r
SRARY
OF THE
UNIVERSITY OF CALIFORNIA.
; i
Deceived
Successions
MAR '23 1&94
189
No
Class No.
ORIGINAL PAPERS
ON
DYNAMO MACHINERY
AND ALLIED SUBJECTS.
BY
JOHN HOPKINSON, M.A., D.So., F.B.S.
NEW YORK :
THE W. J. JOHNSTON COMPANY, LIMITBB,
41 PARK Row (TIMES BUILDING).
LONDON :
WHITTAKER & CO.,
2, WHITEHART STREET, PATERNOSTER SQUARE.
1893.
AUTHORIZED AMERICAN EDITIOK
PEEFACE.
THE following short collection of papers includes all that
I have written of an original character on electrotechnical
subjects. Here and there errors have been corrected;
otherwise the papers are republished exactly as they
first appeared. The chronological order is not . strictly
adhered to. The papers are arranged rather according to
subject. Thus, five papers relating wholly or in part to the
continuous current dynamo come first; then follow four
on converters ; lastly, there are a note on the theory of al-
ternate current machines and a paper on the applications
of electricity to lighthouses.
The motive of this publication has been that I have
understood that one or two of these papers are out of
print and are not so accessible to American readers as an
author who very greatly values the good opinion of Ameri-
can electrical engineers would desire.
J. HOPKI^SOtf.
LONDON, September, 1892.
3
CONTENTS.
PAGE
I. ON ELECTRIC LIGHTING, . . . - 7
(Proceedings of the Institution of Mechanical Engineers, April 25, 1879.)
II. ON ELECTEIC LIGHTING, (Second Paper) . . 26
(Proceedings of the Institution of Mechanical Engineers, April 23, 1880.)
III. SOME POINTS IN ELECTRIC LIGHTING, ... 40
(Proceedings of the Institution of Civil Engineers, April 5, 1883.)
IV. DYNAMO-ELECTRIC MACHINERY, 79
(Philosophical Transactions of the Royal Society, May 6, 1886.)
V. DYNAMO-ELECTRIC MACHiNERY,(Second Paper) 134
(Proceedings of the Royal Society, February 15, 1892.)
VI. THEORY or ALTERNATING CURRENTS, . . . 148
(Institution of Electrical Engineers, November 13, 1884.)
VII. AN UNNOTICED DANGER IN CERTAIN APPA-
RATUS FOR DISTRIBUTION OF ELECTRICITY, 177
(Philosophical Magazine, September, 1885.)
VIII. INDUCTION COILS OR TRANSFORMERS, . . .182
(Proceedings of the Royal Society, February 17, 1887.)
IX. EEPORT TO THE WESTINGHOUSE COMPANY OF
THE TEST OF Two 6,500-WATT TRANS-
FORMERS, MAY 31, 1892, .187
X. THEORY OF THE ALTERNATE CURRENT DYNAMO, 211
(Proceedings of the Royal Society, February 17, 1887.)
XL THE ELECTRIC LIGHTHOUSES OF MACQUARIE
AND OF TINO, 217
(Proceedings of the Institution of Civil Engineers, December 7, 18S6.)
5
ORIGINAL PAPEES
ON
DYNAMO MACHINERY
AND ALLIED SUBJECTS.
ON ELECTRIC LIGHTING.
FIRST PAPER.
DURIKG the last year much has been written and much
information communicated concerning the production of
light from mechanical power by means of an electric cur-
rent. The major portion of what has appeared has been
either descriptive of particular machines for producing the
current, and of lamps for manifesting a portion of its
energy as light, or a statement of practical results con-
necting the light obtained with the power applied and the
money expended in producing it.
While fully appreciating the present value of such in-
formation, the author has felt that it did not tell all that
was interesting or practically useful to know. It is de-
sirable to know what the various machines can do with
varied and known resistances in the circuit, and with va-
ried speeds of rotation; and what amount of power is
absorbed in each case. It is a question of interest whether
7
8 DYNAMO MACHINERY AND ALLIED SUBJECTS.
a machine intended for one light can or cannot produce
two in the same circuit, and if not, why not ; whether a
machine such as the Wallace-Farmer, intended as it is for
many lights, will give economical results when used for
one; and so on. It is clear that the attempt to examine
all separate combinations of so many variables would be
hopeless, and that the work must be systematized.
The mechanical energy communicated by the steam en-
gine or 'other motor is not immediately converted into the
energy of heat, but is first converted into the energy of
an electric current in a conducting circuit; of this a
portion only becomes localized as heat between the car-
bons of the electric arc ; and of this again a part only be-
comes sensible to the eye as light. The whole of what we
need to know may be more easily ascertained and more
shortly expressed if the inquiry is divided into two parts :
(a) What current will a machine produce under various
conditions of circuit, and at what expenditure of mechani-
cal power ? (b) Having given the electric conditions under
which the arc is placed, no matter how these conditions
are produced, what light will be obtained therefrom ?
Parts of the subject have been treated more or less in this
sense by Edlund (Pogg. Ann., 1867 and 1868), Houston
and Thomson in America, Mascart (Journal de Physique,
March, 1878), Abney (Proceedings of the Royal Society,
1878), Trowbridge (Philosophical Magazine, March, 1879),
Schwendler (Report on Electric Light Experiments), etc.,
but not so completely that nothing remains to be done ;
nor does the author doubt that a great deal of information
is in the hands of makers of machines, which they have
not thought it necessary to make known. The present
ON ELECTRIC LIGHTING. 9
communication is limited to an account of some experi-
ments on the production of currents by a Siemens medium-
sized machine; that is, the machine which is advertised to
produce a light of 6,000 candles by an expenditure of 3J
horse power.
All the machines for converting mechanical power into
an electric current consist ultimately of a conducting wire
moving in a magnetic field; and approximately the elec-
tromotive force of the machine will be proportional to the
velocity with which the circuit moves through the field,
and to the intensity of the field. In general the intensity
of the field is not constant; and in such machines as the
Siemens and the ordinary Gramme machine it may be re-
garded as a function of the current passing. We must
learn what this function is for the machine in question ;
or which comes to exactly the same thing, and is better
so long as the facts are merely the result of experiment
we must construct a curve in which the abscissae represent
the intensities of currents passing, and the ordinates the
corresponding electromotive forces for a given speed of
rotation. But the power of a current, that is, its energy
per second, is the product of the electromotive force and
the intensity, or, in the case of the curve, the product of
the ordinate and the abscissa; this is in all cases less than
the power required to drive the machine, and the ratio be-
tween the two may fairly be called the efficiency of the
machine.
The object of the inquiry may perhaps be made clearer
by an illustration. Consider the case of a pump forcing
water through a pipe against friction; then the electric
current corresponds to the volume of water passing per
10 DYNAMO MACHINERY AND ALLIED SUBJECTS.
second, and the electromotive force to the difference of
pressure on the two sides of the pump; and just as the
product of pressure and volume per second is power, so
the product of electromotive force and current is power,
which is directly comparable with the power expended in
driving the machine or the pump,, as the case may be.
The peculiarity of the so-called dynamo-electric machine
lies in this, that what corresponds to the difference of
pressure (the electromotive force) depends directly on
what corresponds to the volume passing (the current).
Each experiment requires the determination of the
speed, the driving power, the resistances in circuit, and
the current passing; or of the difference of potential be-
tween the two ends of a known resistance of the circuit.
The apparatus employed by the author was arranged,
not alone with an aim to accuracy, but in part to make use
of such instruments as he happened to possess or could
easily construct, and in part with a view to ready erection
and transportation. Much more accurate results may be
obtained by any one who will arrange apparatus with a single
aim to attain the greatest accuracy possible. The author's
apparatus will, however, be briefly described, that others
may form their own opinion of the importance of the va-
rious sources of error.
The speed counter was that supplied with the electric
machine.
Concerning the steam engine nothing need be said, save
that its speed was maintained very constant by means of a
governor, shown in Fig. 1, specially arranged for great
sensibility. By placing the joint A above the joint B, in-
stead of below it, as in Porter's governor, any degree of
ON ELECTRIC LIGHTING.
11
FIG. 1. GOVERNOR.
sensibility up to instability may be obtained. The speed
was varied by means of a weight and a spring attached to
a lever on the throttle valve
spindle. The ungainly ap-
pearance of this governor could
easily be remedied by any one
proposing to manufacture it.
The power is transmitted
from the engine to a counter-
shaft by means of a strap, and
by a second strap from the
countershaft to the pulley of
the electric machine. On this
second strap is the dynamom-
eter shown in Fig. 2.
This dynamometer has for some time been used by
Messrs. Siemens, and was also used by Mr. Schwendler; its
invention is due to Herr von Hefner- Alteneck. A is the
driving pulley ; B the pulley of the electric machine ; C C
are a pair of loose pulleys between which the strap passes ;
these are carried in a double triangular frame, which can
turn about a bar D. This bar might form part of a per-
manent structure ; but in order to place the dynamometer
readily on any strap, the bar was in this case provided with
eyes at either end, and secured in position by six or eight
ropes. This plan answers well, as there is very little stress
on the bar. Immediately above the pulleys C C a cord
leads from the frame through a Salter spring balance over
snatch blocks to a back balance weight ; the tension of this
cord is read on the spring balance. At first the spring
balance was omitted, and the weight at the end of the cord
12 DYNAMO MACHINERY AND ALLIED SUBJECTS.
ON ELECTKIC LIGHTING. 13
was observed ; but the friction of the snatch block pulleys
was found objectionable. The pulley frame carries a
pointer, which is adjusted so as to coincide with a datum
mark when the line A B bisects the distance between the
loose pulleys. Let W be the tension of the cord required
to bring the pulley frame to its standard position when no
work is being transmitted, W" the tension which is
required to bring the pointer back to the datum mark when
an observation is made, and let W = W W". Let
T', T" be the tensions on the tight and slack halves of the
strap; R l9 # 2 , r the radii of the pulleys A, B and C, plus
half the thickness of the strap; c,, e a the distances AJ,
J B; 2d the distance apart of the centres (7, C; a l} # 2 the
inclinations of the two parts of the strap, on either side of
C, C, to the line A B. Then
(T f - T")(sin a, + sin a,) = W;
R, + r - d . d (R, + r - dV
and sm a. = --- \- - -- ,
c l 2<?,\ c l I '
R, + r - d , d fR, + r -
--
very nearly.
The value of T' T" and the velocity of rotation of the
electric machine being known, the power received by it is
readily obtained, expressed in gram-centimetres per second.
Multiplying by 981, the value of gravity in centimetres
and seconds, the power is then expressed in ergs* per
* The dyne is the force which will in one second impart to one gram a
velocity of one centimetre per second, and an erg is. the work done by a dyne
working through a centimetre; a horse power may be taken as three-quarters
14 DYXAMO MACHINERY AND ALLIED SrBJBCTS.
is ready for comparison with the results of the
electrical experiments.
As already stated, the dynamo-electric machine in the
present case was a Siemens medium size; the armature coil
has fifty-ax divisions, and the brushes are single, not
divided, that is, each brash is in connection with one
segment of the commutator at any instant
The leading wire is 100 yards of Siemens No. 90, con-
sisting of seven copper wires, insulated with tape and India
rubber, and having a diameter of about 9J mm.
The method of determining the current is shown in the
diagram, Fig. 3. The current is conveyed from the
machine A through a set of coils of brass wire r, and in
some eases through a resistance coil placed in a calorimeter
B, and so back to the machine, the connections being
made through cups of mercury excavated in a piece of
wood />. The current passing may be ascertained by the
heating of the calorimeter, or by measuring the difference
of potential at the extremities of the resistance r. all the
resistances of the circuit being supposed known. This
difference of potential could of course be very easily
measured by "means of a quadrant electrometer; but, as
the instrument had to be frequently removed, a galva-
nometer appeared more convenient. The two points to be
measured are connected to the ends of two series of resist-
ance coils a. b. The galvanometer G is placed in a second
derived current, passing from a junction in a b through a
battery H 9 then through a set of high resistances J for
being M"erg. Bee Report of fW Brit.
G. S- System of Unto," pvJbfiaked by tfce
OS KLECTB1C UGHTIXG.
15
_
: ~"
16 DYNAMO MACHINERY AND ALLIED SUBJECTS.
adjusting sensibility, a reversing key K, the galvanometer
6r, the reversing key K again, and so to the other extremity
of b. The electromotive force is ascertained by adjusting
the resistance b so that the deflection of the galvanometer
is nil.
The resistance coils c comprise ten coils of common
brass wire, each wound round a couple of wooden uprights
driven into a baseboard common to the set; each wire is
about 60 metres long, and of No. 17 Birmingham wire
gauge (.06 inch or 1-J mm. diameter), weighing about 14.6
grams per metre. Each terminal is connected to a cup of
mercury excavated in the baseboard, so that the coils can
be placed in series or in parallel circuit at pleasure. The
resistance of each coil being about 3 ohms, this set may be
arranged to give resistances varying from 0.3 to 30 ohms.
The calorimeter B is a Siemens pyrometer with the top
scale removed; a resistance coil of uncovered German
silver wire nearly 2 m. long, 1J mm. in diameter, and
having a resistance of about 0.2 ohm, is suspended within
it from an ebonite cover, which also carries a little brass
stirrer, and the calorimeter is filled with water to a level
determined by the mark of a scriber. It was of course
necessary to know the capacity of the calorimeter for heat.
It was filled with warm water up to the mark, and the coil
placed in position ; 120 grams of water were then with-
drawn, and the temperature of the calorimeter was ob-
served to be 58.8 C. ; after the lapse of one minute it was
58.3 C.; after a second minute 57.9 0.; 120 grams of
cold water, temperature 13.3 C., were then suddenly in-
troduced through a hole in the ebonite cover, and it was
found that, two minutes after the reading of 57.9 C., the
ON ELECTEIC LIGHTING. 17
temperature was 50.0 C.; hence we may infer that the
capacity of the calorimeter is equal to that of 740 grams of
water. Two similar experiments at lower temperatures
gave respectively the numbers 749 and 750. Estimating
the capacity from the weight of the copper cylinder sup-
plied with the pyrometer, it should be 747, to which must
be added the capacity of the German silver wire and
stirrer. Taking everything into consideration, 750 grams
may be assumed as the most probable result.
The resistance coils a, b are of German silver, made by
Messrs. Elliott Brothers ; they are on the binary scale from
-J ohm to 1,024 ohms. Separate coils were used, instead of
a regular resistance box, because they were more readily
applicable to any other purpose for which they might be
required; and the binary scale was adopted, because the
coils could at once be used as conductivity coils in parallel
circuit, also on the binary scale. Each coil as supplied
terminated in two stout copper legs ; these were fitted with
cups of india rubber tubing for mercury, whereby any con-
nections whatever could readily be made. This arrange-
ment, though rude, was very convenient, and perhaps even
safer from error than a box with brass plugs to make the
connections. By a slight alteration of the connections the
whole was instantly available as a Wheatstone bridge to
determine resistances.
The battery H is a single element of Daniell's battery,
in which the sulphate of zinc solution floats on the sul-
phate of copper; its electromotive force is assumed to be
| volt.
The resistances J added in the battery circuit are pencil
lines on glass, such as are described in the Philosophical
18 DYNAMO MACHINERY AND ALLIED SUBJECTS.
Magazine of February, 1879. Three were used, giving a
range of sensibility approximately in the proportions 1, 25,
170, 700 the last figure being when all were short cir-
cuited ; they are very useful in adjusting the resistance b
so as to give no deflection of the galvanometer.
The reversing key K belongs to Sir W. Thomson's elec-
trometer, and is quite suitable when high resistances and
nil methods are used.
The galvanometer G is far more sensitive than necessary,
and has a resistance of 7,000 ohms.
Preliminary to experiments on the current, determina-
tions of resistances were made. The resistance of each
brass coil c was first determined, to afford the means of.
calculating the value of this resistance in any subsequent
experiment. When the ten coils were coupled in parallel
circuit, the calculated resistance was 0.29 ohm, while 0.292
was obtained by direct measurement. The leading wire
was then examined; the further ends being disconnected,
the insulation resistance was found to be over 60,000 ohms ;
how much over, it was immaterial to learn. When the
ends of the wire were connected, the resistance was found
to be 0.129 ohm. The resistances in the dynamo-electric
machine A were found to be as follows when cold: magnet
coils, 0.156 and 0.152 respectively; armature coil, 0.324;
total, 0.632 ohm. Direct examination was made of the
whole machine in eight positions of the commutator,
giving 0.643 ohm, with a maximum variation of 0.6 per
cent, from the mean. After running the machine for
some time the resistance was found to be 0.683, an increase
which would be accounted for by a rise of temperature of
12 0. or thereabouts. The resistance of the calorimeter
Otf ELECTKIC LIGHTING. 19
B is 0.20 ohm, without its leading wire, which may be
taken as 0.01. We have then in circuit three resistances
which must be considered: (1) The resistance of the
machine A and leading wire, assumed throughout as
together 0.81 ohm, and denoted bye,; (2) the resistance
of the brass coils c, calculated from the several determina-
tions, with the addition of 0.02 ohm, the resistance of the
leading wire, and denoted by c 2 ; (3) when present, the
resistance of the calorimeter B and leading wire, denoted
by c 3 .
Two approximate corrections were employed, and should
be detailed. The first is the correction for the consider-
able heating of the resistance coils c. These were arranged
in two sets of five each, five being in parallel circuit, and
the two sets in series. The current from the machine,
being about 7.4 webers in each wire, was passed for three
or four minutes; the circuit was then broken, and the
resistance c 2 was determined within one second of breaking
circuit, when it was found to be about 5 per cent, greater
than when cold. As the resistance was falling, the follow-
ing was adopted as a rule of correction : square the current
in a single wire, and increase the resistance c 2 by ^ per
cent, for every unit in the square. The second correction
is due to the fact that the calorimeter was losing heat all
the time it was being used. It was assumed that it loses
0.01 C. per minute for every 1 0. by which the tempera-
ture of the calorimeter exceeds that of the air; this cor-
rection is of course based on the experiment already
mentioned.
The method of calculation may now be explained:
20 DYNAMO MACHINERY AND ALLIED SUBJECTS.
R is the total resistance of the circuit in ohms, equal to
CI + C.H-CS;
Q is the current passing in webers;
E is the electromotive force round the circuit in volts;
W l is the work per second converted into heat in the
circuit, as determined by the galvanometer, measured
in erg-tens per second ;
W a is the work per second as determined by the
calorimeter;
TF 3 is the work per second as determined by the dyna-
mometer, less the power required to drive the machine
when the circuit is open;
HP is the equivalent of W 3 in horse power;
n is the number of revolutions per minute of the
armature.
As already mentioned, the standard resistance coils a, b
are adjusted in each experiment so that the galvanometer
gives no deflection, and the value of b is then noted.
The values of c lt c 2 , c 3 are known from previous observa-
tions. Then
_
~'
E = Q x R,
W, = E x Q,
mechanical equivalent of heat
generated per second in calorimeter.
The results of the experiments are given in the accom-
panying table.
ON ELECTRIC LIGHTING.
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22 DYNAMO MACHINERY AND ALLIED SUBJECTS.
A power of 0.21 erg-ten, or 0.28 horse power, was re-
quired to drive the machine at 720 revolutions on open
circuit. An examination of the table shows that the
efficiency of the machine is about 90 per cent., exclusive
of friction. Comparing experiments 11 and 13, and also
the last four experiments, it is seen that the electromotive
force is proportional to the speed of rotation within the
errors of observation. Experiments 14, 15, and 16 were
intended to ascertain the effect of displacing the com-
mutator brushes.
The principal object of the experiments was to ascertain
how the electromotive force depended on the current.
This relation is represented by the curve shown in Fig. 4,
Curves of Force and Current
Speed 720 revolutions per minute
40 50 60 TOWebcrs
FIG. 4. CURVE OF FORCE AND CURRENT.
in which the abscissae represent the currents flowing, or the
values of Q in the table, and the ord mates the electro-
motive forces, or the values of E reduced to a speed of 720
revolutions per minute. The curve may also be taken to
represent the intensity of the magnetic field, It will be.
ON ELECTRIC LIGHTING. 23
remarked that there is a point of inflection in the curve
somewhere near the origin. The experiments 1 to 5 indi-
cate that this is the true form of the curve, and it is con-
firmed in a remarkable manner by a special experiment.
A resistance intermediate between 5J and 4 (experiments
3 and 4) was used in circuit, and E and Q were determined
in two different ways: first, by starting with an open
circuit, which was then closed ; secondly, by starting with
a portion of the resistance short circuited, and a very
powerful current passing, and then breaking the short
circuit. It was found that ' E and Q were four times as
great in the latter case as in the former. Unfortunately
the numbers are not sufficiently accurate to be given, as
the solutions of the standard battery had become mixed.
The curve really gives a great deal more information
than appears at first sight. It will determine what current
will flow at any given speed of rotation of the machine,
and under any conditions of the circuit, whether of resist-
ances or of opposed electromotive forces. It will also give
very approximate indications of the corresponding curve
for other machines of the same configuration, but in which
the number of times the wire passes round the electro-
magnet or the armature is different.
It will be well to compare these results with those
obtained by others. M. Mascart worked on a Gramme
machine with comparatively low currents: he represents
his results approximately by the formula
E = n (a + b Q),
where a and b are constants. This corresponds to the
rapidly rising part of the curve in Fig. 4, Mr, Trowbridge
24 DYNAMO MACHINEBY AND ALLIED SUBJECTS.
with a Siemens machine obtained a maximum efficiency of
76 per cent., and states that the machine was running
below its normal velocity. Mr. Schwendler's results, when
fully published, will probably be found to be the most
complete and most accurate existing. In the precis he
states that the loss of power with a Siemens machine in
producing currents of over 20 webers is 12 per cent.
Now, taking the author's experiments 4 to 19, the mean
value of W, is 3.027 erg-tens and of W 3 3.304; adding to
the latter 0.21, the power required to drive the machine
when no current passes, it appears that 13.8 per cent, of
the power applied is wasted. Again, taking experiments
4, 6, 8, 10, and 12, the mean value of JF 2 is 2.888 erg-tens
and of W s 3.076, indicating a waste of power amounting to
12 per cent. Of this, as already stated, 0.21 erg-ten, or
0.28 horse power, is accounted for by friction of the
journals and commutator brush; the remainder is ex-
pended in local currents, or by loss of kinetic energy of
current when sparks occur at the commutator.
According to Weber's theory of induced magnetism, as
set forth in Maxwell's "Electricity and Magnetism,"
vol. II., if X be the magnetizing force and / the intensity
of magnetization,
2 X
1= a , until X rises to the value b,
6 o
and I=
where a and b are constants. We should naturally expect
that a similar formula would be approximately applicable
to dynamo-electric machines.
ON ELECTKIC LIGHTING. 25
In the present experiments, let 1 be the electromotive
force, X the current passing, and assume a to be 60 and b
to be 15; we then obtain results not far from those of
experiment. The capacity of any continuous current
machine may thus be shortly stated by giving the values of
a and b; or, which comes to the same thing, by stating the
electromotive force at a given speed when the -current is
as great as possible, and also the total resistance through
which the machine will exert an electromotive force two-
thirds of this greatest electromotive force. To this should
be added a statement of the resistance of the machine,
and of the power it absorbs, with known conditions of the
circuit.
The author has not yet tried any quantitative experi-
ments with the electric light, but hopes shortly to do so.
In the meantime he would remark that, as the lamp is
usually adjusted, only half the energy of the current
appears in the arc, or 44 per cent, of the energy trans-
mitted to the machine by the strap.
In conclusion the author would express the obligation
he is under to Messrs. Chance Brothers & Co., on account
of the facilities he has enjoyed for making these experi-
ments at their works. It may be mentioned that one
principal object of the research of which this is a beginning
is to obtain a minute knowledge of the electric light, with
a view to lighthouse illumination.
26 DYNAMO MACHINERY AND ALLIED SUBJECTS.
ON ELECTRIC LIGHTING.
SECOND PAPER.
Dynamo-Electric Machines. Since the date of the
author's former paper in April, 1879, other observers have
published the results of experiments similar to those de-
scribed by him. It may be well to exhibit some of these
'0 Webers
FIG. 5. CURVES OF ELECTROMOTIVE FORCE AND CURRENT OP SIEMENS MEDIUM
SIZE MACHINE.
results reduced to the form he has adopted, namely, a curve,
such as that previously shown in Fig. 4 of the preceding
paper, and now reproduced, with slight alterations, in Fig.
5. Here any abscissa represents a current passing through
the dynamo-electric machine, and the corresponding ordi-
ON ELECTRIC LIGHTING. 27
nate represents the electromotive force of the machine for
a certain speed of revolution, when that current is passing
through it. It will be found (1) that with varying speed
the ordinate, or electromotive force, corresponding to any
abscissa or current is proportional to the speed; (2) that
the electromotive force does not increase indefinitely with
increasing current, but that the curve approaches an asymp-
tote; (3) that the earlier part of the curve is, roughly
speaking, a straight line, until the current attains a certain
value, and that at that point the electromotive force has
reached about two-thirds of its maximum value. When the
current is such that the electromotive force is not more
than two-thirds of its maximum, a very small change in the
resistance with speed of engine constant, or in the speed of
the engine with resistance constant, causes a great change
in the current. For this reason the greatest of these cur-
rents, which is that corresponding to the point where the
curve breaks away from a straight line, and which is the
same for all speeds of revolution, since the curves for dif-
ferent speeds differ only in the scale of ordinates, may be
called the " critical current " of the machine. The effect
of a change of speed is exhibited in Fig. 5, where the lower
dotted line represents the curve for a speed of 660 revolu-
tions per minute, instead of 720. The resistance, varying as
electromotive force . . -, 41 i 4. ,-, v ^ n
, is given by the slope of the line P.
current
But since the resistance is constant, the slope of this line
must be constant; and it will be seen that it cuts the
upper curve at a point corresponding to a current of 15
webers, and the lower at a point corresponding to a current
of 5 webers only.
