, upon the presence or absence of any
  currents of air set up by the rotation of itself or surrounding parts,
  and upon the presence of neighbouring masses of metal to carry away
  the heat by conduction. In the field-magnet coils the rate at which
  heat is being generated is easily determined, since it is equal to the
  square of the current passing through them multiplied by their
  resistance. Further, the magnet is usually stationary, and only
  indirectly affected by draughts of air due to the rotating armature.
  Hence for machines of a given type and of similar proportions, it is
  not difficult to decide upon some method of reckoning the cooling
  surface of the magnet coils S_c, such that the rise of temperature
  above that of the surrounding air may be predicted from an equation of
  the form t° = kW/S_c, where W = the rate in watts at which heat is
  generated in the coils, and k is some constant depending upon the
  exact method of reckoning their cooling surface. As a general rule the
  cooling surface of a field-coil is reckoned as equal to the exposed
  outer surface of its wire, the influence of the end flanges being
  neglected, or only taken into account in the case of very short
  bobbins wound with a considerable depth of wire. In the case of the
  rotating armature a similar formula must be constructed, but with the
  addition of a factor to allow for the increase in the effectiveness of
  any given cooling surface due to the rotation causing convection
  currents in the surrounding air. Only experiment can determine the
  exact effect of this, and even with a given type of armature it is
  dependent on the number of poles, each of which helps to break up the
  air-currents, and so to dissipate the heat. For example, in two-pole
  machines with drum bar-armatures, if the cooling surface be reckoned
  as equal to the cylindrical exterior plus the area of the two ends,
  the heating coefficient for a peripheral speed of 1500 ft. per minute
  is less than half of that for the same armature when at rest. A
  further difficulty still meets the designer in the correct
  predetermination of the total loss of watts in an armature before the
  machine has been tested. It is made up of three separate items,
  namely, the copper loss in the armature winding, the loss by
  hysteresis in the iron, and the loss by eddy currents, which again may
  be divided into those in the armature bars and end-connexions, and
  those in the core and its end-plates. The two latter items are both
  dependent upon the speed of the machine; but whereas the hysteresis
  loss is proportional to the speed for a given density of flux in the
  armature, the eddy current loss is proportional to the square of the
  speed, and owing to this difference, the one loss can be separated
  from the other by testing an armature at varying speeds. Thus for a
  given rise of temperature, the question of the amount of current which
  can be taken out of an armature at different speeds depends upon the
  proportion which the hysteresis and eddy watts bear to the copper
  loss, and the ratio in which the effectiveness of the cooling surface
  is altered by the alteration in speed. Experimental data, again, can
  alone decide upon the amount of eddy currents that may be expected in
  given armatures, and caution is required in applying the results of
  one machine to another in which any of the conditions, such as the
  number of poles, density in the teeth, proportions of slot depth to
  width, &c., are radically altered.

  It remains to add, that the rise of temperature which may be permitted
  in any part of a dynamo after a prolonged run is very generally placed
  at about 70° Fahr. above the surrounding air. Such a limit in ordinary
  conditions of working leads to a final temperature of about 170°
  Fahr., beyond which the durability of the insulation of the wires is
  liable to be injuriously affected. Upon some such basis the output of
  a dynamo in continuous working is rated, although for short periods
  of, say, two hours the normal full-load current of a large machine may
  be exceeded by some 25% without unduly heating the armature.

  Uses of continuous current dynamos.

For the electro-deposition of metals or the electrolytic treatment of
ores a continuous current is a necessity; but, apart from such use, the
purposes from which the continuous-current dynamo is well adapted are so
numerous that they cover nearly the whole field of electrical
engineering, with one important exception. To meet these various uses,
the pressures for which the machine is designed are of equally wide
range; for the transmission of power over long distances they may be as
high as 3000 volts, and for electrolytic work as low as five. Each
electrolytic bath, with its leads, requires on an average only some four
or five volts, so that even when several are worked in series the
voltage of the dynamo seldom exceeds 60. On the other hand, the current
is large and may amount to as much as from 1000 to 14,000 amperes,
necessitating the use of two commutators, one at either end of the
armature, in order to collect the current without excessive heating of
the sectors and brushes. The field-magnets are invariably shunt-wound,
in order to avoid reversal of the current through polarization at the
electrodes of the bath. For incandescent lighting by glow lamps, the
requirements of small isolated installations and of central stations for
the distribution of electrical energy over large areas must be
distinguished. For the lighting of a private house or small factory, the
dynamo giving from 5 to 100 kilo-watts of output is commonly wound for a
voltage of 100, and is driven by pulley and belt from a gas, oil or
steam-engine; or, if approaching the higher limit above mentioned, it is
often directly coupled to the crank-shaft of the steam-engine. If used
in conjunction with an accumulator of secondary cells, it is
shunt-wound, and must give the higher voltage necessary to charge the
battery; otherwise it is compound-wound, in order to maintain the
pressure on the lamps constant under all loads within its capacity. The
compound-wound dynamo is likewise the most usual for the lighting of
steamships, and is then directly coupled to its steam-engine; its output
seldom exceeds 100 kilo-watts, at a voltage of 100 or 110. For larger
installations a voltage of 250 is commonly used, while for
central-station work, economy in the distributing mains dictates a
higher voltage, especially in connexion with a three-wire system; the
larger dynamos may then give 500 volts, and be connected directly across
the two outer wires. A pair of smaller machines coupled together, and
each capable of giving 250 volts, are often placed in series across the
system, with their common junction connected to the middle wire; the one
which at any time is on the side carrying the smaller current will act
as a motor and drive the other as a dynamo, so as to balance the system.
The directly-coupled steam dynamo may be said to have practically
displaced the belt- or rope-driven sets which were formerly common in
central stations. The generating units of the central station are
arranged in progressive sizes, rising from, it may be, 250 or 500
horse-power up to 750 or 1000, or in large towns to as much as 5000
horse-power. If for lighting only, they are usually shunt-wound, the
regulation of the voltage, to keep the pressure constant on the
distributing system under the gradual changes of load, being effected by
variable resistances in the shunt circuit of the field-magnets.

Generators used for supplying current to electric tramways are commonly
wound for 500 volts at no load and are over-compounded, so that the
voltage rises to 550 volts at the maximum load, and thus compensates for
the loss of volts over the transmitting lines. For arc lighting it was
formerly usual to employ a class of dynamo which, from the nature of its
construction, was called an "open-coil" machine, and which gave a
unidirectional but pulsating current. Of such machines the Brush and
Thomson-Houston types were very widely used; their E.M.F. ranged from
2000 to 3000 volts for working a large number of arcs in series, and by
means of special regulators their current was maintained constant over a
wide range of voltage. But as their efficiency was low and they could
not be applied to any other purpose, they have been largely superseded
in central stations by closed-coil dynamos or alternators, which can
also be used for incandescent lighting. In cases where the central
station is situated at some distance from the district to which the
electric energy is to be supplied, voltages from 1000 to 2000 are
employed, and these are transformed down at certain distributing centres
by continuous-current transformers (see TRANSFORMERS and ELECTRICITY
SUPPLY). These latter machines are in reality motor-driven dynamos, and
hence are also called _motor-generators_; the armatures of the motor and
dynamo are often wound on the same core, with a commutator at either
end, the one to receive the high-pressure motor current, and the other
to collect the low-pressure current furnished by the dynamo.

  In all large central stations it is necessary that the dynamos should
  be capable of being run _in parallel_, so that their outputs may be
  combined on the same "omnibus bars" and thence distributed to the
  network of feeders. With simple shunt-wound machines this is easily
  effected by coupling together terminals of like sign when the voltage
  of the two or more machines are closely equal. With compound-wound
  dynamos not only must the external terminals of like sign be coupled
  together, but the junctions of the brush leads with the series winding
  must be connected by an "equalizing" lead of low resistance;
  otherwise, should the E.M.F. of one machine for any reason fall below
  the voltage of the omnibus bars, there is a danger of its polarity
  being reversed by a back current from the others with which it is in
  parallel.

  Owing to the necessary presence in the continuous-current dynamo of
  the commutator, with its attendant liability to sparking at the
  brushes, and further, owing to the difficulty of insulating the
  rotating armature wires, a pressure of 3000 volts has seldom been
  exceeded in any one continuous-current machine, and has been given
  above as the limiting voltage of the class. If therefore it is
  required to work with higher pressures in order to secure economy in
  the transmitting lines, two or more machines must be coupled _in
  series_ by connecting together terminals which are of unlike sign.[19]
  The stress of the total voltage may still fall on the insulation of
  the winding from the body of the machine; hence for high-voltage
  transmission of power over very long distances, the continuous-current
  dynamo in certain points yields in convenience to the alternator. In
  this there is no commutator, the armature coils may be stationary and
  can be more thoroughly insulated, while further, if it be thought
  undesirable to design the machine for the full transmitting voltage,
  it is easy to wind the armature for a low pressure; this can be
  subsequently transformed up to a high pressure by means of the
  alternating-current transformer, which has stationary windings and so
  high an efficiency that but little loss arises from its use. With
  these remarks, the transition may be made to the fuller discussion of
  the alternator.

_Alternators._

  Frequency.

The frequency employed in alternating-current systems for distributing
power and light varies between such wide limits as 25 and 133; yet in
recent times the tendency has been towards standard frequencies of 25,
50 and 100 as a maximum. High frequencies involve more copper in the
magnet coils, owing to the greater number of poles, and a greater loss
of power in their excitation, but the alternator as a whole is somewhat
lighter, and the transformers are cheaper. On the other hand, high
frequency may cause prejudicial effects, due to the inductance and
capacity of the distributing lines; and in asynchronous motors used on
polyphase systems the increased number of poles necessary to obtain
reasonable speeds reduces their efficiency, and is otherwise
disadvantageous, especially for small horse-powers. A frequency lower
than 40 is, however, not permissible where arc lighting is to form any
considerable portion of the work and is to be effected by the
alternating current without rectification, since below this value the
eye can detect the periodic alteration in the light as the carbons
alternately cool and become heated. Thus for combined lighting and power
50 or 60 are the most usual frequencies; but if the system is designed
solely or chiefly for the distribution of power, a still lower frequency
is preferable. On this account 25 was selected by the engineers for the
Niagara Falls power transmission, after careful consideration of the
problem, and this frequency has since been widely adopted in similar
cases.