28 DYNAMO MACHINERY AND ALLIED SUBJECTS.
In Germany, Auerbach and Meyer ( Wiedemann Annalen,
Nov., 1879) have experimented fully on a Gramme machine
at various speeds, and with various external resistances.
The resistance of the machine was 0.97 ohm. Their results
are summarized in a table at the end of their paper, which
gives the current passing, with resistances in circuit from
1.75 to 200 Siemens units, and at speeds from 20 to 800
revolutions per minute. In the accompanying diagram,
Fig. 6, the curve G expresses the relation between electro-
Current
70 Webers
FIG. 6. CURVES OP ELECTROMOTIVE FORCE AND CURRENT : GRAMME MACHINE,
G; SIEMENS MEDIUM, SM; SIEMENS SMALLEST, Ss.
motive force and current, as deduced from some of their
observations; the points marked are plotted from their
table, making allowance, where necessary, for difference in
speed. The curve, as actually constructed, is for a speed
of 800 revolutions : at this speed it will be seen that the
maximum electromotive force is about 76 volts; and the
critical current, corresponding to a force of about 51 volts,
is 6.5 webers, with a total resistance of 7.8 ohms. Up to
this point there will be great instability, exactly as was the
ON ELECTRIC LIGHTING. 29
case in the Siemens machine examined by the author, where
the resistance was 4 ohms and the speed 720 revolutions.
The results of an elaborate series of experiments on cer-
tain dynamo-electric machines have recently been presented
to the Koyal Society by Dr. Siemens. One of the machines
examined was an ordinary medium sized machine, substan-
tially similar to that tried by the author in 1879. It is
described as having 24 divisions of the commutator; 336
coils on the armature, with a resistance of 0.4014 Siemens
unit; and 512 coils on the magnets, with a resistance of
0.3065: making a total resistance of 0.7079 Siemens unit
= 0.6654 ohm. The curve 8m, Fig. 6, gives the relation
of electromotive force and current, reduced to a speed of
700 revolutions per minute, the actual speeds ranging from
450 to 800 revolutions. The maximum electromotive
force appears to be probably 76 volts, and the critical
current 15 webers; which is the same as in the author's
first experiments on a similar machine.
In the summer of 1879 the author examined a Siemens
machine of the smallest size. This machine is generally
sold as an exciter* for their alternate current machine. It
has an internal resistance of 0.74 ohm, of which 0.395 is in
the armature or helix. The machine is marked to run at
1,130 revolutions per minute. The following Table II.
gives, for a speed of 1,000 revolutions, the total resistance,
current, electromotive force and horse power developed as
current. The horse power expended was not determined.
The curve S s, Fig. 6, gives as usual the relations olelec-
tromotive force and current. From this curve it will be seen
that the critical current is 11.2 webers, and the maximum
electromotive force, at the speed of 1,000 revolutions, is
30 DYNAMO MACHINERY AND ALLIED SUBJECTS.
TABLE II. EXPERIMENTS ON SMALLEST-SIZED SIEMENS DYNAMO-
ELECTRIC MACHINE.
Resistance.
Electric Current.
Electromotive
Force.
Horse Power Devel-
oped as Current.
2.634 ohms.
5.10 webers.
13.2 volts.
0.09H.P.
2 221
12.15
27.0
0.44
1.967
'
17.0
33.6
0.76
1.784
20.4
36.4
0.99
1.668
22.3
37.2
1.11
1.579
23.2
36.6
1.14
1.503
25.6
39.3
1.34
1.440
27.8
40.0
1.49 "
1.145
36.2 "
41.5
2.00 "
about 42 volts. The determinations for this machine were
made in exactly the same manner as in the experiments
on the medium sized machine, using the galvanometer, but
omitting the experiment with the calorimeter (compare
Table L, p. 21).
The time required to develop the current in a Gramme
machine has been examined by Herwig (Wiedemann, June,
1879). He established the following facts for the machine
he examined : A reversed current, having an electromotive
force of 0.9 Grove cell, sufficed to destroy the residual
magnetism of the electromagnets. If the residual mag-
netism was as far as possible reduced, it took a much longer
time to get up the current than when the machine was in
its usual state. A longer time was required to get up the
current when the external resistance was great than when
it was small. With ordinary resistance the current required
from f second to 1 second to attain its maximum.
Brightness of the Electric Arc. The measurement of
the light emitted by an electric arc presents certain peculiar
difficulties. The light itself is of a different color from
ON ELECTRIC LIGHTING. 31
that of a standard candle, in terms of which it is usual to
express luminous intensities. The statement, without
qualification, that a certain electric lamp and machine give
a light of a specified number of candles, is therefore want-
ing in definite meaning. A red light cannot with pro-
priety be said to be any particular multiple of a green
light; nor can one light which is a mixture of colors be
said with strictness to be a multiple of another, unless the
proportions of the colors in the two cases are the same.
Captain Abney (Proceedings of the Royal Society, March
7, 1878, p. 157) has given the results of measurements of
the red, blue, and actinic light of electric arcs in terms of
the red, blue, and actinic light of a standard candle. The
fact that the electric light is a very different mixture of
rays from the light of gas or of a candle has long been
known, but has been ignored in statements intended for
practical purposes.
Again, the emission of rays from the heated carbons and
arc is by no means the same in all directions. Determi-
nations have been made in Paris of the intensity in differ-
ent directions, in particular cases. If the measurement is
made in a horizontal direction, a very small obliquity in
the crater of the positive carbon will throw the light much
more on one side than on the other, causing great dis-
cordance in the results obtained.
If the electric light be compared directly with a stand-
ard candle, a dark chamber of great length is needed a
convenience not always attainable. In the experiments
made at the South Foreland by Dr. Tyndall and Mr.
Douglass, an intermediate standard was employed; the
electric light was measured in terms of a large oil lamp,
32 DYNAMO MACHINERY AND ALLIED SUBJECTS.
and this latter was frequently compared with a standard
candle.
Other engagements have prevented the author from
fairly attacking these difficulties; but since May, 1879, he
has had in occasional use a photometer with which power-
ful lights can be measured in .moderate space. This
photometer is shown in Figs. 7 and 8, and an enlargement
5T
rU
^Longitudinal Section
FIG. 7. PHOTOMETER FOR POWERFUL LIGHTS.
STANDARD
LIGHT
of the field piece in Fig. 9. A convex lens A, of short
focus, forms an image at B of the powerful source of
light which it is desired to examine. The intensity of
the light from this image will be less than that of the
actual source by a calculable amount; and when the dis-
tance of the lens from the light is suitable, the reduction
is such that the reduced light becomes
comparable with a candle or a carcel
lamp. Diaphragms C C are arranged
in the cell which contains the lens, to
cut off stray light. One of these is
placed at the focus of the lens, and has
a small aperture. It is easy to see that
this diaphragm will cut off all light
entering from a direction other than
" that of the source; so effectually does it
do so, that observations may be made in
broad daylight on any source of light, if a dark screen
ON ELECTRIC LIGHTING.
33
be placed behind it. The long box E E, Fig. 7, of
about 7 feet length, is lined with black velvet, the old-
fashioned dull velvet, not that now sold with a finish, which
reflects a great deal of the light incident at a certain angle.
This box serves as a dark chamber, in which the intensity
of the image formed by the lens is compared with a stand-
FIG. 9. FIELD PIECE.
ard light, by means of an ordinary Btmsen's photometer F,
sliding on a graduated bar.
Mr. Dallmeyer kindly had the lens made for the author:
he can therefore rely upon the accuracy of its curvature
and thickness; it is plano-convex, the convex side being
towards the source of light. The curvature is exactly 1
inch radius and the thickness is 0.04 inch; it is made of
Chance's hard crown glass, of which the refractive index for
the D line in the spectrum is 1.517. The focal length/ is
therefore 1.933 inches.
Let u denote the distance of the source of light from
84: DYNAMO MACHINERY AND ALLIED SUBJECTS.
the curved surface of the lens, and v the distance of the
image B of the source from the posterior focal plane.
Neglecting for the moment loss by reflection at the sur-
face of the glass, the intensity of the source is reduced by
the factor ( 1 But | = -r, or v hence the f ac-
W v u f u~f
i f Y
tor of reduction is I -- > The effect of absorption in so
\n fJ
small a thickness of very pure glass may be neglected ; but
the reflection at the surfaces will cause a loss of 8.3 per
cent., which must be allowed for. This percentage is
calculated from Fresners formulae, which are certainly
accurate for glasses of moderate refrangibility, and for
moderate angles of incidence.
Suppose, for example, it is required to measure a light of
8,000 candles; if it be placed at a distance of 40 inches, it
will be reduced in the ratio 467 to 1, and becomes a con-
veniently measurable quantity. By transmitting through
colored glasses both the light from an electric lamp and that
from the standard, a rough comparison may be made of
the red or green in the electric light with the red or green
in the standard.
A dispersive photometer, in which a lens is used in a
somewhat similar manner, is described in Stevenson's
"Lighthouse Illumination;" but in that case the lens is
not used in combination with a Bunsen photometer, nor
with any standard light. Messrs. Ayrton and Perry de-
scribed a dispersive photometer with a concave lens at the
meeting of the Physical Society on December 13, 1879
(Proceedings Physical Society, vol. III., p. 184J. The
convex lens possesses, however, an obvious advantage in
ON ELECTRIC LIGHTING. 35
having a real focus, at which a diaphragm to cut off stray
light may be placed.
Efficiency of the Electric Arc. To define the electrical
condition of an electric arc, two quantities must be stated
the current passing, and the difference of electric
potential at the ends of the two carbons. Instead of
either one of these, we may, if we please, state the ratio
difference of potential d ^ it ^ resistance of the arc>
current
that is to say, the resistance which would replace the arc
without changing the current. But such a use of the term
electric resistance is unscientific; for Ohm's law, on which
the definition of electric resistance -rests, is quite untrue of
the electric arc; while on the other hand, for a given ma-
terial of the electrodes, a given distance between them,
and a given atmospheric pressure, the difference of poten-
tial on the two sides of the arc is approximately constant.
The product of the difference of potential and the current
is of course equal to the work developed in the arc; and
this, divided by the work expended in driving the ma-
chine, may be considered as the efficiency of the whole
combination. It is a very easy matter to measure these
quantities. The difference of potential on the two sides of
the arc may be measured by the method given by the
author in his previous paper, or by an electrometer, or in
other ways. The current may be measured by an Obach
galvanometer, or by a suitable electro-dynamometer, or
best of all, in the author's opinion, by passing the whole
current, on its way to the arc, through a very small known
resistance, which may be regarded as a shunt for a galva-
36 DYNAMO MACHINERY AND ALLIED SUBJECTS.
nometer of very high resistance, or to the circuit of which
a very high resistance has been added.
It appears that with the ordinary carbons, and at ordi-
nary atmospheric pressure, no arc can exist with a less
difference of potential than about 20 volts; and that in
ordinary work, with an arc about i inch long, the differ-
ence of potential is from 30 to 50 volts. Assuming the
former result, about 20 volts, for the difference of poten-
tial, the use of the curve of electromotive forces may be
illustrated by determining the lowest speed at which a
given machine can run and yet be capable of producing a
short arc. Taking as the origin of co-ordinates, Fig.
10, set off upon the axis of ordinates the distance A
Fio. 10.
equal to 20 volts ; draw A B to intersect at B the negative
prolongation of the axis of abscissae, so that the ratio -^=
may represent the necessary metallic resistance of the cir-
cuit. Through .the point B, thus obtained, draw a tangent
to the curve, touching it at C, and cutting A in D.
Then the speed of the machine, corresponding to the par-
ticular curve employed, must be diminished in the ratio
ON ELECTRIC LIGHTING.
37
-- , in order that an exceedingly small arc may be just
possible.
The curve may also be employed to put into a somewhat
different form the explanation given by Dr. Siemens, at
the Koyal Society, respecting the occasional instability of
the electric light as produced by ordinary dynamo-electric
machines. The operation of all ordinary regulators is to
part the carbons when the current is greater than a cer-
tain amount, and to close them when it is less; initially
the carbons are in contact. Through the origin 0, Fig.
11, draw the straight line OA, inclined at the angle repre-
senting the resistances of the circuit other than the arc,
and meeting the curve at A. The abscissa of the point A
represents the current which will pass if the lamp be pre-
vented from operating. Let N represent the current to
which the lamp is adjusted; then if the abscissa of A be
greater than N, the carbons will part. Through N draw
the ordinate B N 9 meeting the curve in the point B; and
parallel to A draw a tangent CD, touching the curve at D.
If the point B is to the right of D, or further from the
38 DYNAMO MACHINERY AND ALLIED SUBJECTS.
origin, the arc will persist; but if B is to the left of D, or
nearer to the origin, the carbons will go on parting, till
the current suddenly fails and the light goes out. If B,
although to the right of D, is very near to it, a very small
reduction in the speed of the machine will suffice to ex-
tinguish the light. Dr. Siemens gives greater stability to
the light by exciting the electromagnets of the machine
by a shunt circuit, instead of by the whole current.
The success of burning more than one regulating lamp
in series depends on the use in the regulator of an electro-
magnet excited by a high resistance wire connecting the
two opposed carbons. The force of this magnet will de-
pend upon the difference of potential in the arc, instead
of depending, as in the ordinary lamp, upon the current
passing. Such a shunt magnet has been employed in a
variety of ways. The author has arranged it as an attach-
ment to an ordinary regulator; the shunt magnet actuates
a key, which short circuits the magnet of the lamp when
the carbons are too far parted, and so causes them to close.
In conclusion the author ventures to remind engineers
of the following rule for determining the efficiency of any
system of electric lighting in which the electric arc is
used, the arc being neither exceptionally long nor excep-
tionally short: Measure the difference of potential of the
arc, and also the current passing through it, in volts and
webers respectively; then the product of these quantities,
divided * by 746, is the horse power developed in that arc.
* With respect to the factor 746, given above, the product of difference of poten-
tial and current was power, which could of course be given as so many foot-
pounds per minute; but the number that was got by multiplying webers and volts
together did not give the power in foot pounds, audit required a factor to reduce
ON ELECTRIC LIGHTING. 39
It is then known that the difference between the horse
power developed in the arc and the horse power expended
to drive the machine must be absolutely wasted, and has
been expended in heating either the iron of the machine or
the copper conducting wires.
the one to the oth r, just as it required a factor to reduce gramme-centimetres,
or any other measure of power, to foot-pounds. The factor in this case hap-
pened to be 740, as would be seen by referring to Everett, "Units and Physical
Constants." The product of a weber and a volt was 10 7 ergs per second (p. 138),
while a horse power was 7.46 x 10 9 = 740 X 10 7 ergs per second (p. 5J5); hence the
rule given.
40 DYNAMO MACHINERY AND ALLIED SUBJECTS.
SOME POINTS IN ELECTRIC LIGHTING.
ARTIFICIAL light is generally produced by raising some
body to a high temperature. If the temperature of a body
be greater than that of surrounding bodies it parts with
some of its energy in the form of radiation. While the
temperature is low these radiations are not of a kind to
which the eye is sensitive; they are exclusively radiations
less refrangible and of greater wave length than red light,
and may be called infra red. As the temperature is in-
creased the infra red radiations increase, but presently
there are added radiations which the eye perceives as red
light. As the temperature is further increased, the red
light increases, and yellow, green and blue rays are succes-
sively thrown off in addition. On pushing the temperature
to a still higher point, radiations of a wave length shorter
even than violet light are produced, to which the eye is
insensitive, but which act strongly on certain chemical
substances; these may be called ultra violet rays. It is
thus seen that a very hot body in general throws out rays
of various wave lengths, our eyes, it so happens, being only
sensitive to certain of these, viz., those not very long and
not very short, and that the hotter the body the more of
every kind of radiation will it throw out ; but the propor-
tion of short waves to long waves becomes vastly greater as
the temperature is increased, The problem of the artificial
SOME POINTS IN ELECTRIC LIGHTING. 41
production of light with economy of energy is the same as
that of raising some body to such a temperature that it
shall give as large a proportion as possible of those rays
which the eye happens to be capable of feeling. For prac-
tical purposes this temperature is the highest temperature
we can produce. Owing to the high temperature at
which it remains solid, and to its great emissive power, the
radiant body used for artificial illumination is nearly always
some form of carbon. In the electric current we have an
agent whereby we can convert more energy of other forms
into heat in a small space than in any other way; and
fortunately carbon is a conductor of electricity as well as a
very refractory substance.
The science of lighting by electricity very naturally
divides itself into two principal parts the methods of
production of electric currents, and of conversion of the
energy of those currents into heat at such a temperature
as to be given oif in radiations to which our eyes are sensi-
ble. There are other subordinate branches of the subject,
such as the consideration of the conductors through which
the electric energy is transmitted, and the measurement of
the quantity of electricity passing and its potential or elec-
tric pressure. Although I shall have a word or two to say on
the other branches of the subject, I propose to occupy most
of the time at my disposal this evening with certain points
concerning the conversion of mechanical energy into elec-
trical energy. We know nothing as to what electricity is,
and its appeals to our senses are in general less direct than
those of the mechanical phenomena of matter. The laws,
however, which we know to connect together those phe-
nomena which we call electrical are essentially mechanical
42 DYNAMO MACHINEKY AND ALLIED SUBJECTS.
in form, are closely correlated with mechanical laws, and
may be most aptly illustrated by mechanical analogues.
For example, the terms " potential/' " current " and " re-
sistance/' with which we are becoming familiar in electric-
ity, have close analogues respectively in "head," "rate of
flow" and "coefficient of friction" in the hydraulic trans-
mission of power. Exactly as in hydraulics head multi-
plied by velocity of flow is power measured in foot-pounds
per second or in horse power, so potential multiplied by
current is power and is measurable in the same units. The
horse power not being a convenient elec-
trical unit, Dr. Siemens has suggested that
the electrical unit of power or volt-ampere
should be called a watt : 746 watts are equal
to one horse power. Again, just as water
flowing in a pipe has inertia and requires an
expenditure of work to set it in motion, and
is capable of producing disruptive effects if
its motion is too suddenly arrested, as, for
example, when a plug tap is suddenly closed
in a pipe through which water is flowing
rapidly, so a current of electricity in a wire
has inertia; to set it moving electromotive
force must work for a finite time, and if we
r in iiiiiiim attempt to arrest it suddenly by breaking the
1 circuit, the electricity forces its way across
the interval as a spark. Corresponding to
mass and moments of inertia in mechanics
FIG. 12. we have in electricity coefficients of self
induction. We will now show that an
electric circuit behaves as though it had inertia. The ap-
SOME POINTS IN ELECTRIC LIGHTING.
43
paratus we shall use is shown diagrammatically in Fig. 12.
A current from a Sellon battery A circulates round an
electromagnet Z?/ it can be made and broken at pleasure
at C. Connected to the two extremities of the wire on the
FIG. 13.
magnet is a small incandescent lamp D, lent to me by Mr.
Crompton, of many times the resistance of the coil. On
breaking the circuit, the current in the coil, in virtue of its
momentum, forces its way through the lamp, and renders
it momentarily incandescent, although all connection with
the battery, which in any case would be too feeble to send
sufficient current through the lamp, has ceased. Let us.
try the experiment, make contact, break contact. You
44 DYNAMO MACHINERY AND ALLIED SUBJECTS.
observe the lamp lights up. Compare with the diagram
(Fig. 13) ^of the hydraulic analogue, the hydraulic ram.
There a current of water suddenly arrested forces a way
for a portion of its quantity to a greater height than that
from which it fell. A B corresponds to the electromag-
net, the valve C to the contact breaker, and D E to the
lamp. There is, however, this difference between the in-
ertia of water in a pipe and the inertia of an electric cur-
rent : the inertia of the water is confined to the water,
whereas the inertia of the electric current resides in the
surrounding medium. Hence arise the phenomena of in-
duction of currents upon currents, and of magnets upon
moving conductors phenomena which have no immediate
analogues in hydraulics. There is thus little difficulty to
any one accustomed to the laws of rational mechanics in
adapting the expression of those laws to fit electrical
phenomena; indeed we may go so far as to say that the
part of electrical science with which we have to deal this
evening is essentially a branch of mechanics, and as such
I shall endeavor to treat it.
This is neither the time nor the place for setting forth
the fundamental laws of electricity, but I cannot forbear
from showing you a mechanical illustration, or set of
mechanical illustrations, of the laws of electrical induction,
first discovered by Faraday. I have here a model, Fig. 14,
which was made to the instructions of the late Professor
Clerk Maxwell, to illustrate the laws of induction. It
consists of a pulley P, which I now turn with my hand,
and which represents one electric circuit, its motion the
current therein. Here is a second pulley, S, representing
a second electric circuit. These two pulleys are geared
SOME POINTS IN ELECTBIC LIGHTING. 45
FIGK 14,
46 DYNAMO MACHINERY AND ALLIED SUBJECTS.
together by a simple differential train, such as is some-
times used for a dynamometer. The intermediate wheel
of the train, however, is attached to a balanced flywheel,
the moment of inertia of which can be varied by moving
inwards or outwards these four brass weights. The resist-
ances of the two electric circuits are represented by the
friction on the pulleys of two strings, the tension of which
can be varied by tightening these elastic bands. The dif-
ferential train, with its flywheel, represents the medium,
whatever it may be, between the two electric conductors.
The mechanical properties of this me del are of course
obvious enough. Although the mathematical equations
which represent the relation between one electric conduct-
or and another in its neighborhood are the same in form
as the mathematical equations which represent the mechan-
ical connection between these two pulleys, it must not be as-
sumed that the magnetic mechanism is completely repre-
sented by the model. We shall now see how the model
illustrates the action of one electric circuit upon another.
You know that Faraday discovered that if you have two
closed conductors arranged near to and parallel to each
other, and if you cause a current of electricity to begin to
flow in the first, there will arise a temporary current in the
opposite direction in the second. This pulley, marked P
on the diagram, represents the primary circuit, and the
pulley marked 8 on the diagram the secondary circuit.
We cause a current to begin to flow in the primary, or turn
the pulley P; an opposite current is induced in the sec-
ondary circuit, or the pulley 8 turns in the opposite
direction to that in which we began to move the pulley P.
The effect is only temporary; resistance speedily stops the
SOME POINTS IN ELECTRIC LIGHTING. 47
current in the secondary circuit, or, in the mechanical
model, friction the rotation of the pulley S. I now grad-
ually stop the motion of P; the pulley S moves in the
direction in which P was previously moving, just as Far-
aday found that the cessation of the primary current in-
duced in the secondary circuit a current in the same direc-
tion as that which had existed in the primary. If there
were a large number of convolutions or coils in the second-
ary circuit, but that circuit were not completed, but had
an air space interrupting its continuity, an experiment
with the well known Kuhmkorff coil would show you that
when the current was suddenly made to cease to flow in
the primary circuit, so great 'an electromotive force would
be exerted in the secondary circuit that the electricity
would leap across the space as a spark. I will now show
you what corresponds to a spark with this mechanical
model. The secondary pulley S shall be held by passing a
thread several times round it. I gradually produce the
current in the primary circuit. I will now suddenly stop
this primary current: you observe that the electromotive
force is sufficient to break the thread. The inductive
effects of one electric circuit upon another depend not
alone on the dimensions and form of the two circuits, but
on the nature of the material between them. For example,
if we had two parallel circular coils, their inductive effects
would be very considerably enhanced by introducing a bar
of iron in their common axis. We can imitate this effect
by moving outwards or inwards these brass weights. In
the experiment I have shown you the weights have been
some distance from the axis in order to obtain considerable
effect, just as in the Ruhmkorff coil an iron core is intro-
48 DYNAMO MACHINERY A.ND ALLIED SUBJECTS.
duced within the primary circuit. I will now do what is
equivalent to removing the core : I will bring the weights
nearer to the axis, so that my flywheel shall have less
moment of inertia. You observe that the inductive effects
are very much less marked than they were before. With
the same electromagnet which we used before, but differ-
ently arranged, we will show what we have
just illustrated the induction of one
circuit on another. Referring to Fig. 15,
coil A B corresponds to wheel P ; C D to
wheel 8, and the iron core to the fly-
wheel and differential gear. The resist-
ance of a lamp takes the place of the
friction of the string on S. As we make
and break the circuit you see the effect
of the induced current in rendering the
lamp incandescent. So far I have been
illustrating the phenomena of the induc-
tion of one current upon another. I will
now show on the model that a current
in a single electric circuit has momen-
tum. The secondary wheel shall be
firmly held ; it shall have no conductivity
at all that is, its electrical effect shall
be as though it were not there. I now
cause a current to begin to flow in the primary circuit,
and it is obvious enough that a certain amount of work
must be done to bring it up to a certain speed. The an-
gular velocity of the flywheel is half that of the pulley
representing the primary circuit. Now suppose that the
two pulleys were connected together in such a way that
FIG. 15.
SOME POINTS IN ELECTRIC LIGHTING.