  Alternator construction.

The most usual type of heteropolar alternator has an internal rotating
field-magnet system, and an external stationary armature, as in fig. 10.
The coils of the armature, which must for high voltages be heavily
insulated, are then not subjected to the additional stresses due to
centrifugal force; and further, the collecting rings which must be
attached to the rotating portion need only transmit the exciting current
at a low voltage.

[Illustration: FIG. 36.]

The homopolar machine possesses the advantages that only a single
exciting coil is required, whatever the number of polar projections, and
that both the armature and field-magnet coils may be stationary. From
fig. 8 it will be seen that it is not essential that the exciting coil
should revolve with the internal magnet, but it may be supported from
the external stationary armature while still embracing the central part
of the rotor. The E.M.F. is set up in the armature coils through the
periodic variation of the flux through them as the iron projections
sweep past, and these latter may be likened to a number of "keepers,"
which complete the magnetic circuit. From the action of the rotating
iron masses they may also be considered as the inducing elements or
"inductors," and the homopolar machine is thence also known as the
"inductor alternator." If the end of the rotor marked S in fig. 8 is
split up into a number of S polar projections similar to the N poles, a
second set of armature coils may be arranged opposite to them, and we
obtain an inductor alternator with double armature. Or the polar
projections at the two ends may be staggered, and a single armature
winding be passed straight through the armature, as in fig. 36, which
shows at the side the appearance of the revolving inductor with its
crown of polar projections in one ring opposite to the gaps between the
polar projections of the other ring. But in spite of its advantage of
the single stationary exciting coil, the inductor alternator has such a
high degree of leakage, and the effect of armature reaction is so
detrimental in it, that the type has been gradually abandoned, and a
return has been almost universally made to the heteropolar alternator
with internal poles radiating outwards from a circular yoke-ring. The
construction of a typical machine of this class is illustrated in fig.
37.

[Illustration: FIG. 37.]

Since the field-magnet coils rotate, they must be carefully designed to
withstand centrifugal force, and are best composed of flat copper strip
wound on edge with thin insulation between adjacent layers. The coil is
secured by the edges of the pole-shoes which overhang the pole and
tightly compress the coil against the yoke-ring; the only effect from
centrifugal force is then to compress still further the flat turns of
copper against the pole-shoes without deformation. The poles are either
of cast steel of circular or oblong section, bolted to the rim of the
yoke-ring, or are built up of thin laminations of sheet steel. When the
peripheral speed is very high, the yoke-ring will be of cast steel or
may itself be built up of sheet steel laminations, this material being
reliable and easily tested to ensure its sound mechanical strength. If
the armature slots are open, the pole-pieces will in any case be
laminated to reduce the eddy currents set up by the variation of the
flux-density.

Owing to the great number of poles[20] of the alternator when driven by
a reciprocating steam-engine, the diameter of its rotor is usually
larger and its length less than in the continuous-current dynamo of
corresponding output. The support of the armature core when of large
diameter is therefore a more difficult problem, since, apart from any
magnetic strains to which it may be subjected, its own weight tends to
deform it. The segmental core-disks are usually secured to the internal
circumference of a circular cast iron frame; the latter has a box
section of considerable radial depth to give stiffness to it, and the
disks are tightly clamped between internal flanges, one being a fixed
part of the frame and the other loose, with transverse bolts passing
right through from side to side (fig. 37). In order to lessen the weight
of the structure and its expense in material, the cast iron frame has in
some cases been entirely dispensed with, and braced tie-rods have been
used to render the effective iron of the armature core-disks
self-supporting.

[Illustration: FIG. 38.]

Owing to the high speed of the turbo-alternator, its rotor calls for the
utmost care in its design to withstand the effect of centrifugal force
without any shifting of the exciting coils, and to secure a perfect
balance.

The appearance of the armature of a typical three-phase alternator is
illustrated in fig. 38, which shows a portion of the lower half after
removal of the field-magnet.

With open slots the coils, after being wound on formers to the required
shape, are thoroughly impregnated with insulating compound, dried, and
after a further wrapping with several layers of insulating material,
finally pressed into the slots together with a sheet of leatheroid or
flexible micanite. The end-connexions of each group of coils of one
phase project straight out from the slots or are bent upwards
alternately with those of the other phases, so that they may clear one
another (fig. 37). A wooden wedge driven into a groove at the top of
each slot is often used to lock the coil in place. With slots nearly
closed at the top, the coils are formed by hand by threading the wire
through tubes of micanite or specially prepared paper lining the slots;
or with single-turn loops, stout bars of copper of [U]-shape can be
driven through the slots and closed by soldered connexions at the other
end.

    Shape of E.M.F. curve.