49
they must have the same angular velocity in the same
direction. This represents the coil having twice as many
convolutions as it had before. A little
consideration will show that I must do
four times as much work to give the
primary pulley the same velocity that
it attained before; that is to say, that
the coefficient of self induction of a coil
of wire is proportional to the square of
the number of convolutions. Again,
suppose that these two wheels were so
geared together that they must always
have equal and opposite velocities, you
can see that a very small amount of
work must be done in order to give the
primary wheel the velocity which we
gave to it before. Such an arrangement
of the model represents an electric cir-
cuit, the coefficient of induction of which
is exceedingly small, such as the coils
that are wound for standard resistances;
the wire is there wound double, and
the current returns upon itself, as shown
in Fig. 16.
In the widest sense, the dynamo-electric machine may
be defined as an apparatus for converting mechanical
energy into the energy of electrostatic charge, or mechan-
ical power into its equivalent electric current through a
conductor. Under this definition would be included the
electrophorus and all f rictional machines ; but the term is
used, in a more restricted sense, for those machines which
FIG. 16.
50 DYtfAMO MACHINEHY AND ALLIED SUBJECTS.
produce electric currents by the motion of conductors in a
magnetic field, or by the motion of a magnetic field in the
neighborhood of a conductor. The laws on which the
action of such machines is based have been the subject of
a series of discoveries. Oersted discovered that an electric
current in a conductor exerted force upon a magnet;
Ampere that two conductors conveying currents generally
exerted a mechanical force upon each other. Faraday dis-
covered what Helmholtz and Thomson subsequently
proved to be the necessary consequence of the mechanical
reactions between conductors conveying currents and mag-
nets that if a closed conductor move in a magnetic field,
there will be a current induced in that conductor in one
direction if the number of lines of magnetic force passing
through the conductor was increased by the movement; in
the other direction if diminished. Now all dynamo-electric
machines are based upon Faraday's discovery. Not only
so ; but however elaborate we may wish to make the analysis
of the action of a dynamo machine, Faraday's way of pre-
senting the phenomena of electromagnetism to the mind
is in general our best point of departure. The dynamo
machine, then, essentially consists of a conductor made to
move in a magnetic field. This conductor, with the exter-
nal circuit, forms a closed circuit in which electric currents
are induced as the number of lines of magnetic force pass-
ing through the closed circuit varies. Since, then, if the
current in a closed circuit be in one direction when the
number of lines of force is increasing, and in the opposite
direction when they are diminishing, it is clear that the
current in each part of such circuit which passes through
the magnetic field must be alternating in direction, unless,
SOME POINTS IN ELECTRIC LIGHTING. 51
indeed, the circuit be such that it is continually cutting
more and more lines of force, always in the same direction.
Since the current in the wire of the machine is alternating,
so also must be the current outside the machine, unless
something in the nature of a commutator be employed to
reverse the connections of the internal wires in which the
current is induced, and of the external circuit. We have,
then, broadly, two classes of dynamo-electric machines
the simplest, the alternating current machine, where no
commutator is used; and the continuous current machine,
in which a commutator is used to change the connection
of the external circuit just at the moment when the direc-
tion of the current would change. The mathematical
theory of the alternate current machine is comparatively
simple. To fix ideas, I will ask you to think of the alter-
nate current Siemens machine, which Dr. Siemens exhibited
here three weeks ago. We have there a series of magnetic
fields of alternate polarity, and through these fields we
have coils of wire moving; these coils constitute what is
called the armature; in them are induced the currents
which give a useful effect outside the machine. Now I
am not going to trouble you to go through the mathematical
equations, simple though they are, by which the following
formulae are obtained:
n t /T ,
r (I.)
2 n A 2 Ttt
E= --cos- (II.)
52 DYNAMO MACHINERY AND ALLIED
= (in.)
(IV.)
(VL)
T represents the periodic time of the machine ; that is, in
the case of a Siemens machine having eight magnets on
each side of the armature, T represents the time of one-
fourth of a revolution. / represents the number of lines
of force embraced by the coils of the armature at the time
t. I must be a periodic function of /, in the simplest form
represented by Equation I. Equation II. gives E the elec-
tromotive force acting at time / upon the circuit. Having
given the electromotive force acting at any time, it would
appear at first sight that we had nothing to do but to
divide that electromotive force by the resistance R of the
whole circuit, to obtain the current flowing at that time.
But if we were to do so we should be landed in error, for
the conducting circuit has other properties besides resist-
ance. I pointed out to you that it had a property of mo-
mentum represented by its coefficient of self induction,
LIGHTING.
53
with
it |iijii at important a part as
DI. gives die
wiD obeerre that it
Hlesstkanitwoaldbeif
byfte
br Foonia IV.
of deefetical work
--;,-_:_, ::::_.: : -^
54 DYNAMO "MACHINERY AND ALLIED SUBJECTS.
In some cases this phenomenon is so marked that the
machine actually takes more to drive it, when the machine
is on open circuit, than when it is short circuited. The ex-
planation is that on open circuit currents are induced in
the iron cores, but that when the copper coils are closed
the current in them diminishes by induction the current in
the iron. The effect of currents in the iron cores is not
alone to waste eiwrgy and heat the machine; but for a
given intensity of field and speed of revolution the exter-
nal current produced is diminished. The cure of the evil
is to subdivide the moving iron as much as possible, in di-
rections perpendicular to those in which the current tends
to circulate.
There remains one point of great practical interest in
connection with alternate current machines: How will
they behave when two or more are coupled together to aid
each other in doing the same work ? With galvanic bat-
teries we know very well how to couple them, either in
parallel circuit or in series, so that they shall aid, and not
oppose, the effects of each other; but with alternate cur-
rent machines, independently driven, it is not quite obvi-
ous what the result will be, for the polarity of each
machine is constantly changing. Will two machines,
coupled together, run independently of each other, or will
one control the movement of the other in such wise
that they settle down to conspire to produce the same
effect, or will it be into mutual opposition ? It is obvious
that a great deal turns upon the answer to this question,
for in the general distribution of electric light it will be
desirable to be able to supply the system of conductors
from which the consumers draw by separate machines,
SOME POINTS IN ELECTRIC LIGHTING. OO
which can be thrown in and out at pleasure. Now I know
it is a common impression that alternate current machines
cannot be worked together, and that it is almost a necessity
to have one enormous machine to supply all the consumers
drawing from one system of conductors. Let us see how
the matter stands. Consider two machines independently
driven, so as to have approximately the same periodic time
FIG. 17.
and the same electromotive force. If these two machines
are to be worked together, they may be connected in one
of two ways : they may be in parallel circuit with regard to
the external conductor, as shown by the full line in Fig. 1 7,
that is, their currents may be added algebraically and sent
to the external circuit, or they may be coupled in series, as
shown by the dotted line, that is, the whole current may
pass successively through the two machines, and the
electromotive force of the two machines may be added ?
56 DYNAMO MACHINERY AND ALLIED SUBJECTS.
instead of their currents. The latter case is simpler. Let
us consider it first. I am going to show that if you couple
two such alternate current machines in series they will so
control each other's phase as to nullify each other, and
that you will get no effect from them ; and, as a corollary
from that, I am going to show that if you couple them in
parallel circuit they will work perfectly well together, and
the currents they produce will be added; in fact, that you
cannot drive alternate current machines tandem, but that
you may drive them as a pair, or, indeed, any number
abreast. In diagram, Fig. 18, the horizontal line of ab-
1JIL11IV
scissae represents the time advancing from left to right;
the full curves represent the electromotive forces of the
two machines not supposed to be in the same phase. We
want to see whether they will tend to get into the same
phase or to get into opposite phases. Now, if the machines
are coupled in series, the resultant electromotive force
on the circuit will be the sum of the electromotive
forces of the two machines. This resultant electromotive
force is represented by the broken curve III. By what we
have already seen in Formula IV., the phase of the cur-
SOME POINTS IN ELECTRIC LIGHTING. 57
reut must lag behind the phase of the electromotive force,
as is shown in the diagram by curve 7F, thus . .
. Now the work done in any machine is represented
by the sum of the products of the currents and of the
electromotive forces, and it is clear that, as the phase of
the current is more near to the phase of the lagging
machine // than to that of the leading machine /, the lag-
ging machine must do more work in producing electricity
than the leading machine; consequently its velocity
will be retarded, and its retardation will go on until the
two machines settle down into exactly opposite phases,
when no current will pass. The moral, therefore, is, do
not attempt to couple two independently driven alternate
current machines in series. Now for the corollary: A, B,
Fig. 17, represent the two terminals of an alternate cur-
rent machine; , b the two terminals of another machine
independently driven. A and a are connected together,
and B and b. So regarded, the two machines are in
series, and we have just proved that they will exactly
oppose each other's effects, that is, when A is positive, a
will be positive also; when A is negative, a is also nega-
tive. Now, connecting A and a through the compara-
tively high resistance of the external circuit with B and b, the
current passing through that circuit will not much disturb,
if at all, the relations of the two machines. Hence, when
A is positive, a will be positive, and when A is negative, a
will be negative also; precisely the condition required that
the two machines may work together to send a current into
the external circuit. You may, therefore, with confi-
dence, attempt to run alternate current machines in
parallel circuit for the purpose of producing any external
58 DYNAMO MACHINERY AND ALLIED SUBJECTS.
effect. I might easily show that the same applies to a
larger number; hence there ic no more difficulty in feed-
ing a system of conductors from a number of alternate cur-
rent machines than there is in feeding it from a number
of continuous current machines. A little care is only re-
quired that the machine shall be thrown in when it has
attained something like its proper velocity. A further
corollary is that alternate currents with alternate current
machines as motors may theoretically be used for the trans-
mission of power.*
It is easy to see that, by introducing a commutator re-
volving with the armature, in an alternate current machine,
and so arranged as to reverse the connection between the
armature and the external circuit just at the time when
the current would reverse, it is possible to obtain a cur-
rent constant always in direction; but such a current
would be far from constant in intensity, and would cer-
tainly not accomplish all the results that are obtained in
modern continuous current machines. This irregularity
may, however, be reduced to any extent by multiplying
the wires of the armature, giving eacli its own connection
to the outer circuit, and so placing them that the electro-
motive force attains a maximum successively in the several
coils. A practically uniform electric current was first com-
mercially produced with the ring armature of Pacinotti,
as perfected by Gramme. The Gramme machine is repre-
sented diagram matically in Fig. 19. The armature consists
*Of course in applying these conclusions it is necessary to remember that
the machines only tend to control each other, and that the control of the
motive power may be predominant, and compel th two or more machines to
run at different speeds.
SOME POINTS IN ELECTRIC LIGHTING.
59
of an anchor ring of iron wire, the strands more or less
insulated from each other. Round this anchor ring is
wound a continuous endless coil
of copper wire; the armature
moves in a magnetic field, pro-
duced by permanent or electro-
magnets with diametrically oppo-
site poles, marked N and S. The
lines of magnetic force may be
regarded as passing into the ring
from N, dividing, passing round
the ring and across to S. Thus
the coils of wire, both near to N
and near to S, are cutting through
a very strong magnetic field; con-
sequently there will be an intense
inductive action. The inductive
action of the coils near JV being
equal and opposite to the induc-
tive action of the coils near S,
it results that there will be strong
positive and negative electric po-
tential at the extremities of a
diameter perpendicular to the line
NS. The electromotive force pro-
duced is made use of to produce a
current external to the machine; thus the endless coil of
the armature is divided into any number of sections, in the
diagram into six for convenience, usually into sixty or
eighty, and the junction of each pair of sections is con-
nected by a wire to a plate of the commutator fixed upon
FIG. 19.
60 DYNAMO MACHINERY AND ALLIED SUBJECTS.
the shaft which carries the armature; collecting brushes
make contact with the commutator, as shown in the
diagram. If the external resistance were enormously
high, so that very little current, or none at all, passed
through the armature, the greatest difference of potential
between the two brushes would be found when they made
contact at points at right angles to the line between the
magnets; but when a current passes in the armature, this
current causes a disturbing effect upon the magnetic field.
Every time the contact of the brushes changes from one
contact plate to the next, the current in a section of the
copper coil is reversed, and this reversal has an inductive
effect upon all the other coils of the armature. You may
take it from me that the net result on any one coil is approxi-
mately the same as if that coil alone were moved, and all
the other coils were fixed, and there were no reversals of
current in them. Now you can easily see that the mag-
netic effect of the current circulating in the coils of
the armature will be to produce a north pole at n
and a south pole at s. This will displace the magnetic
field in the direction of rotation. If, then, we were to
keep the contact points the same as when no current was
passing, we should short circuit the sections of the arma-
ture at a time when they were cutting through the lines
of magnetic force, with a result that there would be vigor-
ous sparks between the collecting brushes and the com-
mutator. To avoid this, the brushes must follow the
magnetic field, and also be displaced in the direction of
rotation, this displacement being greater as the current in
the armature is greater in proportion to the magnetic field.
The net effect of this disturbing effect of the current in.
SOME POINTS IN ELECTRIC LIGHTING. 61
the armature reacting upon itself is, then, to displace the
neutral points upon the commutator, and consequently
somewhat to diminish the effective electromotive force.
It is best to adjust the brushes to make contact at a point
such that, with the current then passing, flashing is re-
duced to a minimum; but this point does not necessarily
coincide with the point which gives maximum difference
of potential. The magnetic field' in the Gramme and
other continuous dynamo-electric machines may be pro-
duced in several ways. Permanent magnets of steel may be
used, as in some of the smaller machines now made, and in
all the earlier machines; these are frequently called mag-
neto machines. Electromagnets excited by a current
from a small dynamo-electric machine were introduced
by Wilde; these may be described shortly as dynamos
with separate exciters. The plan of using the whole
current from the armature of the machine itself, for
exciting the magnets, was proposed almost simultaneously
by Siemens, Wheatstone, and S. A. Varley. A dynamo
so excited is now called a series dynamo. Another method
is to divide the current from the armature, sending the
greater part into the external circuit, and a smaller por-
tion through the electromagnet, which is then of very
much higher resistance. Such an arrangement is called a
shunt dynamo. A combination of the last two methods
has been recently introduced, for the purpose of main-
taining constant potential. The magnet is partly ex-
cited by a circuit of high resistance, a shunt to the
external circuit, and partly by coils conveying the
whole current from the armature. All but the first
two arrangements named depend on residual magnetism
62 DYNAMO MACHINERY AND ALLIED SUBJECTS.
to initiate the current, and below a certain speed of rotation
give no practically useful electromotive force. A dynamo
machine is, of course, not a perfect instrument for converting
mechanical energy into the energy of electric current. Cer-
tain losses inevitably occur. There is, of course, the loss
due to friction of bearings, and of the collecting brushes
upon the commutator; there is also the loss due to the
production of electric currents in the iron of the machine.
When these are accounted for, we have the actual electrical
effect of the machine in the conducting wire; but all of
this is not available for external work. The current has to
circulate through the armature, which inevitably has elec-
trical resistance; electrical energy must, therefore, be con-
verted into heat in the armature of the machine. Energy
must also be expended in the wire of the electromagnet
which produces the field, for the resistance of this also cannot
be reduced beyond a certain limit. The loss by the resistance
of the wires of the armature and of the magnets greatly
depends on the dimensions of the machine. About this
I shall have to say a word or two presently. To know the
properties of any machine thoroughly, it is not enough to
know its efficiency and the amount of work it is capable
of doing; wo need to know what it will do under all cir-
cumstances of varying resistance or varying electromotive
force. We must know, under any given conditions, what
will be the electromotive force of the armature. Now this
electromotive force depends on the intensity of the mag-
netic field, and the intensity of the magnetic field depends
on the current passing round the electromagnet and the
current in the armature. The current, then, in the machine
is the proper independent variable in terms of which to
SOME POINTS IN ELECTRIC LIGHTING. 63
express the electromotive force. The simplest case is that
of the series dynamo, in which the current in the electro-
magnet and in the armature is the same, for then we have
only one independent variable. The relation between the
electromotive force and current is represented by such a
curve as is shown in the diagram, Fig. 20. The abscissae,
Fio. 20.
measured along X, represent the current, and the ordi-
nates represent the* electromotive force in the armature.
When four years ago I first used this curve, for the pur-
pose of expressing the results of my experiments on the
Siemens dynamo machine, I pointed out that it was capable
of solving almost any problem relating to a particular
machine, and that it was also capable of giving good indi-
cations of the results of changes in the winding of the
magnets or of the armatures of such machines. Since then
M. Marcel Deprez has happily named such curves " char-
64 DYNAMO MACHINERY AND ALLIED SUBJECTS.
acteristic curves." I will give you one or two illustrations
of their use. A complete characteristic of a series dynamo
does not terminate at the origin, but has a negative branch,
as shown in the diagram ; for it is clear that by reversing
the current through the whole machine the electromotive
force is also reversed. Suppose a series dynamo is used for
charging an accumulator, and is driven at a given speed,
what current will pass through it ? The problem is easily
solved. Along Y, Fig. 20, set off E to represent the
electromotive force of the accumulator, and through ^draw
the line C E B A, making an angle with X, such that its
tangent is equal to the resistance of the whole circuit, and
cutting the characteristic curve, as it in general will do, in
three points, A, B, and C. We have, then, three answers to
the question. The current passing through the dynamo
will be either L, M, or N t the abscissae of the points
where the line cuts the curve. L represents the current
when the dynamo is actually charging the accumulator.
M represents a current which could exist for an instant,
but which would be unstable, for the least variation would
tend to increase. N is the current which passes if the
current in the dynamo should get reversed, as it is very
apt to do when used for this purpose. THie next illustration
is rather outside my subject, but shows another method of
using the characteristic curve. Many of you have heard of
Jacobi's law of maximum effect of transmitting work by
dynamo machines. It is this: Supposing that the two
dynamo machines were perfect instruments for converting
mechanical energy into electrical energy, and that the gen-
erating machine were run at constant velocity, while the
receiving machine had a variable velocity, the greatest
SOME POINTS IN ELECTRIC LIGHTING.
65
amount of work would be developed in the receiving
machine when its electromotive force was one-half that of
the generating machine; then the efficiency would be one-
half, and the electrical work done by the generating machine
would be just one-half of what it would be if the receiving
machine were forcibly held at rest. Now this law is strictly
true if, and only if, the electromotive force of the generat-
ing machine is independent of the current passing through
its armature. What I am now going to do is to give you a
construction for determining the maximum work which
can be transmitted when the electromotive force of the
generating machine depends on the current passing through
the armature, as, indeed, it nearly always does. Referring to
Fig. 21, PB is the characteristic curve of the generating
machine. Construct a derived curve thus: at successive
66 DYNAMO MACHINERY ANt> ALLIED
points P of the characteristic curve draw tangents P T;
draw T N parallel to X, cutting P j^in N; produce M P
to L, making L P equal P N; the point L gives the derived
curve, which I want. Now, to find the maximum work
which can be transmitted, draw A at such an angle with
X that its tangent is equal to twice the resistance of the
whole circuit, cutting the derived curve in A. Draw the
ordinate A C, cutting the characteristic curve in B; bisect
A (7 at D. The work expended upon the generating machine
would be represented by the parallelogram C B R, the
work wasted in resistance by CD S, and the work de-
veloped in the receiving machine by the parallelogram
SDBR.
When the dynamo machine is not a series dynamo, but
the currents in the armature and in the electromagnet,
though possibly dependent upon each other, are not nece.s-
sarily equal, the problem is not quite so simple. We have,
then, two variables, the current in the electromagnet and
the current in the armature; and the proper representation
of the properties of the machine will be by a characteristic
surface such as that illustrated by this model, Fig. 22. Of
the three co-ordinate axes, X represents the current in
the magnet, Y represents the current in the armature,
not necessarily to the same scale, and Z the electromo-
tive force. By the aid of such a surface as this, one may
deal with any problem relating to a dynamo machine, no
matter how its electromagnets and its armature are con-
nected together. Let us apply the model to find the
characteristic of a series dynamo. Take a plane through
Z y the axis of electromotive force, and making such an
angle with the plane X, Z that its tangent is equal to
SOME POINTS IN ELECTRIC LIGHTING.
67
current unity on axis Y, divided by current unity on
axis X. This plane cuts the surface in a curve. The
projection of this curve on the plane OX, OZ is the
characteristic curve of the series dynamo. This model only
shows an eighth part of the complete surface. If any of
you should interest yourselves about the other seven parts,
which are not without interest, remember that it is assumed
FIG. 22.
that the brushes always make contact with the commu-
tator at the point of no flashing, if there is one. Of course
in actual practice one would not use the model of the
surface, but the projections of its sections. While I am
speaking of characteristic curves there is one point I will
just take this opportunity of mentioning. Three years ago
Mr. Shoolbred exhibited the characteristic curve of a
Gramme machine, in which, after the current attained to a
68 DYNAMO MACHINERY AND ALLIED SUBJECTS.
certain amount, the electromotive force began to fall. I
then said that I thought there must be some mistake in the
experiment. However, subsequent experiments have veri-
fied the fact; and when one considers it, it is not very
difficult to see the explanation. It lies in this : after the
current attains to a certain amount the iron in the machines
becomes magnetically nearly saturated, and consequently
an increase in the current does not produce a correspond-
ing increase in the magnetic field. The reaction, however,
between the different sections of the wire on the armature
goes on increasing indefinitely, and its effect is to diminish
the electromotive force.
A little while ago I said that the dimensions of the
machine had a good deal to do with its efficiency. Let us
see how the properties of a machine depend upon its dimen-
sions. Suppose two machines alike in every particular ex-
cepting that the one has all its linear dimensions double
those of the other; obviously enough all the surfaces in the
larger would be four times the corresponding surfaces in
the smaller, and the weights and volumes of the larger
would be eight times the corresponding weights in the
smaller machine. The electrical resistances in the larger
machine would be one-half those of the smaller. The cur-
rent required to produce a given intensity of magnetic field
would be twice as great in the larger machine as in the
smaller. In the diagram (Fig. 23) are shown the compara-
tive characteristic curves of the two machines, when driven
at the same speed. You will observe that one curve
is the projection of the other, having corresponding
points with abscissae in the ratio of one to two, and the
ordinates in the ratio of one to four. Now at first sight it
SOME POINTS IN ELECTRIC LIGHTING.
69
would seem as though, since the wire on the magnet and
armature of the larger machine has four times the section
of that of the smaller, four times the current could be
carried, that consequently the intensity of the magnetic
field would be twice as great and its area would be four
times as great, and hence the electromotive force eight
times as great; and, since the current in the armature also
is supposed to be four times as great, that the work done
by the larger machine would be thirty-two times as much
as that which would be done by the smaller. Practically,
however, no such result can possibly be obtained, for a
whole series of reasons. First of all, the iron of the mag-
nets becomes saturated, and consequently, instead of getting
eight times the electromotive force, we should only get four
times the electromotive force. Secondly, the current which
we can carry in the armature is limited by the rate at which
we can get rid of the heat generated in the armature. This
we may consider as proportional to its surface; consequently
70 DYNAMO MACHINERY AND ALLIED SUBJECTS.
we must only waste four times as much energy in the arma-
ture of the larger machine as in the smaller one, instead of
eight times, as would be the case if we carried the current
in proportion to the section of the wire. Again, the larger
machine cannot run at so great an angular velocity as the
smaller one. And lastly, since in the larger machine the
current in the armature is greater in proportion to the
saturated magnetic field than it is in the smaller one, the
displacement of the point of contact of the brushes with
the commutator will be greater. However, to cut the
matter, about which one might say a great deal, short, one
may say that the capacity of similar dynamo machines is
pretty much proportionate to their weight, that is, to the
cube of their linear dimensions; that the work wasted in
producing the magnetic field will be directly as the linear
dimensions; and that the work wasted in heating the wires
of the armature will be as the square of the linear dimensions.
Now let us see how this would practically apply. Suppose
we had a small machine capable of producing an electric
current of 4 h. p., that of this 4 h. p. 1 was wasted in heat-
ing the wires of the armature, and 1 in heating the wires
of the magnet; 2 would be usefully applied outside. Now
if we doubled the linear dimensions we should have a ca-
pacity of 32 h. p., of which 2 only, if suitably applied, would
be required to produce the magnetic field, and 4 would be
wasted in heating the wires of the armature, leaving 26 h. p.
available for useful work outside the machine a very dif-
ferent economy from that of the smaller machines. But
if we again doubled the linear dimensions of our machine,
we should by no means obtain a similar increase of effect.
A consideration of the properties of similar machines has
SOME POINTS IN ELECTRIC LIGHTING. 71
another very important practical use. As you all know,
Mr. Froude was able to control the design of ironclad ships
by experiments upon models made in paraffin wax. Now
it is a very much easier thing to predict what the perform-
ance of a large dynamo machine will be, from laboratory
experiments made upon a model of a very small fraction of
its dimensions. As a proof of the practical utility of such
methods, I may say that by laboratory experiments I have
succeeded in increasing the capacity of the Edison machines
without increasing their cost, and with a small increase of
their percentage of efficiency, remarkably high as that
efficiency already was.
I might occupy your time with considerations as to the
proper proportion of conductors, and explain Sir W.
Thomson's law that the most economical size of a copper
conductor is such that the annual charge for interest and
depreciation of the copper of which it is made shall be
equal to the cost of producing the power which is wasted
by its resistance. But the remaining time will, perhaps, be
best spent in considering the production of light from the
energy of electric currents. You all know that this is done
commercially in two ways by the electric arc, and by the
incandescent lamp ; as the arc lamp preceded the incandes-
cent lamp historically, we will examine one or two points
connected with it first.
I have here all that is necessary to illustrate the electric
arc, viz., two rods of carbon supported in line with each
other, and so mounted that they can be approached or with-
drawn. Each carbon is connected with one of the poles of
the Edison dynamo machine which is supplying electricity
to the incandescent lamps which illuminate the whole of
72 DYNAMO MACHINERY AND ALLIED SUBJECTS.
this building. A resistance is interposed in the circuit of
the lamp, because the electromotive force of the machine
is much in excess of what the lamp requires. I now ap-
proach the carbons, bring them into contact, and again
separate them slightly; you observe that the break does
not stop the current, which forces its way across the space.
I increase the distance between the carbons, and you observe
the electric arc between their extremities ; at last it breaks,
having attained a length of about 1 inch. Now the current
has hard work to cross this air space between the carbons,
and the energy there developed is converted into heat,
which raises the temperature of the ends of the carbon be-
yond any other terrestrial temperature. There are several
points of interest I wish to notice in the electric arc. Both
carbons burn away in the air, but there is also a transference
of carbon from the positive to the negative carbon; there-
fore, although both waste away, the positive carbon wastes
about twice as fast as the negative. With a continuous
current, such as we are using now, the negative carbon be-
comes pointed, while the positive carbon forms a crater or
hollow; it is this crater which becomes most intensely hot
and radiates most of the light; hence the light is not by any
means uniformly distributed in all directions, but is mainly
thrown forward from the crater in the positive carbon.
This peculiarity is of great advantage for some purposes,
such, for example, as military or naval search lights; but it
necessitates, in describing the illuminating power of an arc
light, some statement of the direction in which the measure-
ment was made. On account of its very high temperature
the arc light sends forth a very large amount of visible
radiation, and is therefore very economical of electrical
SOME POINTS IN ELECTRIC LIGHTING.
73
energy. For the same reason its light contains a very large
proportion of rays of high refrangibility, blue and ultra
violet. I have measured the red light of an electric arc
against the red of a candle, and have found it to be 4,700
times as great, and I have measured the blue of the same
arc light against the blue of the same candle, and found it
to be 11,380 times as great. The properties of an electric
arc are not those of an ordinary conductor. Ohm's law
does not apply. The electromotive force and the current
do not by any means bear to each other a constant ratio.
Strictly speaking, an electric arc cannot be said to have an
electric resistance measurable in ohms. We will now ex-
amine the electrical properties of the arc experimentally.
In the circuit with the lamp is a Thomson graded current
galvanometer for measuring the current passing in amperes;
connected to the two carbons is a Thomson graded poten-
tial galvanometer for measuring the difference of potential
between them in volts. We have the means of varying
the current by varying the resistance, which I have already
told you is introduced into the circuit. We will first put
in circuit the whole resistance available, and will adjust
the carbons so that the distance between them is, as near
as I can judge, inch. We will afterwards increase the cur-
rent and repeat the readings. The results are given in
Table III.
TABLE III.
Current
Galvanometer.
Potential
Galvanometer.
Amperes.
Volts.
Watts.
H. P.
6.2
12.0
9.9
35
346
0.46
9.3
12.0
14.9
35
521
0.70
11.5
11.8
18.4
34
626
0.84
74 DYNAMO MACHINERY AND ALLIED SUBJECTS.
If the electrical properties of the arc were the same as
those of a continuous conductor, the volts would be in pro-
portion to the amperes, if correction were made for change
of temperature ; you observe that instead of that the poten-
tial is nearly the same in the two cases. We may say,
with some approach to accuracy, that, with a given length
of arc, the arc opposes to the current an electromotive force
nearly constant, almost independent of the current. This
was first pointed out by Edlund. If you will speak of the
resistance of the electric arc, you may say that the resist-
ance varies inversely as the current. Take the last exper-
iment: by burning 4 cubic feet of gas per hour we should
produce heat energy at about the same rate. I leave any
of you to judge of the comparative illuminating effects. It
is not my purpose to describe the mechanisms which have
been invented for controlling the feeding of the carbons as
they waste away. Several lamps lent by Messrs. Siemens
Brothers to whom I am indebted for the lamp and resist-
ance I have just been using lie upon the table for inspec-
tion. An electric arc can also be produced by an alternate
current. Its theory may be treated mathematically, and is
very interesting, but time will not allow us to go into it.
I will merely point out this: there is some theoretical reason
to suppose that an alternate current arc is in some measure
less efficient than one produced by a continuous current.
The efficiency of a source of light is greater as the mean
temperature of the radiating surface is greater. The max-
imum temperature in an arc is limited probably by the
temperature of volatilization of carbon; in an alternate
current arc the current is not constant, therefore the mean
temperature is less than the maximum temperature; in a
SOME POINTS IN ELECTRIC LIGHTING. 75
continuous current arc, the current being constant, the
mean and maximum temperatures are equal, therefore in a
continuous current arc the mean temperature is likely to
be somewhat higher than in an alternate current arc.
We will now pass to the simpler incandescent light.
When a current of electricity passes through a continuous
conductor, it encounters resistance, and heat is generated,
as was shown by Joule, at a rate represented by the resist-
ance multiplied by the square of the current. If the cur-
rent is sufficiently great, the heat will be generated at such
a rate that the conductor rises in temperature so far
that it becomes incandescent and radiates light. At-
tempts have been made to use platinum and platinum-
iridium as the incandescent conductor, but these bodies
are too expensive for general use, and besides, refractory
though they are, they are not refractory enough to stand
the high temperature required for economical incandescent
lighting. Commercial success was not realized until very
thin and very uniform threads or filaments of carbon were
produced and enclosed in reservoirs of glass, from which
the air was exhausted to the utmost possible limit. Such
are the lamps made by Mr. Edison with which this build-
ing is lighted to-night. Let us examine the electrical
properties of such a lamp. Here is a lamp intended to
carry the same current as those overhead, but of half the
resistance, selected because it leaves us a margin of electro-
motive force wherewith to vary our experiment. Into its
circuit I am able to introduce a resistance for checking the
current, composed of other incandescent lamps for con-
venience, but which I shall cover over that they may not
distract your attention. As before, we have two galva-
76 DYNAMO MACHINERY AND ALLIED SUBJECTS.
nometers one to measure the current passing through the
lamp, the other the difference of potential at its terminals.
First of all, we will introduce ar considerable resistance;
you observe that, although the lamp gives some light, it
is feeble and red, indicating a low temperature. We take
our galvanometer readings. We now diminish the resist-
ance. The lamp is now a little short of its standard in-
tensity; with this current it would last 1,000 hours without
giving way. We again read the galvanometers. The re-
sistance is diminished still further. You observe a great
increase of brightness, and the light is much whiter than
before. With this current the lamp would not last very
long. The results are given in Table IV.
TABLE IV.
Current
Galvanometer.
Potential
Galvanometer.
Amperes.
Volts.
Watts.
Resistance,
Ohins.
5.2
12.8
0.38
87
14
97
6.0
14.3
(' 11
41
18
93
11.5
i 28.4
0.84
68
5?
81
There are three things I want you to notice in these
experiments: first, the light is whiter as the current in-
creases; second, the quantity of light increases very much
faster than the power expended increases; and third, the
resistance of the carbon filament diminishes as its tem-
perature increases, which is just the opposite of what we
should find with a metallic conductor. This resistance is
given in ohms in the last column. To the second point,
which has been very clearly put by Dr. Siemens in his British
Association address, I shall return in a minute or two.
SOME POINTS IN ELECTRIC LIGHTING. 77
The building is this evening lighted by about 200
lamps, each giving sixteen candles' light when 75 watts of
power are developed in the lamp. To produce the same
sixteen candles' light in ordinary flat flame gas burners
would require between seven and eight cubic feet of gas per
hour, contributing heat to the atmosphere at the rate of
3,400,000 foot-pounds per hour, equivalent to 1,250 watts;
that is to say, equivalent gas lighting would heat the air
nearly seventeen times as much as the incandescent lamps.
Look at it another way. Practically, about eight of these
lamps take one indicated horse power in the engine to supply
them. If the steam engine were replaced by a large gas
engine this 1 h. p. would be supplied by 25 cubic feet of
gas per hour, or by rather less; therefore by burning gas
in a gas engine driving a dynamo, and using the electricity
in the ordinary way in incandescent lamps, we can obtain
more than five candles per cubic foot of gas, a result you
would be puzzled to obtain in 10-candle gas burners.
With arc lights instead of incandescent Jamps many times
as much light could be obtained.
At the present time, lighting by electricity in London
must cost something more than lighting by gas. Let us
see what are the prospects of reduction of this cost. Be-
ginning with the engine and boiler, the electrician has no
right to look forward to any marked and exceptional
advance in their economy. Next comes the dynamo; the
best of these are so good, converting 80 per cent, of the
work done in driving the machine into electrical work out-
side the machine, that there is little room for economy in
the conversion of mechanical into electrical energy; but
the prime cost of the dynamo machine is sure to be greatly
78 DYNAMO MACHINERY AND ALLIED SUBJECTS.
reduced. Our hope of greatly increased economy must be
mainly based upon probable improvements in the incan-
descent lamp, and to this the greatest attention ought to
be directed. You have seen that a great economy of
power can be obtained by working the lamps at high press-
ure, but then they soon break down. In ordinary prac-
tice from 140 to 200 candles are obtained from a horse
power developed in the lamps, but for a short time I have
seen over 1,000 candles per horse power from incandescent
lamps. The problem, then, is so to improve the lamp in
detail that it will last a reasonable time when pressed to
that degree of efficiency. There is no theoretical bar to
such improvements, and it must be remembered that in-
candescent lamps have only been articles of commerce for
about three years, and already much has been done. If
such an improvement were realized, it would mean that
you would get five times as much light for a sovereign as
you can now. As things now stand, so soon as those who
supply electricity have reasonable facilities for reaching
their customers, electric lighting will succeed commercially
where other considerations than cost have weight. We
are sure of some considerable improvements in the lamps,
and there is a probability that these improvements may
go so far as to reduce the cost to one-fifth of what it now
is. I leave you to judge whether or not it is probable, nay,
almost certain, that lighting by electricity is the lighting
of the future.
MAOHlNEKY.
DYNAMO-ELECTKIC MACHINEKY.
THEORETICAL CONSTRUCTION" OF CHARACTERISTIC CURVE.
OMITTING the inductive effects of the current in the
armature itself, all the properties of a dynamo machine are
most conveniently deduced from a statement of the rela-
tion between the magnetic field and the magnetizing force
required to produce that field, or, which comes to the same
thing but more frequently used in practice, the relation
between the electromotive force of the machine at a stated
speed and the current around the magnets. This relation
given, it is easy to deduce what the result will be in all
employments of the machine, whether as a motor or to
produce a current through resistance, through an electric
arc, or in charging accumulators; also the result of vary-
ing the winding of the machine, whether in the armature
or magnets. The proper independent variable to choose
for discussing the effect of a dynamo machine is the cur-
rent around the magnets; and the primary relation it is
necessary to know concerning the machine is the relation
of the electromotive force of the armature to the magnet
current. This primary relation may be expressed by a
curve (Fig. 4, p. 22 et seq., and Fig. 5, p. 26), now called
the characteristic of the machine, and all consequences
deduced therefrom graphically; or it may be expressed by
80 DYNAMO MACHINERY AND ALLIED SUBJECTS.
stating the E.M.F. as an empirical function of the magnet-
izing current. Many such empirical formulaB have been
proposed; as an instance we may mention that known as
Frohlich's, according to whom, if c be the current in the
magnets, E the resulting E.M.F., E = ~r-. For some
J. J~ o c
machines this formula is said to express observed results
fairly accurately, but in our experience it does not suf-
ficiently approximate to a straight line in the part of the
curve near the origin. The character of the error in
Frohlich's formula is apparent by reference to Figs. 24
and 25, which give a series of observations on a dynamo
machine, and for comparison therewith a hyperbola F,
drawn as favorably as possible to accord with the observa-
tions.* Such empirical formulaB possess no advantage over
the graphical method aided by algebraic processes, and
tend to mask much that is of importance.
One purpose of the present investigation is to give an
approximately complete construction of the characteristic
curve of a dynanlo of given form from the ordinary laws
of electromagnetism and the known properties of iron,
and to compare the result of such construction with the
actual characteristic of the machine. The laws of electro-
magnetism needed are simply (Thomson, papers on " Elec-
* Added Aug. 17. That Frfihlich's formula cannot be a thoroughly satisfac-
tory expression of the characteristic of a dynamo machine is evident from the
consideration that E should simply change its sign with c, that is, be an odd
function of c. There should be a point of inflection in the characteristic curve
at the origin. Another empirical formula, = tan ~ 1 -, is free from this objec-
tion, but still fails to fully represent the approximation of the curve to a
straight line on either side of the origin, and it is equally uninstructive with
any other purely empirical formula.
DYNAMO-ELECTEIC MACHINERY
81
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Fio. 25. APPKOXIMATK SYNTHESIS OF CHARACTERISTIC CURVE.
, armature; B, air space; C, magnets; D, deduced curve; ,E, observed
results, -f ascending, descending; F, Frfihlich's curve. This figure is
the same as the left-hand part of Fig. 24, but on a larger scale.
DYNAMO-ELECTRIC MACHINERY. 83
trostatics and Magnetism;" Maxwell, "Electricity and
Magnetism/' vol. ii., pp. 24, 26, and 143), (1) that the
line integral of magnetic force around any closed curve,
whether in iron, in air, or in both, is equal to 4;r n c, where
c is the current passing through the closed curve, and n is
the number of times it passes through; (2) the solenoidal
condition for magnetic induction, that is, if the lines of
force or of induction be supposed drawn, then the induc-
tion through any tube of induction is the same for every
section. Regarding the iron itself, we require to know
from experiments on the material in any shape the relation
between , the induction, and a, the magnetic force at any
point; for convenience write a=f~ l (ae), or a = f(a).
From these premises, without any further assumption, it is
easy to see that a sufficiently powerful and laborious analysis
would be capable of deducing the characteristic of any
dynamo to any desired degree of accuracy. This we do not
attempt, as, even if successful, the analysis would not be
likely to throw any useful light on the practical problem.
We shall calculate the characteristic, first making certain
assumptions to simplify matters. We shall next point out
the nature of the errors introduced by these assumptions,
and make certain small corrections in the method to ac-
count for these sources of error, merely proving that the
amount of these corrections is probable or deducing it
from a separate experiment, and again compare the theo-
retical and the actual characteristic.
First Approximation. Assume that by some miracle
the tubes of magnetic induction are entirely confined to
the iron excepting that they pass directly across from the
bored faces of the pole pieces to the cylindrical face of the
84 DYNAMO MACHINERY AND ALLIED SUBJECTS.
armature core. This, we shall find, introduces minor
sources of error, affecting different parts of the charac-
teristic curve to a material extent. Let / be total in-
duction through the armature, A l the area of section of
the iron of the armature, 7, the mean length of lines of
force in the armature; .1, the area of each of the two
spaces between core of armature and the pole pieces of the
magnets, 7, the distance between the core and the pole
piece; A t the area of core of magnet, 7, the total length of
the magnets. All the tubes of induction which pass
through the armature pass through the space A 9 and the
magnet cores, and by our assumption there are no others.
We now assume further that these tubes are uniformly
distributed over these areas. The induction per square
centimetre is then -.- in the armature core, - in the non-
A l A 9
magnetic spaces, -- in the magnet cores; the correspond-
ing magnetic forces per centimetre linear must be/( - -), -y-,
\AJ A t
The line integral of magnetic force round a closed
curve must be 7,/f-;- ) + 27, - - + J/(~r ) ^ n this a P -
XAJ A t \A t J
proximation we neglect the force required to magnetize
pole pieces and other parts not within the magnet coils, to
avoid complication. The equation of the characteristic
curve is, then, 4* n c = 7,/fl + 27, -.- + 7, f(-\ This
\AJ A 9 \A 3 /
curve is, of course, readily constructed graphically from
the magnetic property of the material expressed by the
DYNAMO-ELECTRIC MACHINERY.
85
curve a =f(a). In Figs. 24 and 25 curve A represents
x.= Z, f[ -J-), the straight line B x = 2Z,-j-, curve G
\AJ Ji
x = Z, /(?'), and curve D the calculated characteristic.
When we compare this with an actual characteristic E, we
shall see that, broadly speaking, it deviates from truth in
FIG. 26.
two respects: (1) it does not rise sufficiently rapidly at
first; (2) it attains a higher maximum than is actually
realized. Let us examine these errors in detail.
(1) The angle the characteristic makes with the axis of
abscissae near the origin is mainly determined by the line
B (Fig. 26). "We have in fact a very considerable exten-
86 DYNAMO MACHINERY AND ALLIED SUBJECTS.
sion of the area of the field beyond that which lies under
the bored face of the pole piece. The following considera-
tion will show that the extension may be considerable:
Imagine an infinite plane slab, and parallel with it a second
slab cut off by a second plane making an angle a. We
want a rough idea of the extension of the area between the
plates by the spreading of the lines of induction beyond
the boundary. We know that the actual extension of the
area will be greater than we shall calculate it to be if we
prescribe an arbitrary distribution of lines of force other
than that which is consistent with Laplace's equation.
Assume, then, the lines of force to be segments of circles
centre 0, and straight lines perpendicular to A. The
y
induction along a line P Q R will be -T r 7-, V
t
being difference of potential between the planes; and the
added induction from P B will be
Vdx V (T- a)x + t
(it - a)x 4- t ~~ n - a g " t
7t
Thus, if n = , we have for x = t, 21, etc.,
t
2t
a)x -f t
lUi^
TT a
0.599
0.904
1.109
1.263
, 1.387
1.793
t
V IS
DYNAMO-ELECTRIC MACHINERY. 87
showing that the extension of the area of the field is likely
to be considerable.
(2) The failure of the actual curve to reach the max-
imum indicated by approximate theory is because the
theory assumes that all tubes of induction passing through
the magnets pass also through the armature. Familial-
observations round the pole pieces of the magnets show
that this is not the case. If v be the ratio of the total
induction through the magnets to the induction in the
armature, we must, in our expression for the line integral of
magnetizing force, replace the term /f-j-J by /( ~ J :
not strictly a constant, as we shall see later; it is somewhat
increased as / increases, owing to magnetization of the core
of the armature, and it is also affected by the current in
the armature. For our present purpose we treat it as con-
stant.
There is yet another source of error which it is necessary
to examine. Some part of the induction in the armature
may pass through the shaft instead of through the iron
plates. An idea of the amount of this disturbance may be
readily obtained. Consider the closed curve A B C D E F:
A B and FED C are drawn along lines of force; A F and
B C are orthogonal to lines of force (Fig. 27). Since this
closed curve has no currents passing through it, the line
integral of force around it is nil; therefore, neglecting
force along E D, we have force along A B equal to force
along F E and D C. In the machine presently described
we may safely neglect the induction through the shaft;
the error is comparable with the uncertainty as to the value
of ^; but in another machine, ' with magnets of much
88 DYNAMO MACHINERY AND ALLIED SUBJECTS.
greater section, the effect of the shaft would become very
sensible when the core is practically saturated.
Fio. 27.
The amended formula now becomes
n c = 1 . 1 1
where 1 4 is the mean length of lines of force in the
wrought-iron yoke, A 4 the area of the yoke, l t and A t cor-
responding quantities for the pole pieces, the last two
terms being introduced for the forces required to magnet-
ize the yoke and the two pole pieces.
DYNAMO-ELECTRIC MACHINERY. 89
"We now repeat the graphical method of construction
exactly as before, the actual observations of induction in
armature and current being plotted on the same diagram,
Figs. 28 and 29, in which curve G represents the force
required to magnetize the yoke, and curve H that required
to magnetize the pole pieces. Before discussing these
curves further, and comparing the results with those of
actual observation, it may be convenient to describe the
machine upon which the experiments have been made,
confining the description strictly to so much as is perti-
nent to our present inquiry.
DESCRIPTION OF MACHINE.
The dynamo has a single magnetic circuit, consisting of
two vertical limbs, extended at their lower extremities to
form the pole pieces, and having their upper extremities
connected by a yoke of rectangular section. Each limb,
together with its pole piece, is formed of a single forging
of wrought iron. These forgings, as also that for the yoke,
are built up of hammered scrap and afterwards carefully
annealed, and have a magnetic permeability but little in-
ferior to the best Swedish charcoal iron. The yoke is
held to the limbs by two bolts, the surfaces of contact
being truly planed. In section the limb is oblong, with
the corners rounded in order to facilitate the winding of
the magnetizing coils. A zinc base, bolted to the bed-
plate of the machine, supports the pole pieces.
The magnetizing coils are wound directly on the limbs,
and consist of 11 layers on each limb, of copper wire 2.413
mms, diameter (No. 13, B.W.Gr.), making 3,260 convolu-
90 DYNAMO MACHINERY AND ALLIED SUBJECTS.
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DYNAMO-ELECTRIC MACHINERY.
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Fio. 29. CORRECT SYNTHESIS OP CHARACTERISTIC CURVE.
A, armature; B, air space; C, magnets; D, calculated curve; 7. observa-
tions, -(-ascending, descending; (?, yoke; H, pole piece. This figure
is the same as the left-hand part of Fig. 28, but on a larger scale,
92 DYNAMO MACHINERY AND ALLIED SUBJECTS.
tions in all, the total length being approximately 4,570
metres. The pole pieces are bored to receive the arma-
ture, leaving a gap above and below, subtending an angle
of 51 at the centre of the fields. The opposing surfaces
of the gap are 8 mms. deep.
The following table gives the leading dimensions of the
machine:
cms.
Length of magnet limb = 45.7
Width of magnet limb = 22.1
Breadth of magnet limb = 44.45
Length of yoke = il 6
Width of yoke = 48.3
Depth of yoke = 23 2
Distances between ceni res of limbs = 88.1
Bore of fields = 27.5
Depth of pole piece '. = 25 4
Width of pole piece measured 'parallel to the shaft = 48.3
Thickness of zinc base = 12.7
Width of gap = 12.7
The armature is built up of about 1,000 iron plates, insu-
lated one from another by sheets of paper, and held between
two end plates, one of which is secured by a washer
shrunk on to the shaft, and the other by a nut and lock-
nut screwed on the shaft itself. The plates are cut from
sheets of soft iron, having probably about the same mag-
netic permeability as the magnet cores. The shaft is of
Bessemer steel, and is insulated before the plates are
threaded on.
The following table gives the leading dimensions of the
armature :
cms.
Diameter of core = 24.5
Diameter of internal hole = 7.62
Length of core over the end plates = 50.8
Diameter of shaft = 6,985
DYNAMO-ELECTRIC MACHINERY.
93
The core is wound longitudinally according to the
Hefner von Alteneck principle with 40 convolutions, each
consisting of 16 strands of wire 1.753 inm. diameter, the
convolutions being placed in two layers of 20 each. The
commutator is formed of 40 copper bars, insulated with
mica, and the connections to the armature so made that
the plane of commutation in the commutator is horizontal
when no current is passing through the armature.
Fig. 30 shows a side elevation of the dynamo; Fig* 31 a
FIG 30.
cross section through the centres of the magnets; Fig 32
a section of the core of the armature, in a plane through
the axis of the shaft.
The dynamo is intended for a normal output of 105
volts 320 amperes at a speed of 750 revolutions per minute.
94 DYNAMO MACHINERY AND ALLIED SUBJECTS.
The resistance of the armature measured between opposite
bars of the commutator is 0.009947 ohm, and of the mag-
Fio. 81.
net coils 16.93 ohms, both at a temperature of 13.5 Centi-
grade; Lord Rayleigh's determination of the ohm being
assumed.
Fio. 32.
We have now to estimate the lengths and areas required
in the synthesis of the characteristic curve.
-4,; from the length of the core of the armature (50.8
cms.) must be deducted 3.4 cms. for the thickness of
DYHAMO-ELECTKIC MACHINERY. 95
insulating material between the plates ; the resultant area
is, on the other hand, as has already been stated, slightly
augmented by the presence of the steel shaft. A 1 is taken
as 810 sq. cms.
/! ; this is assumed to be 13 cms., i.e., slightly in excess
of the shortest distance (12.6 cms.) between the pole pieces.
A^j the angle subtended by the bored face of the pole
piece at the axis is 129, the breadth of the pole piece is
48.3 cms., the diameter of the bore of the field is 27.5 cms.,
and, as already stated, the diameter of core 24.5 cms.; thus
the area of pole piece is 1,513 sq. cms., and the area of 129
of the cylinder at the mean radius of 13.0 cms. is 1,410 sq.
cms. ; this value is taken for A^ in the curves drawn in Figs.
24 and 25. In Figs. 28 and 29 A^ is taken as 1,600, an
allowance of 190 sq. cms. being made for the spreading of
the field at the edges of the pole pieces, or -- = 1.2 cm. all
1 2
round the periphery, that is, -^= 0.8 of the distance from
l.o
iron of pole pieces to iron of core.
1 9 is 1.5 cm.
A 9 is a little uncertain, as the forgings are not tooled
all over; it is here taken as 980 sq. cms.,
but this value may be slightly too high.
l s is 91.4 cms.
A 4 is 1,120 sq. cms,
1 4 is 49 cms., being measured along a
quadrant from the centre of the magnet
(see Fig. 33). FIG. 33.
AI is 1,230 sq. cms., intermediate between the area of
magnet and face of pole piece.
96 DYNAMO MACHINERY AND ALLIED SUBJECTS.
1 6 is 11 cms.
v was determined by experiment as described below, and
its value is taken as 1.32; when the magnetizing current is
more than 5.62 amperes its value should be a little greater.