  The first experimental determination of the shape of the E.M.F. curve
  of an alternator was made by J. Joubert in 1880. A revolving
  contact-maker charged a condenser with the E.M.F. produced by the
  armature at a particular instant during each period. The condenser was
  discharged through a ballistic galvanometer, and from the measured
  throw the instantaneous E.M.F. could be deduced. The contact-maker was
  then shifted through a small angle, and the instantaneous E.M.F. at
  the new position corresponding to a different moment in the period was
  measured; this process was repeated until the E.M.F. curve for a
  complete period could be traced. Various modifications of the same
  principle have since been used, and a form of "oscillograph" (q.v.)
  has been perfected which is well adapted for the purpose of tracing
  the curves both of E.M.F. and of current. The machine on which Joubert
  carried out his experiments was a Siemens disk alternator having no
  iron in its armature, and it was found that the curve of E.M.F. was
  practically identical with a sine curve. The same law has also been
  found to hold true for a smooth-core ring or drum armature, but the
  presence of the iron core enables the armature current to produce
  greater distorting effect, so that the curves under load may vary
  considerably from their shape at no load. In toothed armatures, the
  broken surface of the core, and the still greater reaction from the
  armature current, may produce wide variations from the sine law, the
  general tendency being to give the E.M.F. curve a more peaked form.
  The great convenience of the assumption that the E.M.F. obeys the sine
  law has led to its being very commonly used as the basis for the
  mathematical analysis of alternator problems; but any deductions made
  from this premiss require to be applied with caution if they are
  likely to be modified by a different shape of the curve. Further, the
  same alternator will give widely different curves even of E.M.F., and
  still more so of current, according to the nature of the external
  circuit to which it is connected. As will be explained later, the
  phase of the current relatively to the E.M.F. depends not only on the
  inductance of the alternator itself, but also upon the inductance and
  capacity of the external circuit, so that the same current will
  produce different effects according to the amount by which it lags or
  leads. The question as to the relative advantages of differently
  shaped E.M.F. curves has led to much discussion, but can only be
  answered by reference to the nature of the work that the alternator
  has to do--i.e. whether it be arc lighting, motor driving, or
  incandescent lighting through transformers. The shape of the E.M.F.
  curve is, however, of great importance in one respect, since upon it
  depends the ratio of the maximum instantaneous E.M.F. to the effective
  value, and the insulation of the entire circuit, both external and
  internal, must be capable of withstanding the maximum E.M.F. While the
  maximum value of the sine curve is [root]2 or 1.414 times the
  effective value, the maximum value of a [Lambda] curve is 1.732 times
  the effective value, so that for the same effective E.M.F. the
  armature wires must not only be more heavily insulated than in the
  continuous-current dynamo, but also the more peaked the curve the
  better must be the insulation.

    Excitation.

  Since an alternating current cannot be used for exciting the
  field-magnet, recourse must be had to some source of a direct current.
  This is usually obtained from a small auxiliary continuous-current
  dynamo, called an _exciter_, which may be an entirely separate
  machine, separately driven and used for exciting several alternators,
  or may be driven from the alternator itself; in the latter case the
  armature of the exciter is often coupled directly to the rotating
  shaft of the alternator, while its field-magnet is attached to the
  bed-plate. Although separate excitation is the more usual method, the
  alternator can also be made self-exciting if a part or the whole of
  the alternating current is "rectified," and thus converted into a
  direct current.

    Quarter-phase alternators.

  The general idea of the polyphase alternator giving two or more
  E.M.F.'s of the same frequency, but displaced in phase, has been
  already described. The several phases may be entirely independent, and
  such was the case with the early polyphase machines of Gramme, who
  used four independent circuits, and also in the large two-phase
  alternators designed by J.E.H. Gordon in 1883. If the phases are thus
  entirely separate, each requires two collector rings and two wires to
  its external circuit, i.e. four in all for two-phase and six for
  three-phase machines. The only advantage of the polyphase machine as
  thus used is that the whole of the surface of the armature core may be
  efficiently covered with winding, and the output of the alternator for
  a given size be thereby increased. It is, however, also possible so to
  interlink the several circuits of the armature that the necessary
  number of transmitting lines to the external circuits may be reduced,
  and also the weight of copper in them for a given loss in the
  transmission.[21] The condition which obviously must be fulfilled,
  for such interlinking of the phases to be possible, is that in the
  lines which are to meet at any common junction the algebraic sum of
  the instantaneous currents, reckoned as positive if away from such
  junction and as negative if towards it, must be zero. Thus if the
  phases be diagrammatically represented by the relative angular
  position of the coils in fig. 39, the current in the coils A and B
  differs in phase from the current in the coils C and D by a quarter of
  a period or 90°; hence if the two wires b and d be replaced by the
  single wire bd, this third wire will serve as a common path for the
  currents of the two phases either outwards or on their return. At any
  instant the value of the current in the third wire must be the vector
  sum of the two currents in the other wires, and if the shape of the
  curves of instantaneous E.M.F. and current are identical, and are
  assumed to be sinusoidal, the effective value of the current in the
  third wire will be the vector sum of the effective values of the
  currents in the other wires; in other words, if the system is
  balanced, the effective current in the third wire is [root]2, or 1.414
  times the current in either of the two outer wires. Since the currents
  of the two phases do not reach their maximum values at the same time,
  the sectional area of the third wire need not be twice that of the
  others; in order to secure maximum efficiency by employing the same
  current density in all three wires, it need only be 40% greater than
  that of either of the outer wires. The effective voltage between the
  external leads may in the same way be calculated by a vector diagram,
  and with the above _star connexion_ the voltage between the outer pair
  of wires a and c is [root]2, or 1.414 times the voltage between either
  of the outer wires and the common wire bd. Next, if the four coils are
  joined up into a continuous helix, just as in the winding of a
  continuous-current machine, four wires may be attached to equidistant
  points at the opposite ends of two diameters at right angles to each
  other (fig. 40). Such a method is known as the _mesh connexion_, and
  gives a perfectly symmetrical four-phase system of distribution. Four
  collecting rings are necessary if the armature rotates, and there is
  no saving in copper in the transmitting lines; but the importance of
  the arrangement lies in its use in connexion with rotary converters,
  in which it is necessary that the winding of the armature should form
  a closed circuit. If e = the effective voltage of one phase A, the
  voltage between any pair of adjacent lines in the diagram is e, and
  between m and o or n and p is e [root]2. The current in any line is
  the resultant of the currents in the two phases connected to it, and
  its effective value is c [root]2, where c is the current of one phase.