The function/(rt) is taken from Hopkinson, Phil. Trans.,
vol. clxxvi, 1885, p. 455 ; the wrought iron there referred
to was not procured at the same time as, and its properties
may differ to a certain extent from, the wrought iron of
these magnets.
The curves now explain themselves : the abscissas in each
case represent the line integral of magnetizing force in the
part of the magnetic circuit referred to; the ordinates, the
number of lines of induction which also pass through the
armature.
The results of the actual observations on the machine
are indicated, those when the magnetizing force is increas-
ing +> when it is decreasing . The measurements of the
currents in the magnets which were separately excited, and
of the potential difference between the bmshes, the circuit
being open, were made with Sir W. Thomson's graded
galvanometers, standardized at the time of use. The irreg-
ularities of the observations are probably due to the varia-
tion of speed, the engine being not quite perfectly governed.
The second construction exhibits quite as close an agree-
ment between observation and calculation as could be
expected; the deviation at high magnetizing forces is
probably due to three causes increase in the value of v
when the core of the armature is partially saturated, un-
certainty as to the area J 3 , difference in the quality of the
iron. It is interesting to see how clearly theory predicts -
the difference between the ascending and descending curves
DYNAMO-ELECTRIC MACHINERY. 97
of a dynamo. Consideration of the diagram proves that
this machine is nearly perfect in its magnetic proportions.
The core might be diminished without detriment by in-
creasing the hole through it to a small, but very small,
extent. Any reduction of area of magnets would be inju-
rious ; they might, indeed, be slightly increased with advan-
tage. An increase in the length of the magnets would be
very distinctly detrimental. Again, little advantage results
from increasing the magnetizing force beyond the point at
which the permeability of the iron of the magnets begins
to rapidly diminish. For iron of the same quality as that of
the machine under consideration, a magnetizing force of
2.6x10' or 28.4 per centimetre is suitable. To get the
same induction in other parts of the circuit, the diagram
shows that for the air space a magnetizing force of 21 X 10 s
is required, for the pole pieces 0.1 X 10 8 , for the armature
0.2 XlO 3 , for the yoke 0.6X10 8 ; making a total force re-
quired of 24.5 X 10". Any alteration in the length of the
area of any portion of the magnetic circuit entails a corre-
sponding alteration in the magnetizing forces required for
that portion, at once deducible from the diagram. Similar
machines must have the magnetizing forces proportional
to the linear dimensions, and consequently, if the electro-
motive force of the machines is the same, the diameter of
the wire of the magnet coils must be proportional to the
linear dimensions. If the lengths of the several portions
of the magnetic circuit remain the same, but the areas are
similarly altered, the section of the wire must be altered in
proportion to the alteration in the periphery of the section.
DYNAMO MACHINERY AND ALLIED SUBJECTS.
EXPERIMENT TO DETERMINE V.
Around the middle of one of the magnet limbs a single
coil of wire was taken, forming one complete convolution,
and its ends connected to a Thomson's mirror galvanom-
eter rendered fairly ballistic. If the circuit of the field
magnets, while the exciting current is passing, be suddenly
short circuited, the elongation of the galvanometer is a
measure of the total induction within the core of the
limbs, neglecting the residual magnetization. If the short
circuit be suddenly removed, so that the current again
passes round the field magnets, the elongation of the
galvanometer will be equal in magnitude and opposite in
direction.
The readings taken were :
Zero 71 left.
Deflection .... 332 " magnets made.
" .... 196 right; magnets short circuited,
llence, deflection to right = 267
left = 261
Mean deflection = 264
To determine the induction through the armature, the
leads to the ballistic galvanometer were soldered to con-
secutive bars of the commutator, connected to that convo-
lution of the armature which lay in the plane of commu-
tation.
DYNAMO-ELECTKIC MACHINERY. 99
The readings taken were :
Zero 23 left.
Deflection .... 223 " magnets made.
' ' ' ' j- right ; magnets short circuited.
Hence, deflection to right and left = 200
It thus appears that out of 264 lines of force passing
through the cores of the magnet limbs at their centre, 200
go through the core of the armature, whence v equals 1.32.
The magnetizing current round the fields during these
experiments was 5.G amperes.
EXPERIMENTS ON" WASTE FIELD NOT PASSING THROUGH
ARMATURE.
As in the determination of v, a single convolution was
taken around the middle of one of the limbs, and con-
nected to the ballistic galvanometer; the deflections, when
a current of 5.6 amperes was suddenly passed through the
fields or short circuited, were :
Zero 34 left.
Deflection .... 148 " magnets made.
" .... 82 right; magnets short circuited.
Hence, deflection to right =116
left = 114
Mean deflection = 115
I. Four convolutions were then wound round the zinc
plate and the cast-iron bed in a vertical plane, passing
100 DYNAMO MACHINERY AND ALLIED SUBJECTS.
through the axis of the armature; and the deflections
noted were:
Zero. .' . . ... . 15 left.
Deflection 61 " magnets short circuited.
" 40 right; magnets made.
Zero 11 left.
Deflection 64 " magnets short circuited.
" 36 right; magnets made.
Hence, deflection to right = 55
left = 46
and " right = 47
left =53
in the two observations respectively, giving a mean = 50.25;
or, reducing to one convolution, = 12.6.
II. A square wooden frame, 38 cms. x 38 cms., on which
were wound ten convolutions, was then inserted between
the magnet limbs, with one side resting on the armature,
and an adjacent side projecting 5 cms. beyond the coils on
the limbs, or about 7.6 cms. beyond the cores of the limbs.
The deflections were:
Zero 34 left.
Deflection 98 " magnets made.
" 22 right; magnets short circuited.
21 " <s "
" 81 left; magnets made.
Hence, deflection to right = 56
left = 64
and " right = 55
left = 47
DYNAMO-ELECTRIC MACHINERY. 101
in the two observations respectively, giving a mean = 55 ;
or, reducing to one convolution, = 5.5.
III. The same frame was raised a height of 6.35 cms.
above the armature in a vertical plane. The deflections
were:
Zero ...... 21 left.
Deflection .... 98 " magnets made.
Zero ...... 35 left.
Deflection .... 8 right; magnets short circuited.
Hence, deflection to left = 50
right = 43
and mean deflection = 46.5
or, reducing to one convolution, = 4.6
IV. The same frame was again lowered on the armature
and pushed inwards so as to lie symmetrically within the
space between the limbs. The deflections were :
Zero ...... 32 right.
Deflection .... 112 " magnets made.
" .... 48 left; magnets short circuited.
Giving a mean of 80; or, reducing to one convolution,
= 8.0.
Let G represent the leakage through a vertical area
bounded by the armature and a line 7.6 cms. above the
armature and of the same width as the pole pieces; let R
be the remainder of the leakage between the limbs; then
II. and III. give
f * = 4.6;
102 DYNAMO MACHINERY AND ALLIED SUBJECTS.
whence
G = 1.35,
R = 6.9.
Again, IV. gives
|(fl< + *) = 8.0;
therefore
G + R = 9.6,
which shows an agreement as near as might be expected
considering the rough nature of the experiment and that
the leakage is assumed uniform over the areas considered.
We take
G = 1.6,
R = 8.0.
Reducing these losses to percentages we have
i c
G = T 1.4 per cent.
lio
*-ra - '
And from I. the leakage through the ) .103
zinc plate and iron base . . . . )
Hence the two gaps account for . . . 2.8 "
The zinc plate and iron base account for 10.3 "
And the area between the limbs . . . 7.0 "
Making a total loss accounted for . . 20.1 "
Out of an observed loss of 24.24 "
The leakage through the shaft and from pole piece to
yoke, and one pole piece to the other by exterior lines,
will account for the remainder.
DYNAMO-ELECTRIC MACHINERY. 103
EFFECT OF THE CURRENT IN THE ARMATURE.
The currents in the fixed coils around the magnets are
not the only magnetizing forces applied in a dynamo
machine ; the currents in the moving coils of the armature
have also their effect on the resultant field. There are in
general two independent variables in a dynamo machine
the current around the magnets and the current in the
armature; and the relation of E.M.F. to currents is fully
represented by a surface. In well-constructed machines
the eifect of the latter is reduced to a minimum, but it
can be by no means neglected. When a section of the
armature coils is commutated, it must inevitably be
momentarily short circuited; and if at the time of commu-
tation the field in which the section is moving is other
than feeble, a considerable current will arise in that see-
tion, accompanied by waste of power and destructive
sparking. It may be well at once to give an idea of the
possible magnitude of such effects. In the machine al-
ready described the mean E.M.F. in a section of the arma-
ture at a certain speed may be taken as 6 volts, its resist-
ance 0.000995 ohm. Setting aside, then, for the moment
questions of self induction, if a section were commutated
at a time when it was in a field of one tenth part of the
mean intensity of the whole field, there would arise in that
section, while short circuited by the collecting brush, a
current of 600 amperes, four times the current when the
section is doing its normal work. The ideal adjustment
of the collecting brushes is such that during the time they
short circuit the sections of the armature the magnetic
104 DYNAMO MACHINERY AND ALLIED SUBJECTS.
forces shall just suffice to stop the current in the section,
and to reverse it to the same current in the opposite direc-
tion.
Suppose the commutation occurs at an angle A in ad-
vance of the symmetrical position between the fields, and
Fio. 34.
that the total current through the armature be (7, reckoned
positive in the direction of the resultant E.M.F. of the
machine, i.e., positive when the machine is used as
a generator of electricity. Taking any closed line
through magnets and armature, symmetrically drawn as
AB C D E FA (Fig. 34), it is obvious that the line in-
tegral of magnetic force is diminished by the current in
the armature included between angle. A in front and angle
DYNAMO-ELECTRIC MACHINERY. 105
A behind the plane of symmetry. If m be the number of
convolutions of the armature, the value of this magnetizing
force is n C^ = kmC opposed to the magnetizing
Z 7t
force of the fixed coils on the magnets. Thus if we know
the lead of the brushes and the current in the armature we
are at once in a position to calculate the effect on the
electromotive force of the machine. A further effect of
the current in the armature is a material disturbance in
the distribution of the induction over the bored face of
the pole piece; the force along B C (Fig. 34) is by no
means equal to that along D E. Draw the closed curve
B C G H B: the line integral along C G and H B is negli-
gible. Hence the difference between force H G and B C
is equal to 4;r (7 = %Km C, where K is\the angle COG.
This disturbance has no material effect upon the perform-
ance of the machine. Hut the current in the armature
also distorts the arrangement of the comparatively weak
field in the gap between the pole pieces, displacing the
point of zero field in the direction of rotation in a gener-
ator and opposite to the direction of rotation in a motor;
and it is due to this that the non-sparking point of
the brushes is displaced. A satisfactory mathematical
analysis of the displacement of the field in the gap be-
tween the pole pieces by the current in the armature
would be more troublesome than an a priori analysis of
the distribution of field in this space when the magnet
current is the only magnetizing force. Owing to the fact
that the armature is divided into a finite number of sec-
tions, there is a rapid diminution of the displacement of
106 DYNAMO MACHINERY AND ALLIED SUBJECTS.
the field during the time that a section is being commu-
tated, the diminution being recovered while the brush is
in contact with only one bar of the commutator. The
field thus oscillates slightly, owing to the disturbance
caused by reversing the direction of the current in tin-
successive sections of the armature. The number of oscil-
lations in a Gramme armature or in a Siemens armature
with an even number of sections will be p m, where p is
the number of revolutions per second; but in a Siemens
armature with an odd number of sections it will be 2p m.*
This oscillation of the field is only another way of express-
ing the effect of the self induction of the section, but it
must be remembered that if the self induction, multiplied
by change of current, is expressed as a change in the field
we must omit self induction as a separate term in our
electrical equations. The precise lead to be given to the
brushes in order to avoid spa_rking in any given case
depends on many circumstances the form and extent of
the pole pieces, the number of sections in the armature,
and the duration of the short circuit which the brushes
cause in any section of the armature. The adjustment of
the position of the collecting brushes is generally made by
* Added Aug. 1?. Armatures with an odd number of convolutions are open
to one theoretical objection, which would be a practical one if the number of
convolutions were very small The 2m 1 convolutions constitute in them-
selves a closed circuit, having a resistance four times the mean actual resist-
ance of the armature measured between the collecting brushes. When any
one convolution is exactly in the middle of the field, the E.M.F. of the other 2m
convolutions exactly balance, so that there is upon the closed circuit an E.M.F.
due to the single convolution somewhat in excess of part of the actual
E.M.F. of the ?nachine. Thus there will be an alternating E.M.F. around the
closed circuit of the armature capable of causing a considerable waste of
power. This waste is materially checked by the sHf induction of the circuit.
DYNAMO-ELECTRIC MACHINERY. 107
hand at the discretion of the attendant, and is in some
cases fixed once for all to suit an average condition of the
machine. We shall, therefore, treat A. the lead as an inde-
pendent variable, controlled by the attendant.
Let / be total induction through the armature, /-j- 1'
total induction through the magnets, /' being the waste
field. Let C be current in armature, c in the magnets.
Let g 1' be the line integral of magnetic force from a point
on one pole piece to a point on the other; the line being
drawn external to the armature, g will be approximately
constant. Omitting as comparatively unimportant the
magnetizing force in the pole pieces and iron core of the
armature, we have the following equations :
/
4 A, m C -f 21 9 -r g I' = 0;
4\mC+2l,~
~t
When C = 0,vf& observed
1 =
r 1
whence
g= * 8*.
eliminating /',
4-Trnc
108 DYNAMO MACHINERY AND ALLIED SUBJECTS.
The characteristic curve when C = being 7 = F( nnc),
we may write the above as the equation of the character-
istic surface thus:
4XrnC
In applying this equation it must not be forgotten that
the E. M. F. of the machine cannot be determined from /
Fio. 35.
unless the commutation occurs at such a time that the coil
being commutated embraces all, or nearly all, the lines of
induction in the armature.
This equation enables the characteristic surface to be
DYNAMO-ELECTRIC MACHINERY. 109
constructed from the characteristic curve. Let L = 4 n n c
(Fig. 35), LM=m\C; draw MK so that j^=\\
through ./Tdraw ordinate KR, meeting characteristic curve
in R ; draw R Q parallel to L, meeting ordinate Q L in Q ;
p c
draw Q S parallel to L M\ draw Q P so that
. ^y . Then P is a point on the characteristic
surface.
A very important problem is to deduce the characteristic
curve of a series- wound machine from the normal charac-
teristic; in this case c = C, and we have
taking PR (Fig. 36) as ordinate of any point in the nor-
v \ A
mal characteristic, cut off QR equal to -4Afw(7 *
"V t '
that is, draw Q so that
tan$0= \mC^/n(n - \C
_v IA, Am
r 2L A m
* nn
v
Then P Q will represent the induction corresponding to
magnetizing force n\n ^j G. It is noteworthy that as
110 DYNAMO MACHINERY AND ALLIED SUBJECTS.
the current C, and therefore R, increases, PQ, the induc-
tion, will attain a maximum and afterwards diminish, van-
ish, and become negative. That in series-wound machines
the E. M. F. has a maximum value has been many times
observed. The cause lies in the existence of a waste field
Fio. 86.
not passing through the armature, and in the saturation of
the magnet core.
The effect of the current in the armature on the poten-
tial between the brushes of any machine is the same as
that of an addition to the resistance of the armature pro-
portional to the lead of the brushes and to the ratio of the
waste field to the total field, combined with that of taking
the main current times round the magnets in direction
DYNAMO-ELECTRIC MACHINERY. Ill
opposite to the current c. The preceding investigation tells
the whole story of a dynamo machine, excepting only the
relation of A to C in order that the brushes may be so
placed as to avoid sparking. The only constant or func-
tion which has to be determined experimentally for any
particular machine is v, the ratio of total to effective field;
all the rest follows from the configuration of the iron and
the known properties of the material.
The following illustrations of the effect of the current
in the armature and the lead of the brushes are interesting.
In both cases the magnet coils are supposed to be entirely
disconnected, so that c is zero. First, let A be negative,
short circuit the brushes, and drive the machine at a cer-
tain speed; a large current will be produced, the current in
the armature itself forming the magnet.* Second, let A,
be positive, cause a current to pass through the armature:
the armature will turn in the positive direction and will act
as a motor capable of doing work. In either case, partic-
ularly the former, such use of the machine would not be
practical, owing to violent sparking on the commutator.
The following is a further illustration of the formula
given above : If we could put up with the sparking which
* Added Aug. 17. This experiment was tried upon a dynamo machine of
construction generally similar to that shown in Figs. 30, 31, and 32, but with an
armature of half the length intended in normal work to give 400 amperes, 50
volts, at 1,000 revolutions. The magnet coils were disconnected, and the termi-
nals of the armature were connected through a Siemens electrodynamometer,
and the machine was run at 1,380 revolutions. When the brushes were placed in
the normal position (A = 0) the current due to residual magnetism was 52 am-
peres. By giving the brushes a small positive lead the current was reduced to
nearly zero. By giving the brushes a small negative lead a current of over 234
amperes, the maximum measured by the dynamometer, was obtained, and by
varying the lead it was easy to maintain a steady current of any desired
amount.
DYNAMO MACHINERY AND ALLIED SUBJECTS.
would ensue, it would be possible to make A negative in a
generator of electricity, and thereby obtain by the reactions
of the armature itself all the results usually obtained by
compound winding.
EFFICIENCY EXPERIMENTS.
Having discussed the relations subsisting between the
configuration of the magnetic circuit of a dynamo machine
and the induction obtained for given magnetizing forces,
and having compared the results obtained by direct calcu-
lation with the results of actual observation on a partic-
ular machine, the construction of which we have described
at length, it appeared of importance to determine the
efficiency of the machine under consideration 'as a con-
verter of energy, when used either as a generator of elec-
tricity or as a motor. An accurate determination of the
mechanical power transmitted to a dynamo by a driving
belt, or of the power given by a motor, presents formidable
experimental difficulties. Moreover, if the mechanical
power absorbed in driving the dynamo be measured di-
rectly, any error in measurement will involve an error of
the same magnitude in the determination of the efficiency.
To avoid this difficulty, we employed the following device:
Let two dynamos, approximately equal in dimensions
and power, have their shafts coupled by a suitable coup-
ling, which may serve also as a driving pulley ; and let the
electrical connections between the dynamos be made so that
the one drives the other as a motor. If the combination
be driven by a belt passing over the coupling pulley, the
power transmitted by the belt is the waste in the two dyn-
DYNAMO-ELECTRIC MACHINERY. 113
amos and the connections between them. By suitably
varying the magnetic field of one of the dynamos, the
power passing between the two machines can be adjusted
as desired. If, then, the electrical power given out by the
generator is measured, and also the power transmitted by
the belt, the efficiency of the combination can be at once
determined. By this arrangement the measurement, which
presents experimental difficulties, viz., the power trans-
mitted by the belt, is of a small quantity. Consequently
even a considerable error in the determination hasXbtfta.
small effect on the ultimate result. On the other h^Qd
the measurement of the large quantity involved, viz., the
electrical power passing between the two machines, can
without difficulty be made with great accuracy.
The second machine was similar in all respects to that
already described, and each is intended for a normal out-
put of 105 volts, 320 amperes, at a speed of 750 revolutions
per minute.
The power transmitted by the belt was measured by a
dynamometer of the Hefner-Alteneck type, the general
arrangement being as shown in the diagram, Fig. 37. A
is the driving pulley of the engine, B the driven coupling
of the dynamos; /), D are the guide pulleys of the dyna-
mometer, carried on a double frame turning about the ful-
crum C, and supported by a spiral spring, the suspension
of which can be varied by a pair of differential pulley
blocks attached to a fixed support overhead. When a read-
ing is made, the suspension of the spring is adjusted until
the index of the dynamometer comes to a fiducial mark on
a fixed scale; the extension of the spring is then read by a
second index attached to its upper extremity. F 9 F are two
114 DYNAMO MACHINERY AND ALLIED SUBJECTS.
fixed guide pulleys of the same diameter as the pulleys D,
D, and having the same distance between their centres, in
order that the two portions of the belt may be parallel and
the sag as far as possible taken up. The normal from G
Fio. 87.
to the centre line of either portion of the belt between the
pulley B and the guide pulleys = 31.9 cms. The normal
from C to the centre line of either of the parallel por-
tions of the belt = 2.4 cms., and from C to the centre line
of the spring = 92.7 cms.
Take moments about (7; then
92.7
Tension of the belt = j" X tension of spring,
o4.o
= 2.7 X tension of spring.
Also the diameter of the pulley B = 33.6 cms. and the
thickness of the belt = 1.6 cm.
Hence the velocity of the centre of the belt in centime-
DYNAMO-ELECTKIC MACHINERY. 115
tres per second = 1.845 X revolutions of dynamo per minute,
and, therefore,
Power transmitted by the belt in ergs per second = 2.7 X
1.845 X 981 X tension of spring X revolutions per minute,
assuming the value of g to be 981.
We may more conveniently express the power in watts
(= 10 7 ergs per second), and write
Power in watts = 0.0004887 X tension of spring
X revolutions per minute.
The potential between the terminals of the generator
was measured by one of Sir William Thomson's graded
galvanometers, previously standardized by a Clark's cell,
which had been compared with other Clark's cells, of which
the electromotive force was known by comparison with
Lord Rayleigh's standard. The current between the two
machines was measured by passing it through a known re-
sistance, the difference of potential between the ends of the
resistance being determined by direct comparison with the
Clark's standard cell, according to Poggendorff's method.
As experiments were made with currents of large magni-
tude, it was important that the temperature coefficient of
the resistance should be as low as possible. To this end
we found a resistance frame constructed of platinoid wire
of great value. The temperature coefficient of this alloy
is only 0.021 per cent, per degree Centigrade. (Proc. Roy.
Soc., vol. xxxviii, 1885, p. 265.)
The resistances of the armatures and magnets of the
two machines are as follows :
110 DYNAMO MACHINERY AND ALLIED SUBJECTS.
Ohms.
Generator, . . . armature, . . . 0.009947
magnets, . . . 16.93
Motor, .... armature, . . . 0.009947
magnets, . . . 16.44
The resistance of the leads connecting the two machines
was 0.00205 ohm, and of the standard resistance 0.00586
ohm.
In all determinations of resistance the value of the B. A.
TERMINALS Of MACHINE
ACTINGAS MOTOR
Fio. 88.
ohm was taken as 0.9867 X 10' C. G. S. units, according to
Lord Rayleigh's determination.
The diagram, Fig. 38, shows the electrical connections
between the two machines with the rheostat r inserted in
the magnets of the motor dynamo.
DYNAMO- ELECTRIC MACHINERY. 117
In order to ascertain the friction of bending the belt
round the pulley B, and of the journals of the dynamo, a
preliminary experiment was made with the dynamometer.
The combination was run at a speed of 814 revolutions per
minute with the dynamos on open circuit, and the tension
of the spring observed 9,979 grams. The engine was then
reversed and the dynamos run at the same speed, and the
tension of the spring again observed 3,629 grams. The
difference of the two readings gives twice the power ab-
sorbed in friction, viz., 1,262 watts for the two machines,
or 631 watts per machine. This is excluded entirely from
the subsequent determinations of efficiency, as being a
quantity dependent on such arbitrary conditions as the
lubrication of the journals, the weight of the belt, and the
angle it makes with the horizontal.
In Table V., column I. is the speed of the dynamos;
column II. is the reading of the spring in grams; column
III. is the power transmitted by the belt in watts; column
IV. is the potential at the terminals of the generator;
column V. is the current passing in the external circuit be-
tween the two machines; column VI. is the resistance in-
troduced into the magnets of the motor by the rheostat;
column VII. is the power absorbed in the armature of the
generator; column VIII. is the power absorbed in the
armature of the motor; column IX. is the power absorbed
in the magnets of the generator; column X. is the power
absorbed in the magnets of the motor; column XI. is the
power absorbed in the connecting leads between the two
dynamos, in the rheostat resistance r, and in the standard
resistance used for measuring the current; column XII. is
the total electrical power developed in the generator; col-
118 DYNAMO MACHINERY AND ALLIED SUBJECTS.
TABLE V.
I.
II.
III.
IV.
V.
VI.
vn.
Revolutions
per
Grams.
Watts.
Volts.
Amperes.
Ohms.
Watts.
minute.
1
810
8,392
3,322
129.1
21.6
1.39
13
*
801
9,299
3,640
127.2
72.0
1.89
75
3
811
11,113
,">
125.8
150.0
2.72
267
4
808
10,433
4,119
124.4
186.0
2.72
8'.>7
5
792
10,000
4,124
116.5
211.0
2.72
4y
6
798
ltt,S97
t;.:,y.
110.6
351.0
4.59
1,309
7
764
17,0<JO
.;..,,:,
110.12
358.0
4 c'.i
1,300
8
706
17,804
6,065
110.6
360.0
4.59
1,875
9
778
16,556
6,294
102 3
369.0
4.09
1,430
10
756
20,412
7,541
90.8
i ; o
4.59
2,070
11
NIS
9,52(5
3,765
119.3
36.8
2.72
25
12
802
3,855
1,512
113.5
No current
....
13
814
8,175
1,262
....
....
....
VIII.
Watts.
IX.
Watts.
X.
Watts.
XI.
Watts.
XII.
Watts.
XIII.
Watts.
XIV.
Watte.
1
4
984
861
77
4,?a)
691
5,411
2
51
955
837
112
11.096
805
11,901
3
223
985
709
295
20,8%
9K8
21>S|
4
344
914
BBS
388
85,266
691
2.v.y
5
443
801
608
453
26..V.K)
BOO
gr,tto
6
1,222
722
455
1,101
41.433
no
42,323
7
1,268
716
473
1.131
42.087
828
42.915
8
1 289
722
455
1,152
42, 194
Kili
18,880
9
1 354
618
408
1,178
40,314
SAO
40.984
10
1979
554
848
1,670
46.244
459
M.7M
11
13
841
637
116
5,998
1,006
7,064
12
756
13
...
....
631
umn XIII. is half the power absorbed by the combination
less the known losses in the armatures, magnets, and ex-
ternal connections of the two machines; column XIV. is
the total mechanical power given to the generator, being
the sum of the powers given in columns XII. and XIII.
In Table VI. the percentage losses in the armature and
magnets of the generator are given, as also the sum of all
DYNAMO-ELECTRIC MACHINERY.
TABLE VI.
119
I.
II.
III.
IV.
V.
VI.
Per cent.
Per cent.
Per cent
Per cent.
Per cent.
Per cent.
1
0.24
18.20
12.76
68.8
57.28
39.40
2
0.63
8.93
6.76
84.58
82.99
70.19
3
1.88
4.27
4.52
90.00
90.15
81 . 13
4
1.53
3 52 .
2.66
92.28
92.65
85.49
5
1.83
2.94
2.415
92.80
93.12
86.42
6
3.09
1.71
2.10
93.10
93.30
86.86
7
3.17
1.67
1.93
93 23
93.39
87.07
8
3.17
1.67
1.93
93.23
93.43
87.10
9
3.51
1.75
1.59
93.39
93.50
87.32
10
4.43
1.19
0.98
93.39
93.36
87.19
11
0.35
11.9
15.1
72.65
65.77
47.78
other losses as obtained from column XIII. in Table V.;
also the percentage efficiency of the generator, of the motor,
and of the double conversion. Column I. is the percentage
loss in the generator armature; column II. is the percent-
age loss in the generator magnets; column III. is the per-
centage sum of all other losses in the generator; column
IV. is the percentage efficiency of the generator; column
V. is the percentage efficiency of the motor; column VI.
is the percentage efficiency of the double conversion.
In this series of experiments, in all cases from Nos. 1 to
10 inclusive, the brushes, both of the generator and motor,
were set at the non-sparking point; but in No. 11 no lead
was given to the brushes of the generator, and consequently
there was violent sparking throughout the duration of the
experiment.
In No. 12 the magnets were separately excited with a
current giving 113.5 volts across their terminals. The
power absorbed must be due entirely to local currents in
the core of the armature and to the energy for the reversal
of magnetization of the core twice in every revolution of
the armature.
120 DYNAMO MACHINERY AND ALLIED SUBJECTS.
No. 13 gives the results of the experiments on the fric-
tion of the bearings and in bending the belt already
referred to.
It will be observed that the figures in column XIII. are
calculated by deducting the power absorbed in the arma-
tures and magnets and by extraneous resistances from the
total power given to the combination as measured by the
dynamometer. They must therefore include all the energy
dissipated in the core of the armature, whether in local
currents or in the reversal of its magnetization ; also the
energy dissipated in local currents in the pole pieces, if
such exist; also the energy spent in reversing the direction
of the current in each convolution of the armature as they
are successively short circuited by the brushes. Further,
it will include the waste in all the connections of the ma-
chine from the commutator to its terminals and the friction
of the brushes against the commutator. A separate experi-
ment was made to determine the amount of this last
constituent, but it was found to be too small to be capable
of direct measurement by the dynamometer. Moreover,
from the manner in which the figures in this column are
deduced, any error in the dynamometric measurement will
appear wholly in them. Since, undoubtedly, the first two
components enumerated are the most important, and the
conditions determining their amount are practically the
same throughout the series, the close agreement of the
figures in the column is a fair criterion of the accuracy
of the observations. Probably 100 watts is the limit of
error in any of the measurements. Such an error would
affect the determination of the efficiency when the machines
were working up to their full power by less than per cent.
It has been assumed that the sum of these losses is
DYNAMO-ELECTRIC MACHINERY.
equally divided between the two machines. This will not
accurately represent the facts, as the intensities of the
fields and the currents passing through the armatures
differ to some extent in the two machines. The inequality,
however, cannot amount to a great quantity, and if it
diminishes the efficiency of the generator it will increase
the efficiency of the motor by a like amount, and contrari-
wise. In No. 11 of the series the effect of the sparking at
the brushes of the generator is very marked, the power
wasted amounting to at least 250 watts.
If it be assumed that the dissipation of energy is the
same whether the magnetization of the core is reversed by
diminishing and increasing the intensity of magnetization
without altering its direction, or whether it is reversed by
turning round its direction without reducing its amount
to zero, a direct approximation may be made to the value of
this component. (J. Hopkinson, Phil. Trans., vol. clxxvi,
1885, p. 455.)
The core has about 16,400 cubic centimetres of soft iron
plates; hence loss in magnetizing and demagnetizing when
the speed is 800 revolutions per minute = 16,400 X *f- X
13,356 ergs per second = 292 watts.
Eeferring to Table VI., it appears that the efficiency ap-
proaches a maximum when the current, passing externally
between the two machines, is about 400 amperes. Let C
be the current in the armature, p its resistance, W the
power absorbed in all parts of the machine other than the
armature; then, if the speed is constant, the efficiency is
. EC -W-(?p . _ . ,,
approximately - =-~ , where E is the electro-
& L>
W
motive force, This is a maximum when 7* + C p is a
122 DYNAMO MACHINERY AND ALLIED SUBJECTS.
minimum, which occurs when W= C*p; when the loss in
the armature is equal to the sum of all other losses. For
the machines under consideration the experimental results
verify this deduction. But in actual practice the rate of
generation of heat in the armature conductors, when a
current of 400 amperes was passed for a long period, would
be so great as to trench upon the margin of safety de-
sirable in such machines. Of the total space, however,
available for the disposition of the conductors, only about
one fourth part is actually occupied by copper, the re-
mainder being taken up with insulation and the inter-
stices left by the round wire. If the space occupied by
the copper should be increased to three fourths of the total
space available, while the cooling surface remained the
same, the current could be increased 75 per cent, and the
efficiency increased 1.3 per cent, approximately, as all
losses other than that in the armature wires would not be
materially altered.
The loss in the magnets is also susceptible of reduction.
It has already been shown that for a given configuration
of the magnetic circuit and a given electromotive force the
section of the wire of the magnet coils is determinate.
The length is, however, arbitrary, since within limits the
number of ampere convolutions is independent of the
length. An increase in the length will cause a propor-
tionate diminution in the power absorbed in the magnet
coils. If the surface of the magnets is sufficient to dissi-
pate all the heat generated, then the length' of wire is
properly determined by Sir William Thomson's rule that
the cost of the energy absorbed must be equal to the con-
tinuing cost of the conductor.
DYNAMO-ELECTRIC MACHINERY. 123
APPENDIX.
(Added Aug. 17.)
Since the reading of the present communication experi-
ments have been tried on machines having armatures
wound on the plan of Gramme and with differently ar-
ranged magnets; the experiments were carried out in a
closely similar manner to that already described.
DESCRIPTION OF MACHINES.
The construction of these machines is shown in Figs. 39,
Fio. 39.
40, and 41, of which Fig. 39 shows an elevation, Fig. 40 a
section through the magnets, Fig. 41 a longitudinal sec-
tion of the armature. It will be observed that the magnetic
circuit is divided. The pole pieces are of cast iron and
124 DYNAMO MACHINERY AND ALLIED SUBJECTS.
are placed above and below the armature and are extended
laterally. The magnet cores are of wrought iron of cir-
cular section and fit into the extensions of the east iron
Fio. 40.
pole pieces, so that the area of contact of the cast iron is
greater than the area of section of the magnet. The mag-
netizing coils consist of 2,196 convolutions on each limb
Fio. 41.
of copper wire, No. 17, B.W.G., in No. 1 machine, and
2,232 convolutions in No. 2 machine. The pole pieces are
bored to receive the armature, leaving a gap on either side
subtending an angle of 41 at the axis.
MACIUNEkY. 125
The bearings are carried upon an extension of the lower
pole piece.
The following table gives the principal dimensions of
the magnets in No. 1 machine :
cms.
Length of magnet limbs between pole pieces 26.0
Diameter of magnet, limb 15.24
Boreof fields 26.7
Width of pole piece parallel to the shaft 24.1
Width of gap between poles 8.6
The armature is built up of plates as in the machine al-
ready described, and is carried from the shaft by a brass
frame between the arms of which the wires pass.
The principal dimensions are as follows:
cms.
Diameter of core 24.1
Diameter of hole through core I 14.0
Length of core over end plates 24.1
The core is wound on Gramme's principle with 160 con-
volutions, each consisting of a single wire, No. 9, B.W.G.,
the wire lying on the outside of the armature in a single
layer. The commutator has 40 bars.
This dynamo is compound wound, and is intended for a
normal output of 105 volts, 130 amperes, at a speed of
1,050 revolutions per minute. The resistance of the
armature is 0.047 ohm, and of the magnet shunt coils 26.87
ohms.
There is here no yoke, and consequently A t and l t do not
appear in the equation.
It is necessary to bear in mind that the magnetizing
force is that due to the convolutions on one limb, and that
the areas are the sums of the areas of the two limbs. In cal-
126 DYNAMO MACHINERY AND ALLIED SUBJECTS.
dilating induction from E.M.F. it is also necessary to remem-
ber that two convolutions in a Gramme count as one in a
Hefner-Alteneck armature.
A^y the section of the core is 245 sq. cms.; allowances
for insulation reduce this to 220.5 sq. cms.
/, ; this is assumed to be 10 cms., but it will be seen
that an error in this value has a much more marked
effect on the characteristic in this machine than in the
other.
A t ; the angle subtended by the bored face of the
pole pieces is 139; the mean of the radii of the pole pieces
and the core is 12.45 cms. Hence the area of 139 of
the cylinder of this radius is 768.3 sq. cms. ; add to this a
fringe of a width 0.8 of the distance from core to
pole pieces, as already found necessary for the other
machine, and we have 839.5 sq. cms. as the value of A t .
J, is 0.8 cm.
A t is 365 sq. cms. (i.e., the area of two magnet cores).
l t is 26.0 cms.
A t is taken to be 532 sq. cms., viz., double the smallest
section of the pole piece.
7, is a very uncertain quantity; it is assumed to be 15
cms.
The expression already used requires slight modification.
Inasmuch as the pole pieces are of cast iron, a different
function must be used. Different constants for waste field
must be used for the field, the pole pieces, and the magnet
core. We write
DYNAMO-ELECTRIC MACHINERY. 127
The function f is taken from Hopkinson, Phil. Trans., vol.
clxxvi, 1885, p. 455, Plate 52. v^ v w and v b were deter-
mined by experiment, as described below; their values are
v t = 1.05
v, = 1.18
r b = 1.49
Comparing the curves in Figs. 28 and 29 with that in
Figs. 42 and 43, the most notable difference is that in the
present case the armature core is more intensely magnetized
than the magnet cores. No published experiments exist
giving the magnetizing force required to produce the in-
duction here observed in the armature core, amounting to
a maximum of 20,000 per sq. cm. We might, however,
make use of such experiments as the present to construct
roughly the curve of magnetization of the material; thus
we find that with this particular sample of iron a force of
740 per cm. is required to produce induction 20,000 per sq.
cm. : this conclusion must be regarded as liable to consider-
able uncertainty.
The observations on the two machines are plotted to-
gether, but are distinguished from each other as indicated.
They are, unfortunately, less accurate than those of Figs. 28
and 29, and are given here merely as illustrating the method
of synthesis.
EXPERIMENTS TO DETERMINE
The method was essentially the same as is described on
pp. 96 to 99, and was only applied to No. 1 machine.
128 DYNAMO MACHINERY AND ALLIED SUBJECTS.
s
-
1
1
8
I
-
~
-
\
i
oooa
fl
^
1
j
^
4.
*
1
2
<.
1
|
S^
^
^
^
'
.
A
\\
-^ r?
S S
J
t
V
> J
T
-
'
- ^
c
.
[
o
f
'
<
1
'
f-
-.
g
j
c
ri
DYNAMO-ELECTKIO MACHINERY. 129
r/
on in 10
In
/
1
'/
"?"
.//
/
'^
r
f 5 "
/
^
>"
ft
X-'
'//
u
V
/
i
IT/
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o
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^S
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1
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<1
1
f
X
^
i
X
x
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%
/
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^
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^
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^
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lane
ntegra
ofila
netiein
fbrce
FIG. 43. SYNTHESIS OF CHARACTERISTIC CURVE WITH GRAMME ARMATURE.
This figure is the same as the left-hand part of Fig. 42, but on a larger scale.
130 DYNAMO MACHINERY AND ALLIED SUBJECTS.
Keferring to Fig. 44, a wire A A was taken four times round
the middle of one limb of the magnet, a known current was
suddenly passed round the magnets, and the elongation of
the reflecting galvanometer was observed : it was found to
be 214 scale divisions, giving 107 as the induction through
Fio. 44.
the two magnet limbs in terms of an arbitrary unit. The
coil was moved to the top of the limb as at B B ; the elon-
gation was reduced to 206, or 103 for the two limbs; we
take the mean induction in the magnet to be 105. A wire
was taken three times round the whole armature in a hori-
zontal plane as at C C\ the elongation observed was 222
divisions or 74 in terms of the same units. A wire was
taken four times round one half of the armature as at D D\
DYNAMO-ELECTRIC MACHINERY. 131
the elongation was 141, or induction in the iron of the
armature 70.5, whence we have
74 :=1.05.
70.5
It may be well to recall here that r t is essentially depend-
ent on the intensity of the field; strictly the line B in
Figs. 42 and 43 should not be straight, but slightly curved.
Four coils were taken round the upper pole piece at E E\
the elongation was 159, giving 79.5 on the two sides. Coils
at F F give a higher result, 87.5, owing to the lines of in-
duction which pass round by the bearings of the machine,
and across to the upper ends of the magnets. v 6 is taken
to be = 1.18.
EFFICIENCY EXPERIMENTS.
The method and instruments were those already de-
scribed, pp. 110 to 112, excepting that the current was
measured by a Thomson's graded galvanometer, which had
been standardized against a Clark's cell in the position and
at the time when used. The resistance of leading wires
and galvanometer was 0.034 ohm, the series coils introduced
for compounding the machines were also brought into use,
and the losses due to their resistance (0.024 ohm) find a place
in columns XII. and XIII. of Table VII., in which column
I. is lead of brushes of the dynamo, positive for the gene-
rator, negative for the motor; column II., revolutions per
minute; column III., deflection of spring in grams; column
132 DYNAMO MACHINERY AND ALLIED SUBJECTS.
TABLE VII.
I.
n.
III.
IV.
V.
VI.
VII.
VIII.
Degrees.
Revolutions.
Grains.
Watts.
Volts.
Amperes
Ohms.
Watts.
17.5
1098
7711
4419
100.1
139.0
00
955
5
1094
2722
1554
103.8
41.2
18.8
10:.
1114
1814
1063
104.7
7.85
11
IX.
X.
XI.
XII.
xm.
XIV.
XV.
XVI.
XVII.
Watts.
Watts.
Watts.
Watts.
Watts.
Watts.
Watts.
Watts.
Watts.
895
872
497
464
657
16,395
289
16,684
78
400
138
5ft
41
146
5.015
294
r,.:xi
3
408
406
6
1
2
1,687
128
1,765
* In this experiment the direction of the current had become reversed, and
No. 2 machine was generator.
IV., watts by dynamometer; column V., volts at terminals of
generator; column VI., amperes in external circuit; column
VII., rheostat resistance; column VIII., watts in generator
armature; column IX., watts in motor armature; column
X., watts in generator shunt magnet coils; column XL,
watts in motor shunt; column XII., watts in generator
series magnet coils; column XIII., watts in motor series;
column XIV., watts in external resistances; column XV.,
total electrical power of generator; column XVI., half the
sum of losses unaccounted for; column XVII., total me-
chanical power applied to generator.
TABLE VIII.
Generator Generator
Armature; Shunt
Generator
Series
Coils.
Other
Losses.
Efficiency
of
Generator.
Efficiency
of
Motor.
Efficiency
of Double
Conversion.
5.8
2.0
2.2
7.5
3.0
1.0
1.9
5.5
87.1
84.0
89.0
92.0
77.5
77.8
DYNAMO-ELECTRIC MACHINERY. 133
Table VIII. gives the losses and efficiencies as percent-
ages in exactly the same way as in Table VI., excepting
that another column is introduced for the loss in the series
coils of the magnets of the generator.
The core of the armature contains about 6,500 cub. cms.
of iron. Hence energy of magnetizing and demagnetizing
when the speed = 1,100 revolutions per minute = 6,500 X
' X 13,356 in ergs per second = 159 watts.
134 DYNAMO MACHINERY AND ALLIED SUBJECTS.
DYNAMO-ELECTRIC MACHINERY.*
THE following is intended as the completion of a Paperf
by Drs. J. and E. Hopkinson (Phil Trans., 1886). f The
motive is to verify by experiment theoretical results con-
cerning the effect of the currents in the armature of dyna-
mo machines on the amount and distribution of the mag-
netic field which were given in that Paper, but which were
left without verification. For the sake of completeness,
part of the work is given over again.
The two dynamos experimented upon were constructed
by Messrs. Siemens Brothers & Co., and are identical as
far as it is possible to make them. They are mounted
upon a common base plate, their axles being coupled to-
gether, and are referred to in this Paper respectively as
No. 1 and No. 2.
Each dynamo has a single magnetic circuit consisting of
two vertical limbs extended at their lower extremities to
form the pole pieces, and having their upper extremities
connected by a yoke of rectangular section. Each limb,
* It must not be supposed from his name not appearing in this short Paper
that my brother. Dr. E. Hopkinson. had a minor part in the earlier Paper. He
not only did the most laborious part of the experimental work, but contributed
his proper share to whatever there may be of merit in the theoretical part of
the Paper. J. H.
t The Paper here referred to is that reprinted on pages 79 to 133 of this
volume.
DYNAMO-ELECTRIC MACHINERY. 135
together with its pole piece, is formed of a single forging
of wrought iron. These forgings, as also that of the yoke,
are built up of hammered scrap iron, and afterwards care-
fully annealed. Gun-metal castings bolted to the base
plate of the machine support the magnets.
The magnetizing coils on each limb consist of sixteen
layers of copper wire 2 mms. in diameter, making a total of
3,968 convolutions for each machine. The pole pieces are
bored out to receive the armature, leaving a gap above and
below subtending an angle of 68 at the centre of the shaft.
The opposing surfaces of the gap are 1.4 cm. deep.
The following table gives the leading dimensions of the
machine:
cms.
Length of magnet limb 66.04
Width of inaguet limb 11.48
Breadth of magnet limb 38.10
Length ofyoke 38.10
Width of yoke 12.06
Depth ofyoke 11.43
Distance between centres of limbs 23.50
Bore of fields 21.21
Depth of pole piece 20.32
Thickness of gun-metal base 10.80
Width of gap 12.06
The armature core is built up of soft iron disks, No. 24
B. W. G., which are held between two end plates screwed on
the shaft.
The following table gives the leading dimensions of the
armature :
cms.
Diameter of core 18.41
Diameter of shaft. 4.76
Length of core , 38,10
136 DYNAMO MACHINERY AND ALLIED SUBJECTS.
The core is wound longitudinally according to the Hef-
ner von Alteneck principle with 208 bars made of copper
strip, each 9 mms. deep by 1.8 mm. thick. The commuta-
tor is formed of fifty-two hard drawn copper segments in-
sulated with mica, and the connections to the armature so
made that the plane of commutation in the commutator is
vertical when no current is passing through the armature.
Each dynamo is intended for a normal output of 80 am-
peres, 140 volts, at 880 revolutions per minute. The resist-
ance of the armature measured between opposite bars of
the commutator is 0.042 ohm, and of each magnet coil
13.3 ohms.
In the machine the armature core has a greater cross
section than the magnet cores, and consequently the mag-
netizing force used therein may be neglected. The yoke
has the same section as the magnet cores, and is therefore
included therein, as is also the pole piece. The formula
connecting the line integral of the magnetizing force and
the induction takes the short form
where
n is the number of turns round magnet;
c is the current round magnet in absolute measure;
/ Q the distance from iron of armature to rim of magnet;
AI the corrected area of field;
/the total induction through armature;
l a the mean length of lines of magnetic force in magnets ;
A a the area of section of magnets;
* Phil. Trans., 188(5; page 88 of this volume.
DYNAMO-ELECTRIC MACHINERY. 137
v the ratio of induction in magnets to induction in ar-
mature;
/ the function which the magnetizing force is of the in-
duction in the case of the machine actually taken
from Dr. J. Hopkinson on the " Magnetization of
Iron," Phil. Trans., 1885, Figs. 4 and 5, Plate 47.
In estimating A^ we take the mean of the diameter of
the core and of the bore of the magnets 19.8 cms., and the
angle subtended by the pole face 112, and we add a fringe
all round the area of the pole face equal in width to the
distance of the core from the pole face. This is a wider
fringe than was used in the earlier experiments,* because
the form of the magnets differs slightly. The area so
estimated is 906 sq. cms.
Z 3 is taken to be 108.8 cms.
A 3 is 435.5 sq. cms.
v was determined by the ballistic galvanometer to be
1.47. It is to be expected that, as the core is actually
greater in area than the magnets, v will be more nearly
constant than in the earlier experiments. It was found to
be constant within the limits of errors of observation.
Referring to Fig. 45, the curve C is the curve x I 3 f f -jH,
and the straight line B is the curve x = 2 /, -j-, while the
^2
full line D is the characteristic curve of the machine,
as given by calculation.
* Phil. Trans., 1886; page 95 of this volume,
138 DYNAMO MACHINERY AND ALLIED SUBJECTS.
The marks -j- indicate the results of actual observations
on machine No. 1, and the marks the results on machine
No. 2, the total induction / being given by the equation :
potential difference in volts X 10 8
208 X revolutions per second
Experiments made upon the power taken to drive the
machine under different conditions show that it takes about
Line! rteeral of Mae letisinaf Force
*0000
250 watts more power to turn the armature at 660 revolu-
tions when the magnets are normally excited than when
they are not excited at all. The volume of the core is
9,465 cub. cms., or in each complete cycle the loss per cubic
950 ^ ^Q*
centimetre is n x 9 465 = 24 > 000 er g 8 -
The loss by hysteresis is about 13,000 (Phil. Trans.,
1885, p. 463) if the reversals are made by variation of in-
tensity of the magnetizing force and the iron is good
wrought iron. This result is similar to that in the earlier
DYNAMO-ELECTRIC MACHINERY. 139
Paper,* where it is shown that the actual loss in the core,
when magnetized, is greater than can be accounted for
by the known value of hysteresis.
EFFECTS OF THE CURRENT IN THE ARMATURE.
Quoting from the Royal Society Paper [page 103 of this
volume], " The currents in the fixed coils around the mag-
nets are not the only magnetizing forces applied in a
dynamo machine the currents in the moving coils of the
armature have also their effect on the resultant field.
There are in general two independent variables in a
dynamo machine the current around the magnets and
the current in the armature; and the relation of E. M. F.
to currents is fully represented by a surface. In well con-
structed machines the effect of the latter is reduced to a
minimum, but it can be by no means neglected. When a
section of the armature coils is commutated, it must inevi-
tably be momentarily short circuited ; and if at the time of
commutation the field in which the section is moving is
other than feeble, a considerable current will arise in that
section, accompanied by waste of power and destructive
sparking. . . .
" Suppose the commutation occurs at an angle A in advance
of the symmetrical position between the fields, and that the
total current through the armature be C, reckoned positive
in the direction of the resultant E. M. F. of the machine,
i.e., positive when the machine is used as a generator of
electricity. Taking any closed line through magnets and
* See page 121 of this volume.
140 DYNAMO MACHINERY AND ALLIED SUBJECTS.
armature, symmetrically drawn asABCDJS FA [Fig. 46],
it is obvious that the line integral of magnetic force is di-
minished by the current in the armature included between
angle A in front and angle X behind the plane of symme-
try. If m be the number of convolutions of the armature,
the value of this magnetizing force \&
C - =
opposed to the magnetizing force of the fixed coils on the
Fio. 46.
magnets. Thus if we know the lead of the brushes and the
current in the armature we are at once in a position to cal-
culate the effect on the electromotive force of the machine.
A further effect of the current in the armature is a material
disturbance of the distribution of the induction over the
DYNAMO-ELECTRIC MACHINERY. 141
bored face of the pole piece; the force along BC [Fig.
46] is by no means equal to that along D E. Draw the
closed curve B C G H B, the line integral along G, and HB
is negligible. Hence the difference between force H G and
777 1C
B G is equal to 4 n G -= = 2 K m G, where K is the angle
COG."
To verify this formula is one of the principal objects of
this Paper.
A pair of brushes having relatively fixed positions near
together, and insulated from the frame and from one
another, are carried upon a divided circle, and bear upon
the commutator. The difference of potential between these
brushes was measured in various positions round the com-
mutator, the current in the armature, the potential differ-
ence of the main brushes, and the speed of the machine
being also noted.