  [Illustration: FIG. 39.]

  [Illustration: FIG. 40.]

  [Illustration: FIG. 41.]

    Three-phase alternators.

  When we pass to machines giving three phases differing by 120°, the
  same methods of star and mesh connexion find their analogies. If the
  current in coil A (fig. 41) is flowing away from the centre, and has
  its maximum value, the currents in coils B and C are flowing towards
  the centre, and are each of half the magnitude of the current in A;
  the algebraic sum of the currents is therefore zero, and this will
  also be the case for all other instants. Hence the three coils can be
  united together at the centre, and three external wires are alone
  required. In this star or "Y" connexion, if e be the effective voltage
  of each phase, or the voltage between any one of the three collecting
  rings and the common connexion, the volts between any pair of
  transmitting lines will be E = e [root]3 (fig. 41); if the load be
  balanced, the effective current C in each of the three lines will be
  equal, and the total output in watts will be W = 3Ce = 3CE/[root]3 =
  1.732 EC, or 1.732 times the product of the effective voltage between
  the lines and the current in any single line. Next, if the three coils
  are closed upon themselves in a mesh or _delta_ fashion (fig. 42), the
  three transmitting wires may be connected to the junctions of the
  coils (by means of collecting rings if the armature rotates). The
  voltage E between any pair of wires is evidently that generated by
  one phase, and the current in a line wire is the resultant of that in
  two adjacent phases; or in a balanced system, if c be the current in
  each phase, the current in the line wire beyond a collecting ring is C
  = c [root]3, hence the watts are W = 3cE = 3CE/[root]3 = 1.732 EC, as
  before. Thus any three-phase winding may be changed over from the star
  to the delta connexion, and will then give 1.732 times as much
  current, but only 1/1.732 times the voltage, so that the output
  remains the same.

  [Illustration: FIG. 42.]

    Armature reaction in alternators

  The "armature reaction" of the alternator, when the term is used in
  its widest sense to cover all the effects of the alternating current
  in the armature as linked with a magnetic circuit or circuits, may be
  divided into three items which are different in their origin and
  consequences. In the first place the armature current produces a
  self-induced flux in local circuits independent of the main magnetic
  circuit, as e.g. linked with the ends of the coils as they project
  outwards from the armature core; such lines may be called "secondary
  leakage," of which the characteristic feature is that its amount is
  independent of the position of the coils relatively to the poles. The
  alternations of this flux give rise to an inductive voltage lagging
  90° behind the phase of the current, and this leakage or reactance
  voltage must be directly counterbalanced electrically by an equal
  component in the opposite sense in the voltage from the main field.
  The second and third elements are more immediately magnetic and are
  entirely dependent upon the position of the coils in relation to the
  poles and in relation to the phase of the current which they then
  carry. When the side of a drum coil is immediately under the centre of
  a pole, its ampere-turns are cross-magnetizing, i.e. produce a
  distortion of the main flux, displacing its maximum density to one or
  other edge of the pole. When the coil-side is midway between the poles
  and the axes of coil and pole coincide, the coil stands exactly
  opposite to the pole and embraces the same magnetic circuit as the
  field-magnet coils; its turns are therefore directly magnetizing,
  either weakening or strengthening the main flux according to the
  direction of the current. In intermediate positions the ampere-turns
  of the coil gradually pass from cross to direct and vice versa. When
  the instantaneous values of either the cross or direct magnetizing
  effect are integrated over a period and averaged, due account being
  taken of the number of slots per coil-side and of the different phases
  of the currents in the polyphase machine, expressions are obtained for
  the equivalent cross and direct ampere-turns of the armature as acting
  upon a pair of poles. For a given winding and current, the determining
  factor in either the one or the other is found to be the relative
  phase angle between the axis of a coil in its position when carrying
  the maximum current and the centre of a pole, the transverse reaction
  being proportional to the cosine of this angle, and the direct
  reaction to its sine. If the external circuit is inductive, the
  maximum value of the current lags behind the E.M.F. and so behind the
  centre of the pole; such a negative angle of lag causes the direct
  magnetizing turns to become back turns, directly weakening the main
  field and lowering the terminal voltage. Thus, just as in the
  continuous-current dynamo, for a given voltage under load the
  excitation between the pole-pieces X_p must not only supply the net
  excitation required over the air-gaps, armature core and teeth, but
  must also balance the back ampere-turns X_b of the armature.

  Evidently therefore the characteristic curve connecting armature
  current and terminal volts will with a constant exciting current
  depend on the nature of the load, whether inductive or non-inductive,
  and upon the amount of inductance already possessed by the armature
  itself. With an inductive load it will fall more rapidly from its
  initial maximum value, or, conversely, if the initial voltage is to be
  maintained under an increasing load, the exciting current will have to
  be increased more than if the load were non-inductive. In practical
  working many disadvantages result from a rapid drop of the terminal
  E.M.F. under increasing load, so that between no load and full load
  the variation in terminal voltage with constant excitation should not
  exceed 15%. Thus the output of an alternator is limited either by its
  heating or by its armature reaction, just as is the output of a
  continuous-current dynamo; in the case of the alternator, however, the
  limit set by armature reaction is not due to any sparking at the
  brushes, but to the drop in terminal voltage as the current is
  increased, and the consequent difficulty in maintaining a constant
  potential on the external circuit.

    The coupling of alternators.

  The joint operation of several alternators so that their outputs may
  be delivered into the same external circuit is sharply distinguished
  from the corresponding problem in continuous-current dynamos by the
  necessary condition that they must be in synchronism, i.e. not only
  must they be so driven that their frequency is the same, but their
  E.M.F.'s must be in phase or, as it is also expressed, the machines
  must be in step. Although in practice it is impossible to run two
  alternators in series unless they are rigidly coupled together--which
  virtually reduces them to one machine--two or more machines can be run
  in parallel, as was first described by H. Wilde in 1868 and
  subsequently redemonstrated by J. Hopkinson and W.G. Adams in 1884.
  Their E.M.F.'s should be as nearly as possible in synchronism, but,
  as contrasted with series connexion, parallel coupling gives them a
  certain power of recovery if they fall out of step, or are not in
  exact synchronism when thrown into parallel. In such circumstances a
  synchronizing current passes between the two machines, due to the
  difference in their instantaneous pressures; and as this current
  agrees in phase more nearly with the leading than with the lagging
  machine, the former machine does work as a generator on the latter as
  a motor. Hence the lagging machine is accelerated and the leading
  machine is retarded, until their frequencies and phase are again the
  same.

  Uses of alternators.

The chief use of the alternator has already been alluded to. Since it
can be employed to produce very high pressures either directly or
through the medium of transformers, it is specially adapted to the
electrical transmission of energy over long distances.[22] In the early
days of electric lighting, the alternate-current system was adopted for
a great number of central stations; the machines, designed to give a
pressure of 2000 volts, supplied transformers which were situated at
considerable distances and spread over large areas, without an undue
amount of copper in the transmitting lines. While there was later a
tendency to return to the continuous current for central stations, owing
to the introduction of better means for economizing the weight of copper
in the mains, the alternating current again came into favour, as
rendering it possible to place the central station in some convenient
site far away from the district which it was to serve. The pioneer
central station in this direction was the Deptford station of the London
Electric Supply Corporation, which furnished current to the heart of
London from a distance of 7 m. In this case, however, the alternators
were single-phase and gave the high pressure of 10,000 volts
immediately, while more recently the tendency has been to employ step-up
transformers and a polyphase system. The advantage of the latter is that
the current, after reaching the distant sub-stations, can be dealt with
by rotary converters, through which it is transformed into a continuous
current. The alternator is also used for welding, smelting in electric
furnaces, and other metallurgical processes where heating effects are
alone required; the large currents needed therein can be produced
without the disadvantage of the commutator, and, if necessary,
transformers can be interposed to lower the voltage and still further
increase the current. The alternating system can thus meet very various
needs, and its great recommendation may be said to lie in the
flexibility with which it can supply electrical energy through
transformers at any potential, or through rotary converters in
continuous-current form.

  AUTHORITIES.--For the further study of the dynamo, the following may
  be consulted, in addition to the references already given:--

  _General_: S.P. Thompson, _Dynamo-Electric
  Machinery--Continuous-Current Machines_ (1904), _Alternating-Current
  Machinery_ (1905, London); G. Kapp, _Dynamos, Alternators and
  Transformers_ (London, 1893); _Id., Electric Transmission of Energy_
  (London, 1894); Id., _Dynamo Construction; Electrical and Mechanical_
  (London, 1899); H.F. Parshall and H.M. Hobart, _Electric Generators_
  (London, 1900); C.C. Hawkins and F. Wallis, _The Dynamo_ (London,
  1903); E. Arnold, _Konstruktionstafeln für den Dynamobau_ (Stuttgart,
  1902); C.P. Steinmetz, _Elements of Electrical Engineering_ (New York,
  1901).