The results are given in Figs. 47, 48, 49, and 50, in
which the ordinates are measured potential differences,
and the abscissae are angles turned through by the ex-
ploring brushes. The potential differences in Fig. 47
were measured by a Siemens voltmeter, and eacli ordi-
nate is therefore somewhat smaller than the true value,
owing to the time during which the exploring brashes
were not actually in contact with the commutator seg-
ments. But this does not affect the results, because the
area is reduced in the same proportion as the potential
differences. In Figs. 48, 49, and 50 the potential differ-
ences were taken on one of Sir William Thomson's quad-
rant electrometers, and are correct.
Take Fig. 47, in which machine No. 1 is a generator. A
142 DYNAMO MACHINERY AND ALLIED SUBJECTS.
centimetre horizontally represents 10 of lead, and the
ordinates represent differences of potential between the
brushes. The area of the curve is 61.3 sq. cms., and repre-
sents 130 volts and a total field of ? X ^ X 10'
= 4.31 X 10* lines of induction. This is, of course, not the
actual field, which is 3 per cent, greater on account of the
+~^*
>T*~
+^
*~~~^
\
f
*~**^
\
I
\^
**^
6O 1OO ISO 2OO
FlO. 47.
resistance of the armature, but is represented by an area 3
per cent, greater. An ordinate of 1 cm. will represent an
1 ' ' 1
induction of - - x 10" = 7.0 X 10* lines in 10. The area
01. o
of 10 is 39.5 X 1.73 = 68.3 sq. cms.* Hence an ordinate
of 1 cm. represents an induction of 1,024 lines per square
centimetre. The difference between ordinates at 50 and
140 is 2.5; hence the difference of induction is actually
2,560. Theoretically, we have K = n m = 104 C = 9.4.
Therefore 2 K m C = 3,072, and this is the line integral of
magnetizing force round the curve.
Let A be the induction at 50 and A + 6 at 140: these
* In calculating this area, the allowance for fringe at ends of armature is
taken less than before, because the form of opposing faces differs.
DYNAMO-ELECTRIC MACHINERY.
143
also are the magnetizing forces. Hence (^4 -f d) 1.4 A 1.4
= 2 x: w (7 ; 6 = 2,200, as against 2,560 actually observed.
Take Fig. 48, in which No. 2 machine is a motor. The
total field = x . x i 8 = 5.15 x 10' lines of indue-
104 /wO
tion. Since the area of the diagram is 53.5 sq. cms., an
5 15
ordinate of 1 cm. = -^ X 10" = 96 X 10 4 lines of induc-
oo.o
*-H
'"'"* s
c
/
t *"*^
N
X
s
\
310 260 210
FlO. 48.
tion in 10. Hence an ordinate of 1 cm. represents an
9.6 X 10*
induction of ' Q Q = 1,400 lines per square centimetre.
Do.o
The difference between ordinates at 320 and at 230 is 2.0;
hence the difference of induction is actually 2,800. Theo-
2*mC 3| X 104 X 11.4
retically, we have - = - - = 2,666, as
I 1.4
against 2,800 actually observed.
In Fig. 49 No. 1 machine is a generator. The total field
= jjjj X jig X 10" = 3.97 X 10" lines. The area of the
diagram is 90.9 sq. cms., and therefore an ordinate of 1 cm.
O Qiy
= - - x 10" = 4.37 X 10* lines in 10. Hence an ordi-
144 DYNAMO MACHINERY AND ALLIED SUBJECTS.
4 37 X 10 4
nate of 1 cm. represents an induction of - - = 639
Oo.O
lines per square centimetre. The difference between ordi-
200
nates at 50 and at 140 is 4.5; hence the difference of
induction is actually 2,877. Theoretically, we have -
_ 3} X 104 X 12.9
1.4
In Fig. 50 No. 2 machine is a motor. The total field
63.5
x
" " 4 ' 9G x 10 " lines * The area of the
diagram is 112.2 sq. cms., and therefore an ordinate of 1 cm.
4.96
112.2
X 10' = 4.42 X 10 4 lines in 10. Hence an ordi-
4 42
nate of 1 cm. represents an induction of - ~ X 10 4 = 647
Oo.o
lines per square centimetre. The difference between ordi-
nates at 323 and at 233 is 4.2; hence the difference
DYNAMO-ELECTRIC MACHINERY.
145
of induction is actually 2,718. Theoretically, we have
2*mC 3! X 104 X 12.3
j = - -j-j = 2,870, as against 2,718 act-
ually observed.
7
310
26O
810
FIG. 50.
At page 108 of the preceding Paper on Dynamo-Electric
Machinery it is shown that
C\
J,
where /= F(4 7tnc)is the characteristic curve when C= 0,
and X is the lead of the brushes.
The following is an endeavor to verify this formula.
The potentials both upon the magnets and upon the
brushes were taken by a Siemens voltmeter, and are rough.
The speeds were taken by a Buss tachometer, and there is
some uncertainty' about the precise lead of the brushes,
owing to the difficulty in determining the precise position
146 DYNAMO MACHINERY AND ALLIED SUBJECTS.
of the symmetrical position -between the fields, and also to
the width of the contacts on the commutator.
It was necessary, in order to obtain a marked effect of
the armature reaction, that the magnet field should bo
comparatively small, that the current in the armature
should be large, and the leads of the brushes should be
large.
The two machines had their axles coupled so that No. 1
could be run as a generator, and No. 2 as a motor. The
magnets were in each case coupled parallel, and excited by
a battery each through an adjustable resistance. The two
armatures were coupled in series with another battery, and
the following observations were made :
Potential on
Magnets in volts.
Potential on
Brushes.
Speed per
Minute.
Current in
Amperes.
Lead of
Brushes.
No. 1
No. 2
24-24
2929
86-67
86-84
880
880
10-2-108
102-103
26
29
Prom which we infer:
Current in
Magnets.
4wnc.
Corrected Poten-
tial for Resistance
of Armature.
Total
Induction.
/.
No. 1
No. 2
1.78
2.15
8,900
10,750
70.8
80.7
2.80xlO
2.65x10*
As there was uncertainty as to the precise accuracy of
the measurements of potential, it appeared best to remeas-
ure the potentials with no current through the armature
with the Siemens voltmeter placed as in the last experi-
ment. Each machine was therefore run on open circuit
with its magnets excited, and its potential was measured.
DYNAMO-ELECTRIC MACHINERY.
14?
Potential on Mag-
nets in volts.
Potential on
Brushes.
Speed per
Minute.
Potential at
880 Revs.
No. I
No. 2
25-25
2828
90-90
79-80
880
715-710
90.0
98.2
From which, since the formula is reduced to
the characteristic being practically straight, we infer :
Potential on
Magnets.
Potential on
Brushes.
Induction,
I=F(4irnc).
No. 1
No. 2
24
29
86.4
101.7
2.82xlO
3.30xlO
We have further :
.\ = 0.45 for No. 1;
- = 2,920;
A = 0.5 for No. 2;
-4m C = 443,800.
4Am(7\
4Xm(7
"~~*4x r> A ' 2
4XmC
/ 4\mC\
\ v '
v
v 2l t
V
\ v '
^-^-
1
2
1,314
1,460
199,700
221,900
7,586
9,290
2.41xlO
2.90xlO
2.21xlO
2.68xlO
It has already appeared that experiment gives for / in
No. 1 2.3 X 10 6 , and in No. 2 2.65 X 10*. The difference
is probably due to error in estimating the lead of the
brushes, which is difficult, owing to uncertainty in the
position of the neutral line on open circuit.
148 DYNAMO MACHINERY AND ALLIED SUBJECTS.
THEORY OF ALTERNATING CURRENTS, PAR-
TICULARLY IN REFERENCE TO TWO
ALTERNATE CURRENT MACHINES CON-
NECTED TO THE SAME CIRCUIT.
IN my lecture on Electric Lighting, delivered before the
Institution of Civil Engineers last year,* I considered the
question of two alternate current dynamo machines con-
nected to the same circuit, but having no rigid mechanical
connection between them ; and I showed that, if two such
machines be coupled in series, they will tend to nullify
each other's effect ; if parallel, to add their effects. f The
subject is one which already has practical importance and
application, and may have much more in the future; it is
also one suited for discussion, and upon which discussion
is desirable. I therefore venture to bring before the
Society what I said in my lecture some other ways of look-
ing at the same subject, and an experimental verification,
* This Paper is reprinted on pag*>s 40 to 78 of this volume.
t November 22, 1884. My attention has only to-day been called to a paper by
Mr. Wilde, published by the Literary nnd Philosophical Society of Manchester,
December 15, 1868, also Philosophical Magazine, January, 1869. Mr. Wilde
fully describes observations of the synchronizing control between two or more
alternate current machines connected together. I am sorry I did not know of
his observations when I lectured before the Institution of Civil Engineers, that
I might have given him the honor which was his due. If his paper had been
known to those who have lately been working to produce large alternate cur-
rent machines, it would have saved them both labor and money.
THEORY OF ALTEENATING CURRENTS. 149
together with solutions of other problems requiring similar
treatment.
The general explanation, amounting to proof so far as
machines in series are concerned, is given in the following
extract from my lecture :
" There remains one point of great practical interest in
connection with alternate current machines: How will
they behave when two or more are coupled together to aid
each other in doing the same work ? With galvanic bat-
teries we know very well how to couple them, either in
parallel circuit or in series, so that they shall aid, and not
oppose, the effects of each other; bnt with alternate cur-
rent machines, independently driven, it is not quite ob-
vious what the result will be, for the polarity of each
machine is constantly changing. Will two machines
coupled together run independently of each other, or will
one control the movement of the other in such wise that
they settle down to conspire to produce the same effect, or
will it be into mutual opposition ? It is obvious that a
great deal turns upon the answer to this question, for in
the general distribution of electric light it will be desirable
to be able to supply the system of conductors from which
the consumers draw by separate machines, which can be
thrown in and out at pleasure. Now I know it is a com-
mon impression that alternate current machines cannot be
worked together, and that it is almost a necessity to have
one enormous machine to supply all the consumers draw-
ing from one system of conductors. Let us see how the
matter stands. Consider two machines independently
driven, so as to have approximately the same periodic time
and the same electromotive force, If these two machines
150 DYNAMO MACHINERY AND ALLIED SUBJECTS.
are to be worked together, they may be connected in one
of two ways : they may be in parallel circuit with regard
to the external conductor, as shown by the full line in
Fig. 51, that is, their currents may be added algebraically
and sent to the external circuit, or they may be coupled in
series, as shown by the dotted line, that is, the whole cur-
rent may pass successively through the two machines, and
the electromotive force of the two machines may be added,
instead of their currents. The latter case is simpler. Let
us consider it first. I am going to show that if you couple
two such alternate current machines in series they will so
control each other's phase as to nullify each other, and
that you will get no effect from them; and, as a corollary
from that, I am going to show that if you couple them in
parallel circuit they will work perfectly well together, and
the currents they produce will be added; in fact, that you
THEORY OF ALTERNATING CURRENTS.
151
cannot drive alternate current machines tandem, but that
you may drive them as a pair, or, indeed, any number
abreast. In diagram, Fig. 52, the horizontal line of abscissae
represents the time advancing from left to right; the full
curves represent the electromotive forces of the two
machines not supposed to be in the same phase. We want
to see whether they will tend to get into the same phase or
to get into opposite phases. Now, if the machines are
coupled in series, the resultant electromotive force on the
circuit will be the sum of the electromotive forces of the
nur
two machines. This resultant electromotive force is rep-
resented by the broken curve ///; by what we have already
seen in Formula IV. [p. 52, this volume], the phase of
the current must lag behind the phase of the electro-
motive force, as is shown in the diagram by curve IV, thus
. . . Now the work done in any machine is
represented by the sum of the products of the currents
and of the electromotive forces, and it is clear that, as the
phase of the current is more near to the phase of the lag-
ging machine // than to that of the leading machine /, the
lagging machine must do more work in producing elec-
152 DYNAMO MACHINERY AND ALLIED SUBJECTS.
tricity than the leading machine; consequently its velocity
will be retarded, and its retardation will go on until the
two machines settle down into exactly opposite phases,
when no current will pass. The moral, therefore, is, do not
attempt to couple two independently driven alternate cur-
rent machines in series. Now for the corollary: A, B,
Fig. 51, represent the two terminals of an alternate cur-
rent machine; a, b, the two terminals of another machine
independently driven. A and a are connected together,
and B and b. So regarded, the two machines are in series,
and we have just proved that they will exactly oppose each
other's effects, that is, when A is positive, a will be
positive also; when A is negative, a is also negative.
Now, connecting A and a through the comparatively high
resistance of the external circuit with B and b, the cur-
rent passing through that circuit will not much disturb, if
at all, the relations of the two machines. Hence, when A
is positive, a will be positive, and when A is negative, a
will be negative also; precisely the condition required that
the two machines may work together to send a current
into the external circuit. You may, therefore, with con-
fidence, attempt to run alternate current machines in
parallel circuit for the purpose of producing any external
effect. I might easily show that the same applies to a
larger number; hence there is no more difficulty in feed-
ing a system of conductors from a number of alternate
current machines than there is in feeding it from a num-
ber of continuous current machines. A little care only is
required that the machine shall be thrown in when it has
attained something like its proper velocity. A further
corollary is that alternate currents with alternate current
THEORY OF ALTERNATING CURRENTS.
153
machines as motors may theoretically be used for the
transmission of power." *
Although the proof of this corollary regarding motors is
similar to what we have just been going through, it may
be instructive to give it. In the accompanying diagrams,
Figs. 53 and 54, the full lines / and 21 represent the
Fio.68.
electromotive forces of the two machines (generator and
receiver) ; the dotted line, curve 777 (. . . .), the resultant
electromotive force; and the curve IV, the resulting cur-
rent, each in terms of the time, as abscissae. The only dif-
ference between the two diagrams is, that in Fig. 53 the
two machines have equal electromotive forces, while in
Fig. 54 the receiving machine has double the electromotive
force of the generator. In both figures the receiving
machine lags behind the phase of direct opposition to the
generator by one quarter of a period, or something less.
Now observe, the resultant electromotive force must be in
* " Of course in applying these conclusions it is necessary to remember
that the machines only tend to control each other, and that the control of the
motive power may be predominant and compel the two or more machines to
run at different speeds."
154 DYNAMO MACHINERY AND ALLIED SUBJECTS.
phase behind the receiver, but in advance of the generator.
Also observe, the current must be in phase behind the re-
sultant electromotive force, and may be one quarter of a
period behind, provided only the self induction be large
enough compared with the resistance. The current will
then be less than a quarter period behind the generator.
This machine will do work upon the current, but the cur-
<J
FIG. 54.
rent will be more than a quarter period behind the receiv-
ing machine; therefore in the receiver the current does
work upon the machine.
The subject is illustrated by the following problems. Of
course any of them may be treated more generally by con-
sidering the machines as unequal, or by introducing other
periodic terms, but I do not see that this would throw more
light on the subject:
I. Two alternate current machines, equal in all respects,
are connected in series and independently driven at the
same speed, to determine the current, etc., in each.
THEORY OF ALTERNATING CURRENTS. 155
Let y be the coefficient of self induction of each, r the
2 n
resistance, x the current at time t, and E sin =- (t -\- T)
2#
and E sin -^ (t r) the electromotive forces. Then
regarding the coefficient of self induction as constant,
which it is not exactly, and neglecting the effect of currents
other than those in the copper wire, the equation of motion is
= E \ sm -^ (t + i
27r 2 TT r
or ^ a; '+ r x = 12 sm ~- cos ^ ;
whence
I p 27TT V
~^~ ( 2 TT/ 27T X 2?r#
a = /9 ^ -,\ ! sm fff- + ^- cos -^r-
Work done by the leading machine per second
~T~ ( ZTTT Zxy .
From this it at once follows that the leading machine does
T
least work, and will tend to increase its lead until r = - ,
156 DYNAMO MACHINERY AND ALLIED SUBJECTS.
when the two machines will neutralize each other, as al-
ready proved geometrically. The leading machine may ac-
tually become a motor and do mechanical ivorJc, although
its electromotive force is precisely equal to that of the fol-
loiving machine.
Considering the important case when r is negligible, we
have
ZTTT
E cos -. cos
X =
27TX
T~
T
rate of working = - .
4 .'2|Z
T
This is the maximum when r = -, and then it is equal to
o
the maximum work which can be obtained from either
machine when connected to a resistance only, which occurs
when that resistance is ~ ; the current, also, is the same
as when the maximum work is being done on resistance,
and is of the current the machine will give if short
circuited. The difference of potential between the two
leads connecting the machines, whether r = or not, is
E cos ^-Tff- sin jfr If there be no work done on the re-
T
ceiving machine and r = 0, T -, and the amplitude of
THEORY OF ALTERNATING CURRENTS. 157
the difference of potential between the leads is E\ if,
on the other hand, the maximum work is being transmitted,
the potential measured will be of that observed when
either machine is run on open circuit.
II. Two machines are coupled parallel and connected to
an external circuit resistance R.
Let x l , x t be currents in the two machines. The ex-
ternal current will be x l -f # a , and consequently the differ-
ence of potential at the junction, R (x l -J- # 3 ).
Let the electromotive forces of the two machines regarded
in this case as connected parallel be E sin - -i= -- -, and
let the self induction and resistance of each be $-y and 2 r.
The equations of motion then are :
=E sin - R (x,
whence
and
\ T7 ^ 7ft . 2 TIT
- X = E cos -- sm --,
168 DYNAMO MACHINERY AND ALLIED SUBJECTS.
Solving these,
27TT
2 arr
Electrical work done by the leading machiue
7f y , 7T T 7TT )
-- 7^- Bin -^- COS ;- j,
%7T V . %
THEORY OF ALTERNATING CURRENTS. 159
This expression shows that the leading machine does most
work in all cases. Suppose r is small compared with R
~
and , also that R = jr~> we have the work done
per second
T
Make r = --, and we see that the following machine
o
will then do no work; when T exceeds this, the following
machine becomes a motor and absorbs electrical work.
III. Suppose the terminals of an alternate current ma-
chine are connected to a pair of conductors, the difference
of potential between which is completely controlled by con-
nection with other alternate current machines.
Let y and R be the coefficient of self induction and the
resistance of the machine and its own conductors up to the
point at which the potential is completely controlled. Let
the difference of potential of the main conductors be
A sin p- , and let the electromotive force of the machine
, D . 27f(t-r)
be B sin - -^ '- .
Equation of motion is
2 n (t r) 2 7ft
yx' + Rx = B sm ^ * A sm 7fr ,
160 DYNAMO MACHINERY AND ALLIED SUBJECTS,
whence
_**(t-r) *ny
cos
;r(*-T)) j 27T* 2*x 2*n~|
-^r- ^ j- - ^4 | R sin -^- ^- cos -^- j- J,
Electrical work done by the machine in unit of time
-
= x B sin - ,., - =
T
If T be positive, that is, if machine be lagging in its phase,
work done is less than if it be negative; hence T will tend
to zero, or the machine will tend to adjust itself to add its
currents to that of the system of conductors. The machine
may act as a motor even though its electromotive force be
greater than that of the system, for let
R %7T
- = tan
7'
THEORY OF ALTERNATING CURRENTS. 161
work (electric) done by machine
AB
T
T
this has a minimum value when <f> + f = -j- , and then
the mechanical work done by machine or electrical work
received by the machine
B ( RB }
and this is positive, provided
' i> *
There are two or three other problems of sufficient in-
terest to make it worth while giving them here, although
not directly relating to alternate current machines coupled
together.
IV. To determine the law of an alternate current
through an electric arc.
It has been shown by Joubert that in an arc the differ-
ence of potential is of approximately constant numerical
162 I>YNAMO MACHINERY AND ALLIED SUBJECTS.
value, reversing its value discontinuously with the reversal
of the current, probably at the instant of reversal of cur-
rent. We shall assume, then, that there is in the arc a
constant electromotive force, A, always opposed to the
current, except when the current ceases, and that then its
value is zero.
The equation of motion is
yx' + ltx = EBin^^A,
the negative sign being taken when x is + **> the positive
when x is negative. Solving generally,
A E / 27ty 2?rt
% ~T~ ~/S I /rt _ .. \ I 7fi~ COS rn
This equation will continuously hold good for a half period
from x = to x = again, but at each half period the
arbitrary constant C is changed with the sudden change of
sign of A. It 'is determined by the consideration that if,
for a certain value t of t, x should vanish, it shall vanish
T
again when t = t -f- --- . This applies to the case when E
A
is sufficiently large, as is practically the case; but if the
current should cease for a finite time this condition will be
varied, and instead of it we have the condition x = when
9 "jf /
E sin -=- = A. This latter case I do not propose to
consider further.
THEORY OF ALTERNATING CURRENTS. 163
Let
2 n v %7tt.
T
Putting * = t and t = t, + -^ , we have
_R RT
Ce *' .e 2 Y*
equations to determine t and C.
Eliminating C,
RE' .27
- . sin -
164 DYNAMO MACHINERY AND ALLIED SUBJECTS.
Having obtained t , C is given by equation
o A R I R
This gives the complete solution of the problem.
A case of special importance is that in which R is small ;
let us therefore consider the case R = 0; the solution
then is
T 2 nt
yx= - .tf cos -~ A t + C.
In the same way as before,
2 7t t A 71
c=.
The limiting case to which the solution applies is given by
x' = when * = *. +
2 7f t
Ci%
^ ~^~ T)'
or A = E X 0.538.
Roughly, we may say that, in order that the current may
not cease for a finite time, E must be at least double of A;
THEORY OF ALTERNATING CURRENTS. 165
A will of course depend upon the length of the arc. The
work done in the arc will be proportional to the arith-
metical mean value of the current taken without regard to
sign. This is of course quite a different thing from the
mean current as measured by an electro-dynamometer.
Let us examine what error is caused by estimating the
work done in the arc as equal to the current measured by
the dynamometer multiplied by the mean difference of
potential.
The actual work done per second
, T
The mean square of the current as measured by the elec-
tro-dynamometer is
2 /^o
f I
*/*
and the work done by this current is apparently the square
root of the above expression multiplied by A. It is easy
to. see that this is greater in all cases than the work done,
but it is worth while to examine the extent of the error.
If we treated, the arc as an ordinary resistance, we should
assume work per second
166 DYNAMO MACHINERY AND ALLIED SUBJECTS.
2
Taking a fairly practical case, assume A = E; we have
actual work per second
A*T 1
work done estimated by electro-dynamometer
25
= ^ a y 1 7235
X SOY/ 12"'
or nearly part too much. This will suffice to show that
the matter is not a mere theoretical refinement. Another
erroneous method of estimating the power developed in an
arc is to replace by a resistance and adjust this resistance
till the current as measured by an electro-dynamometer
is the same as with the arc, and assume that the work done
in the resistance is the same as the work done in the arc.
Returning to the expression
ny 2
we may inquire, given T A and the dimensions of the ma-
chine, how ought it to be wound or its coils connected that
THEORY OF ALTERNATING CURRENTS. 167
most work may be done in the arc. If the number of con-
volutions be varied, E will vary as the convolutions, y as
their square; therefore y oc E* ; we are therefore to deter-
mine E so that = A IE* is a maximum which
occurs when E = n A. When the resistance of the circuit
is taken into account, this result will be modified. It
suffices to prove that it is desirable that the potential of
the machine should be materially in excess of that required
to maintain the arc.
V.* In all that precedes it is assumed, not only that y is
constant, but that the copper conductor of the armature is
the only conductor moving in the field. If there be iron
cores in the armature, we shall approximate to the effect
by regarding such cores as a second conducting circuit.
Slightly changing the notation, let L be coefficient of self
induction of the copper circuit, N coefficient of self induc-
tion of the iron circuit and R l its resistance, I 1 the mag-
netic induction of the field magnets upon the iron circuit,
and M the coefficient of mutual induction of the two cir-
cuits, y the current in the iron. The equations of motion
are obtained from the expression for the energy, viz.,
%{Lx* -j- %Mxy + Ny* 2 Ix 2 1' y},
and are
r ~/ i i,r / i n d I 2 7t A 27ft
L x' -f M y' -f- R x = -J-T = =, cos =- ,
d P 27fS 27ft
MX' 4- Nyr + R'u = -=-r = m cos ^-,
* Fide also "Encyclopaedia Britannica," article " Lighting."
168 DYNAMO MACHINERY AND ALLIED SUBJECTS.
for in general the iron cores and the copper conductor are
symmetrically arranged. Assume
x = a sm
.
= b cos
27ft
, . 27ft
= a' sm -- b' cos
and substitute in the equations of motion; we have the
following four equations to determine the constants , b,
a', ':
A
or
and
= 0,
= 0.
These equations contain the solution of the problem, but
are too cumbersome to be worth while solving generally;
THEORY OF ALTERNATING CURRENTS. 169
we will, however, prove the statements made in the lecture
before the Civil Engineers.
1. Compare short circuit and open circuit, that is, R =
very nearly, and R = oc*. In the former case 'we find that
work done in the iron is diminished, and if B = =r- we
lj
have the paradoxical result that there are no currents in-
duced in the iron of the cores and no work is required to
drive the machine. This, of course, can never actually
occur, because R can never absolutely vanish. It suffices
to show, however, that the current in the copper circuit
may diminish the whole power required to drive the ma-
chine to an amount less than the power required to drive
the machine on open circuit.
2. The other statement related to the effect of the cur-
rents in the iron upon the currents produced in the copper
circuit. Assume that the effect is a small one, for a first
approximation. Neglect it, that is, treat the currents in
the iron and the currents in the copper as independent of
each other, and then see how each would disturb the other.