  _Continuous-Current Dynamos_: J. Fischer-Hinnen, _Continuous-Current
  Dynamos_ (London, 1899); E. Arnold, _Die Gleichstrommaschine_ (Berlin,
  1902); F. Niethammer, _Berechnung und Konstruktion der
  Gleichstrommaschinen und Gleichstrommotoren_ (Stuttgart, 1904).

  _Alternators_: D.C. Jackson and J.P. Jackson, _Alternating Currents
  and Alternating Current Machinery_ (New York, 1903); J.A. Fleming,
  _The Alternate Current Transformer_ (London, 1899); C.P. Steinmetz,
  _Alternating Current Phenomena_ (New York, 1900); E. Arnold, _Die
  Wechselstromtechnik_ (Berlin, 1904); S.P. Thompson, _Polyphase
  Electric Currents_ (London, 1900); A. Stewart, _Modern Polyphase
  Machinery_ (London, 1906); M. Oudin, _Standard Polyphase Apparatus and
  Systems_ (New York, 1904).     (C. C. H.)

FOOTNOTES:

  [1] _Experimental Researches in Electricity_, series ii. § 6, pars.
    256, 259-260, and series xxviii. § 34.

  [2] _Ibid._ series i. § 4, pars. 84-90.

  [3] "On the Physical Lines of Magnetic Force," _Phil. Mag._, June
    1852.

  [4] Faraday, _Exp. Res._ series xxviii. § 34, pars. 3104, 3114-3115.

  [5] _Id._, ib. series i. § 4, pars. 114-119.

  [6] _Id._, ib. series ii. § 6, pars. 211, 213; series xxviii. § 34,
    par. 3152.

  [7] Invented by Nikola Tesla (_Elec. Eng._ vol. xiii. p. 83. Cf.
    Brit. Pat. Spec. Nos. 2801 and 2812, 1894). Several early inventors,
    e.g. Salvatore dal Negro in 1832 (_Phil. Mag._ third series, vol. i.
    p. 45), adopted reciprocating or oscillatory motion, and this was
    again tried by Edison in 1878.

  [8] The advantage to be obtained by making the poles closely embrace
    the armature core was first realized by Dr Werner von Siemens in his
    "shuttle-wound" armature (Brit. Pat. No. 2107, 1856).

  [9] _Nuovo Cimento_ (1865), 19, 378.

  [10] Brit. Pat. No. 1668 (1870); _Comptes rendus_ (1871), 73, 175.

  [11] _Ann. Chim. Phys._ l. 322.

  [12] Ibid. li. 76. Since in H. Pixii's machine the armature was
    stationary, while both magnet and commutator rotated, four brushes
    were used, and the arrangement was not so simple as the split-ring
    described above, although the result was the same. J. Saxton's
    machine (1833) and E.M. Clarke's machine (1835, see Sturgeon's
    _Annals of Electricity_, i. 145) were similar to one another in that
    a unidirected current was obtained by utilizing every alternate
    half-wave of E.M.F., but the former still employed mercury collecting
    cups, while the latter employed metal brushes. W. Sturgeon in 1835
    followed Pixii in utilizing the entire wave of E.M.F., and abandoned
    the mercury cups in favour of metal brushes pressing on four
    semicircular disks (_Scientific Researches_, p. 252). The simple
    split-ring is described by Sir C. Wheatstone and Sir W.F. Cooke in
    their Patent No. 8345 (1840).

  [13] By the "leading" side of the tooth or of an armature coil or
    sector is to be understood that side which first enters under a pole
    after passing through the interpolar gap, and the edge of the pole
    under which it enters is here termed the "leading" edge as opposed to
    the "trailing" edge or corner from under which a tooth or coil
    emerges into the gap between the poles; cf. fig. 30, where the
    leading and trailing pole-corners are marked ll and tt.

  [14] Such was the arrangement of Wheatstone's machine (Brit. Pat. No.
    9022) of 1841, which was the first to give a more nearly "continuous"
    current, the number of sections and split-rings being five.

  [15] Its development from the split-ring was due to Pacinotti and
    Gramme (Brit. Pat. No. 1668, 1870) in connexion with their ring
    armatures.

  [16] And extended by G. Kapp, "On Modern Continuous-Current
    Dynamo-Electric Machines," _Proc. Inst. C.E._ vol. lxxxiii. p. 136.

  [17] Drs J. and E. Hopkinson, "Dynamo-Electric Machinery," Phil.
    Trans., May 6, 1886; this was further expanded in a second paper on
    "Dynamo-Electric Machinery," _Proc. Roy. Soc._, Feb. 15, 1892, and
    both are reprinted in _Original Papers on Dynamo-Machinery and Allied
    Subjects_.

  [18] _Exp. Res._, series i. § 4, par. 111. In 1845 Wheatstone and
    Cooke patented the use of "voltaic" magnets in place of permanent
    magnets (No. 10,655).

  [19] Between Moutiers and Lyons, a distance of 115 m., energy is
    transmitted on the Thury direct-current system at a maximum pressure
    of 60,000 volts. Four groups of machines in series are employed, each
    group consisting of four machines in series; the rated output of each
    component machine is 75 amperes at 3900 volts or 400 h.p. A water
    turbine drives two pairs of such machines through an insulating
    coupling, and the sub-base of each pair of machines is separately
    insulated from earth, the foundation being also of special insulating
    materials.

  [20] For experiments on high-frequency currents, Nikola Tesla
    constructed an alternator having 384 poles and giving a frequency of
    about 10,000 (_Journ. Inst. Elec. Eng._ 1892, 21, p. 82). The
    opposite extreme is found in alternators directly coupled to the
    Parsons steam-turbine, in which, with a speed of 3000 revs. per min.,
    only two poles are required to give a frequency of 50. By a
    combination of a Parsons steam-turbine running at 12,000 revs. per
    min. with an alternator of 140 poles a frequency of 14,000 has been
    obtained (_Engineering_, 25th of August 1899). For description of an
    experimental machine for 10,000 cycles per second when running at
    3000 revs. per min., see _Trans. Amer. Inst. Elect. Eng._ vol. xxiii.
    p. 417.

  [21] As in the historical transmission of energy from Lauffen to
    Frankfort (1891).

  [22] In the pioneer three-phase transmission between Laufen and
    Frankfort (_Electrician_, vol. xxvi. p. 637, and xxvii. p. 548), the
    three-phase current was transformed up from about 55 to 8500 volts,
    the distance being 110 m. A large number of installations driven by
    water power are now at work, in which energy is transmitted on the
    alternating-current system over distances of about 100 m. at
    pressures ranging from 20,000 to 67,000 volts.

DYNAMOMETER (Gr. [Greek: dynamis], strength, and [Greek: metron], a
measure), an instrument for measuring force exerted by men, animals and
machines. The name has been applied generally to all kinds of
instruments used in the measurement of a force, as for example electric
dynamometers, but the term specially denotes apparatus used in connexion
with the measurement of work, or in the measurement of the horse-power
of engines and motors. If P represent the average value of the component
of a force in the direction of the displacement, s, of its point of
application, the product Ps measures the work done during the
displacement. When the force acts on a body free to turn about a fixed
axis only, it is convenient to express the work done by the transformed
product T[theta], where T is the average turning moment or torque acting
to produce the displacement [theta] radians. The apparatus used to
measure P or T is the dynamometer. The factors s or [theta] are observed
independently. Apparatus is added to some dynamometers by means of which
a curve showing the variations of P on a distance base is drawn
automatically, the area of the diagram representing the work done; with
others, integrating apparatus is combined, from which the work done
during a given interval may be read off directly. It is convenient to
distinguish between absorption and transmission dynamometers. In the
first kind the work done is converted into heat; in the second it is
transmitted, after measurement, for use.

  _Absorption Dynamometers._--Baron Prony's dynamometer (_Ann. Chim.
  Phys._ 1821, vol. 19), which has been modified in various ways,
  consists in its original form of two symmetrically shaped timber beams
  clamped to the engine-shaft. When these are held from turning, their
  frictional resistance may be adjusted by means of nuts on the screwed
  bolts which hold them together until the shaft revolves at a given
  speed. To promote smoothness of action, the rubbing surfaces are
  lubricated. A weight is moved along the arm of one of the beams until
  it just keeps the brake steady midway between the stops which must be
  provided to hold it when the weight fails to do so. The general theory
  of this kind of brake is as follows:-Let F be the whole frictional
  resistance, r the common radius of the rubbing surfaces, W the force
  which holds the brake from turning and whose line of action is at a
  perpendicular distance R from the axis of the shaft, N the revolutions
  of the shaft per minute, [omega] its angular velocity in radians per
  second; then, assuming that the adjustments are made so that the
  engine runs steadily at a uniform speed, and that the brake is held
  still, clear of the stops and without oscillation, by W, the torque T
  exerted by the engine is equal to the frictional torque Fr acting at
  the brake surfaces, and this is measured by the statical moment of the
  weight W about the axis of revolution; that is--

    T = Fr = WR.  (1)

  Hence WR measures the torque T.

  If more than one force be applied to hold the brake from turning, Fr,
  and therefore T, are measured by the algebraical sum of their
  individual moments with respect to the axis. If the brake is not
  balanced, its moment about the axis must be included. Therefore, quite
  generally,

    T = [Sigma]WR.  (2)

  The factor [theta] of the product T[theta] is found by means of a
  revolution counter. The power of a motor is measured by the rate at
  which it works, and this is expressed by T[omega] = T2[pi]N/60 in
  foot-pounds per second, or T2[pi]N/33,000 in horse-power units. The
  latter is commonly referred to as the "brake horse-power." The
  maintenance of the conditions of steadiness implied in equation (1)
  depends upon the constancy of F, and therefore of the coefficient of
  friction µ between the rubbing surfaces. The heating at the surfaces,
  the variations in their smoothness, and the variations of the
  lubrication make [mu] continuously variable, and necessitate frequent
  adjustment of W or of the nuts. J.V. Poncelet (1788-1867) invented a
  form of Prony brake which automatically adjusted its grip as [mu]
  changed, thereby maintaining F constant.