The first approximation then is
AL ,_ EN
/T2 r>2) ** ' rrty pf2>
'+^4 ^ j +^-i-
.TR TR'
~
7,-
"
170 DYNAMO MACHINERY AND ALLIED SUBJECTS.
If we substitute these in the general equations as correc-
tions, we have
4;r
which shows that the disturbing effect of each circuit upon
the other is to diminish the apparent electromotive force,
but to accelerate its phase.
VI. A very similar problem is that of secondary genera-
tors or induction coils, whether used for the conversion of
high potentials to low, or the reverse. To treat it gener-
ally, taking the magnetization of the iron cores, which are
always used, as a non-linear function of the currents in the
coils, would be a matter of much difficulty; we therefore
assume, as is usual, that the coefficients of induction are
constants, noting in passing that this is not strictly the
fact, though it is very nearly the fact, when the cores are
not saturated and when the lines of magnetic induction
pass through non-magnetic space.
Let, then, R, r be the resistances of the primary and
secondary circuits;
L coefficient of self induction of the primary;
^coefficient of self induction of the secondary;
M coefficient of mutual induction of the two circuits;
THEORY OF ALTERNATING CURRENTS. 171
x and y the currents in the two circuits at time t;
JTihe electromotive force applied in the primary circuit
by an alternate current dynamo machine or other-
wise;
the equations of motion will be
Lx' + My' + Rx = X, }
MX' + Ny' + ry = 0. )
Various assumptions may be made as to X, but that most
likely to be adopted in the practical work of secondary
generators is that X is kept so adjusted that
2 n
x = A cos n t where n = ,
and to inquire how X will depend on the resistances
Ny' + r y = n A M sin n t,
y = a - ra . * ( n N cos n t + r sin n t),
9 if N* 4- r a v '
8 .
N
172 DYNAMO MACHINERY AND ALLIED SUBJECTS.
As in the case of the dynamo machine, the work done in
the secondary circuit is greatest when r = n N. The ex-
pression for X serves to show that when the secondary is
short circuited a loiver electromotive force of the generat-
ing circuit is required than when it is on open circuit. In
induction coils the electrostatic capacity of the coils them-
selves has important effects. An illustration of the effect
of electrostatic induction is found in the old-fashioned
Ruhmkorff coils. These were not wound symmetrically, but
in such wise that one end of the secondary coil was on the
whole towards the inside, the other towards the outside of
the bobbin. In such coils a spark to earth may be obtained
from the outside end, but not from the inside. The reason
is that the outer convolutions have smaller electrostatic
capacity than the inner ones. The terminals may be made
to give equal sparks by the simple expedient of laying a
piece of tinfoil around the whole coil and connecting it to
earth.
VII. Some time ago Dr. Muirhead told me that he had
observed that the effect of an alternate current machine
could be increased by connecting it to a condenser. This
is not difficult to explain : it is a case of resonance anal-
ogous to those which are so familiar in the theory of sound
and in many other branches of physics.
Take the simplest case, though some others are almost
as easy to treat. Imagine an alternate current machine
with its terminals connected to a condenser; it is required
to find the amplitude of oscillation of potential between the
two sides of the condenser. Let R y be the resistance and
2 71 t
self induction of the machine, E sin -~- its electromotive
THEORY OF ALTERNATING CURRENTS. 173
force, C the capacity of the condenser, V the difference of
potential sought, and x the current in the machine ; then
C V = x,
and
_ , f* f+ V -
~~ -*-* D fwj W J
whence
. % X . 27ft
+ R 0- sin
. . . T T 27TEC
amplitude of V is therefore
Now suppose E = 100 volts, the machine would light up
an incandescent lamp of about 69 volts. Let T = -% fa second,
174 DYNAMO MACHINERY AND ALLIED SUBJECTS.
2 n y
C = 100 microfarads, and =~ = 8 ohms, and R = -fa
ohm, all figures which could be practically realized; we
have amplitude of V = 80 E roughly, or the apparent
electromotive force would be increased eighty fold.
We now return to the principal subject of the present
communication. Some attempts have been made to verify
the proposition that two alternate current machines can
be advantageously connected parallel, but, I believe, till
recently without success. I had no convenient opportu-
nity for testing the point myself till last summer, when I
had two machines of De Meritens, intended for the light-
house of Tino, in my hands. I have made no determina-
tions of the constants of these machines, but between three
and four years ago I thoroughly tested a pair of similar
machines now in use at a lighthouse in New South Wales.
Each machine haa five rings of sixteen sections, and forty
permanent magnets. The resistance of the whole machine
as connected for lighthouse work (a single arc) was 0.0313,
its electromotive force (E ) when running 830 revolutions
per minute, 95 volts and ( ar-J = 0.044 ohm. It was
further remarked that the loss of power was least with a
maximum load, as is shown in the following table:
Power applied as measured in belt 3.1 4.8 5.6 6.5 5.4
Electric power developed 0.7 8.4 4.3 5.7 3.4
Mean current in amperes 7.7 38.6 51.7 73.6 151
This result illustrates well the conclusion arrived at in
Problem V. above.
Last summer the two machines for Tino were driven
THEORY OF ALTERNATING CURRENTS. 175
from the same countershaft by link bands, at a speed of
850 to 900 revolutions per minute; the pulleys on the
countershaft were sensibly equal in diameter, but those on
the machines differed by rather more than a millimetre,
one being 300, the other 299 mms. in diameter (about);
thus the two machines had not when unconnected exactly
the same speed. The pulleys have since been equalized.
The bands were of course put on as slack as practicable,
but no special appliance for adjusting the tightness of the
bands was used. The experiment succeeded perfectly at
the very first attempt. The two machines, being at rest,
were coupled in series with a pilot incandescent lamp
across the terminals; the two bands were then simulta-
neously thrown on : for some seconds the machines almost
pulled up the engine. As the speed began to increase, the
lamp lit up intermittently, but in a few seconds more the
machines dropped into step together, and the pilot lamp
lit up to full brightness and became perfectly steady and
remained so. An arc lamp was then introduced, and a per-
fectly steady current of over 200 amperes drawn off with-
out disturbing the harmony. The arc lamp being removed,
a Siemens electro-dynamometer was introduced between
the machines, and it was found that the current passing
was only 18 amperes, whereas, if the machines had been in
phase to send the current in the same direction, it would
have been more than ten times as great. On throwing off
the two bands simultaneously, the machines continued to
run by their own momentum, with retarded velocity. It
was observed that the current, instead of diminishing from
diminished electromotive force, steadily increased to about
50 amperes, owing to the diminished electrical control be-
176 DYNAMO MACHINERY AND ALLIED SUBJECTS.
tween the machines, and then dropped off to zero as the
machines stopped. Professor Adams will, I hope, give an
account of experiments he has tried wifh me, and on other
occasions, at the South Foreland. With De Meritens'
machines, I regard coupling two or more machines parallel
as practically the best way of obtaining exceptionally great
currents when required in a lighthouse for penetrating a
thick atmosphere.
AN UNNOTICED DANGER. 177
AN UNNOTICED DANGER IN CERTAIN APPA-
RATUS FOR DISTRIBUTION OF ELECTRICITY.
MANY plans have been proposed, and several have been
to a greater or less extent practically used, for combining
the advantage of economy arising from a high potential in
the conductors which convey the electric current from the
place where it is generated with the advantages of a low
potential at the various points where the electricity is used.
A low potential is necessary where the electricity is used ;
partly because the lamps, whether arc or incandescent, each
require a low potential, and partly because a high potential
may easily become dangerous to life. Among the plans
which have been tried for locally transforming a supply of
high potential to a lower and s,afer, the most promising is
by the use of secondary generators or induction coils. It
has been proved that this method can be used with great
economy of electric power and with convenience; under
proper construction of the induction coils it may also be
perfectly safe. It is, however, easy and very natural so to
construct them that they shall be good in all other respects
but that of safety to life that they shall introduce an un-
expected risk to those using the supply.
In a distribution of electricity by secondary generators,
an alternating current is led in succession through the
primary coils of a series of induction coils, one for each
178 DYNAMO MACHINERY AND ALLIED
group or system of lamps. The lamps connect the two
terminals of the secondary coil of the induction coils. It
is easy to so construct the induction coils that the differ-
ence of potential between the terminals of the secondary
coils may be any suitable number of volts, such as 50 or
100; while the potential of the primary circuit, as meas-
ured between the terminals of the dynamo machine, may
be very great, e.g., 2,000 or 3,000 volts. If the electromag-
netic action between the primary and secondary coils, on
which the useful effect of the arrangement depends, were
the only action, the supply would be perfectly safe to the
n
7
U A
rt
Fio. 55.
user so long as apparatus with which he could not interfere
was in proper order. But the electromagnetic action is
not the only one. Theoretically speaking, every induction
coil is also a condenser, and the primary coil acts electro-
statically as well as electromagnetically upon the secondary
coil. This electrostatic action may easily become danger-
ous if the secondary generator is so constructed that its
electrostatic capacity, regarded as a condenser, is other
than a very small quantity.
AN UNNOTICED DANGER. 179
Imagine an alternate current dynamo machine, A, Fig.
55, its terminals, B, C, connected by a continuous con-
ductor, B D C, on which may be resistances, self induction
coils, secondary generators, or any other appliances : at any
point is a condenser, E, one coating of which is connected
to the conductor, or may indeed be part of it ; the other is
connected to earth through a resistance, R. Let K be the
capacity of the condenser, Fthe potential at time t of the
earth coating of the condenser, U the potential of the other
coating, 2 the current in resistance R to the condenser from
the earth, being taken as positive, and the earth potential
as zero. We have
,
whence, since
U = A sin 2 n n t,
where A is a constant depending on the circumstances of
the dynamo circuit as well as the electromotive force of the
machine, and n is the reciprocal of the periodic time of the
machine, we have
KR % + x = 2 n n KA cosZrtn t,
9 - a { 2 7t n KR sin 2 n n t -j- cos 2 n n t \ ,
x =
-
mean square of x = . mean square of A.
Let us now consider the actual values likely to occur in
practice. Let the condenser E be a secondary generator;
180 DYNAMO MACHINERY AND ALLIED SUBJECTS.
let the resistance R be that of some person touching some
part of the secondary circuit, and also making contact to
earth with some other part of the body ; n may be anything
from 100 to 250, say 150; /Twill depend on the construc-
tion of the secondary generator it may be as high as 0.3
microfarad or even more, but there would be no difficulty
even in large instruments in keeping it down to one hun-
dredth of this or less. The mean square of A will depend
on the circumstances of other parts of the circuit; it might
very easily be as great, or very nearly as great, as the mean
difference of potential between the terminals of the ma-
chine if the primary circuit were to earth at C. Suppose,
however, that the circuit B D C is symmetrical, that E is
at one end, and that another person of the same resistance
as the person at E is touching the secondary circuit of the
secondary generator F at the other end of the circuit. In
that case, if 2,400 be difference of potential of the machine,
mean square of A will be 1,200; in which case we have,
taking R as 2,000 ohms,
mean square of
2 n X 150 X 0.3 X 10
, r.
====
t/(2 n X 150 X 0.3 X 10- 6 X 2,000)' + 1
= about 0.3 ampere.
Experiments are still wanting to show what current may
be considered as certain to kill a man, but it is very doubtful
whether any man could stand 0.3 ampere for a sensible
length of time. It is probable that if the two persons both
'took firm hold of the secondary conductors of E and F 9
both would be killed. If the person at F be replaced by
AN UNNOTICED DANGER. 181
an accidental dead earth on the secondary circuit of F, the
person at E would experience a greater current than 0.3
ampere.
It follows from the preceding consideration that second-
ary generators of large electrostatic capacity are essentially
dangerous, even though the insulation of the primary cir-
cuit and of the primary coils from the secondary coils is
perfect. The moral is for the constructor, Take care that
the secondary generators have not a large electrostatic
capacity, say not more than 0.03 microfarad, better less
than -jlnj- microfarad; for the inspector, Test the system
for safety. The test is very easy. Place a secondary gen-
erator of greatest capacity at one end of the line and con-
nect its secondary circuit to earth through any instrument
suitable for measuring alternate currents under one am-
pere; put the other end of the primary to earth; the read-
ing of the current measuring instrument should not exceed
such a current as it may be demonstrated a man can en-
dure with safety.
182 DYNAMO MACHINERY AND ALLIED SUBJECTS.
INDUCTION COILS OR TRANSFORMERS.
THE transformers considered are those having a con-
tinuous iron magnetic circuit of uniform section.*
Let A be area of section of the core;
m and u the number of convolutions of the primary
and secondary coils, respectively;
R, r, and p their resistances, p being the resistance
of the secondary external to the transformer;
x and y currents in the two coils;
a induction per square centimetre;
a the magnetic force;
I the length of the magnetic circuit;
E = B sin 2 n (t/T), the difference of potentials
between the extremities of the primary ;
T being the periodic time.
We have
4 it (m x + ny) = I a; (1)
E = R x m A a;
= (r + p)y-nAa.
(2)
(3)
* For a discussion of transformers in which there is a considerable gap in the
magnetic circuit, see Ferraris, Torino, Accad. Sci. Mem., vol. 37, 1885 ; also
chapter on the " Theory of Alternating Currents," in this volume,
INDUCTION COILS OR TRANSFORMERS. 183
From (2) and (3),
n E = n R x m (r + p) y. (4)
Substituting from (1),
x\n*R + m*(r + p)\ = <tf E + (la/7t) m(r + p); (5)
y{n*R + m*(r + p)} =-nmE+ (lac/7t)nR; (6)
(r + p)mE laR(r + p) _ , ,
n* 7* + ra* (r + p) T 4 Trjrc 2 7? + m a (/ H- p) {' v ;
We may now advantageously make a first approximation.
Neglect I ty in comparison with knmx, that is, assume the
permeability to be very large; we have
m ..
* *
~ ' *-'
For practical purposes these equations are really suf-
ficient.
We see first that the transformer transforms the poten-
tial in the ratio n/vn, and adds to the external resistance
of the secondary circuit p a resistance (n* R/m*} + r.
This at once gives us the variation of potential caused by
varying the number of lamps used. The phase of the sec-
ondary current is exactly opposite to that of the primary.
In designing a transformer it is particularly necessary to
take note of equation (9), for the assumption is that a is
limited so that I <x may be neglected, The greatest value
184 DYNAMO MACHINERY AND ALLIED SUBJECTS.
of a is R/{(2 Tt/T) mA\, and this must not exceed a
chosen value. We observe that B varies as the number of
reversals of the primary current per unit of time.
But this first approximation, though enough for practical
work, gives no account of what happens when transformers
are worked so that the iron is nearly saturated, or how
energy is wasted in the iron core by the continual reversal
of its magnetism. The amount of such waste is easily
Fio. 66.
estimated from Swing's results when the extreme value of
a is known, but it is more instructive to proceed to a second
approximation, and see how the magnetic properties of the
iron affect the value and phase of x and y. We shall, as a
second approximation, substitute in equations (5), (6), (7)
INDUCTION COILS OR TRANSFORMERS. 185
values of a deduced from the value of a furnished by the
first approximation in equation (9).
In the accompanying diagram, Fig. 56, Ox represents or,
y represents , and z the time t.
The curves A B CD represent the relations of a and a.
E F G the induction a as a function of the time, and HIK
the deduced relation between a and t. We may substitute
the values of a obtained from this curve in equations (5)
and (6), and so obtain the values of x and y to a higher
degree of approximation. If the values of a were expressed
Fro. 57.
by Fourier's theorem in terms of the time, we should find
that the action of the iron core introduced into the ex-
pression for x and y, in addition to a term in cos (2 TC t/T)
which would occur if a and a were proportional, terms in
sin (2 it t/T) and terms in sines and cosines of multiples
of Znt/T. It is through the term in sin (%7tt/T) that
the loss of energy by hysteresis comes in.
A particular case, in which to stay at a first approxima-
tion would be very misleading, is worthy of note. Let an
attempt be made to ascertain the highest possible values of
186 DYNAMO MACHINERY AND ALLIED SUBJECTS.
a by using upon a transformer a very large primary current
and measuring the consequent mean square of potential in
the secondary circuit by means of an electrometer, by the
heating of a conductor, or other such device. The value
of a will be related to the time somewhat as indicated by
AB C D E FO in Fig. 57; for simplicity assume it to bo
as in Fig. 58; the resulting relations of potential in the
Fio. 88.
secondary and the time will be indicated by the dotted line
HIJKOL MNP Q. The mean square observed will be
proportional to ML . ^L P ; but ML . L P is proportional
to EL, hence the potential observed will vary inversely as
^L P, even though the maximum induction remain con-
stant. If, then, the maximum induction be deduced on
the assumption that the induction is a simple harmonic
function of the time, results may readily be obtained vastly
in excess of the truth.
TEST OF WESTINGIIOTJSE TRANSFORMERS. 187
REPORT TO THE WESTINGHOUSE COMPANY
OF THE TEST OF TWO G,500-WATT WEST-
INGHOUSE TRANSFORMERS.
BEFORE giving any of the results of the tests I have
made with your tran sformers, it will be well to explain the
methods of experiment adopted. The instantaneous value
at any epoch in the period of the difference of potential
between any two points of a circuit in which the potential
difference is varied periodically is made effective on the
measuring instrument by means of a rotating contact
maker attached to the shaft of the alternate current gen-
erator. This contact maker was constructed for the King's
College laboratory by Messrs. Siemens Brothers. It makes
contact once in each revolution for a period of about three
quarters of a degree, and breaks it for the rest of the revo-
lution. It is entirely insulated, and so can be connected to
any part of the circuit. The position of the contact can
be varied, and the variation be read off on a graduated
circle of 13J inches diameter divided into degrees, and by
estimation the variation can be read to one tenth of a
degree. The two points between which it is desired to
measure a potential difference are connected through the
contact maker to a. condenser and a quadrant electrometer,
188 DYNAMO MACHINERY AND ALLIED SUBJECTS.
as shown in Fig. 59, in which A and B are the points, the
potential difference of which at a stated epoch is to be
measured, C the revolving contact maker, D the reversing
switch of the electrometer, E the condenser, of which the
capacity can be varied, F the quadrant electrometer. It is
evident that the quadrant electrometer will give a reading
proportional to the potential difference of A and B, when
C makes contact. If there were no leakage, it would at
once give this potential. It is to obviate the effect of
leakage that the condenser is introduced, and the amount
of the effect was determined by varying the condenser
thus: When the condenser had capacity 1, 0.5, and 0.2
microfarads, the readings of the electrometer for a given
potential difference of an alternating current at the posi-
tion in the period of maximum electromotive force were
138, 136, and 132, respectively. The rate of loss of poten-
tial will be proportional to the reciprocal of the capacity,
whence we infer that the true reading, if insulation were
perfect, would be 1394, and hence the readings are always
corrected by adding one per cent. When the potential
difference was too great for the electrometer it was reduced
in any desired ratio by two considerable resistances intro-
duced between the points to be measured in the usual way
(Fig. 60). The potential difference may, of course, be
measured in other ways. An ordinary voltmeter may be
TEST OF WESTINGHOUSE TRANSFORMERS. 189
placed between A and B, in which case it must be standard-
ized with the contact breaker in circuit; and it will depend
for its constant on the duration of the contact, which may
vary. Further, it gives, not the difference of potential
Fio. 60.
at any definite epoch, but the mean difference for the
whole time of the contact. The condenser may be used
and its potential be measured by discharge through a gal-
vanometer: this is open to the objection that if there be
any leakage, the result will depend on the time at which
the contact is broken by the condenser key in relation to
the time at which it was made by the revolving contact
maker. Lastly, a Clark cell may be used, by a method
which Major Cardew pointed out to me (Fig. 61), the re-
iDJUSTABLt RESISTANCES ' (] GALVANO
rmmwms Q C V
FlO. 61.
sistance being adjusted till there is no deflection. This
is open to the same objection as the first, namely, that it
gives the mean of the potential differences which occur
during the contact. By making use of the first-mentioned
method we have the means of measuring accurately any
potential difference at any epoch of the period, and of
knowing the epoch.
190 DYNAMO MACHINERY AND ALLIED SUBJECTS.
For these experiments two transformers intended to be
identical were available, each transforming between 2,400
and 100 volts. It was most convenient on account of the
resistance available to couple these" transformers up from
100 to 2,400 in the first or No. 1 transformer, then down
from 2,400 to 100 in the second or No. 2 transformer, and
to take up the energy from the second in a non-inductive
resistance. The arrangement is shown in Fig. 62.
The obvious way in returning the efficiency of the com-
bination would be to measure, at various epochs of half a
period, the potential differences of the terminals of the
TRANSFORMED NO. 1. TRANSFORMER NO. 2.
FM.OL
machine and the current passing in the No. 1 transformer;
in like manner, at the same epochs, to measure either the
potential differences or the current passing to the non-in-
ductive resistance, thence to deduce the power supplied to
the first transformer and taken from the second. This
would be open to certain objections: we are comparing
two nearly equal magnitudes and desire their ratio; the
ratio will be afflicted with the full error arising from an
error in the determination of either magnitude, and such
errors may be material, as the observations are not simul-
taneous, and conditions may change between one series of
observations and another.
These objections are avoided by the method adopted.
The current from No. 2 is observed at certain epochs, the
TEST OF WESTINGIIOTJSE TfcANSFOttlVlEfcS. 191
difference of current between No. 2 and No. 1, and the
difference of potential difference of No. 2 and No. 1 at the
same epoch. These give the currents and potentials of
No. 1 at the same epochs as the corresponding determina-
tions of No. 2, and the difference will only be afflicted with
the proportion of error of those differences. For example,
suppose the efficiency of the combination were 90 per cent.,
and the possible error of determination of power 1 per
cent., our result might be anything from 38 per cent, to 92
per cent, if made in the obvious way, but if made by dif-
ferences the maximum loss would be 10.1 per cent., and
the possible least determination of the efficiency would be
89.8 per cent. The method is essentially similar to the
>TO NON-INDUCTIVE
* RESISTANCE
NO. 2. 1
TO REVOLVING CONTACT MAKER
FIG. 63.
method I described* and subsequently used for testing
dynamos. The measurements for difference of potential
differences are made as in Fig. 63. For current differences
(Fig. 64), where G is a known small non-inductive resist-
*TO NON-INDUCTIVE
TO REVOLVING CONTACT MAKER
FIG. 64.
ance, the two currents will, of course, slightly disturb each
other, but this is readily allowed for in the calculations.
* Phil. Trans., 1886, page 347.
192 DYNAMO MACHINERY AND ALLIED SUBJECTS.
Another method would be to couple them as in Fig.
65, G v and #, being equal non-inductive resistances.
This arrangement is quite free from disturbance, but re-
quires two resistances adjusted to exact equality. A single
transformer can be tested in the same way, though in this
1
TO REVOLVING CONTACT'MAKER
FIG. 65.
case reliance must be placed upon resistances to reduce the
current of the low potential coil, and to reduce the poten-
tial of the high potential coil in the ratio of the number of
windings in the two coils.
The current was throughout generated by a Siemens
alternator with 12 magnets, run at a speed between 830
and 840 revolutions per minute, which gives a frequency
of 5,000 per minute, or 83 to 84 per second.
The first experiment tried * was with the two transform-
ers coupled, but with No. 2 transformer on open circuit, or
on nearly open circuit, for a high resistance for purposes
of measurement was interposed between the terminals of
the low resistance coil of No. 2 transformer. The actual
* So far as I know, the first discussion of endless magnetic circuit transform-
ers, based on the actual properties of the material, is in a note by myself (Proc.
Roy. Soc., vol. xui., and Tiie Electrician, vol. xvni., p. 421.) Definite results
were obtained by methods generally similar to those now used by Prof. Ryan
(The Electrical World, Dec. 28, 1889). The theory of transformers is well set
forth by Prof. Fleming (The Electrician, April 22 and 29, 1892).
TEST OF WESTINGHOUSE TRANSFORMERS. 193
results are given in Table IX., and are expressed in Fig. 66.
Tables X., XL, and XII. give the results for half power,
f
TABLE IX.
S3
Potential No. 2.
Potential No. 1.
n
Thick Coils.
Thick Coils.
s
S .
m
go
No. 1.
Thick
Coils.
Amperes.
Square of
Volts.
Vmean 2
= 101.9.
Watts
supplied to
No. 1.
Volts.
Square of
Volts.
P. D.
Sec Nos.
1 and 2.
Volts.
Vineau 3
= 101.1
Volts.
267
-2.2
+ 25.4
645
-0.9
+ 26.3
692
- 57.9
270
-0.3
+ 70.2
4,9:28
-1.2
+ 71.4
5,098
- 21.4
273
4-1.1
+ 95.3
9,082
-1.1
+ 96.4
9,292
+ 106.0
276
+ 2.1
+120.4
14,496
-1.1
--121.5
14,761
+ 255.1
279
+ 2.8
+147.7
21,816
-1.1
--148.8
22,140
+ 416.6
282
285
+ 3.2
+ 3.4
+147.2
+119.8
21,668
14,351
+ 0.9
+ 0.7
+148.1
--120.5
21,935
14,520
+ 473.9
+ 409.7
288
291
294
+ 3.5
+ 3.7
+ 3.5
+ 97.8
+ 26io
9,565
5,084
676
+ 0.6
+ 0.4
+ 0.3
+ 98.4
-- 71.7
-- 25.97
9,683
5,140
674
+ 344.4
+ 260.3
+ 90.9
102,311
103,935
2,282.6
194 DYNAMO MACHINERY AND ALLIED
nearly full power, and full power, and the sets of curves of
Figs. 67, 68 and 69 give the results of the table. In
these tables the first column gives the position of the con-
tact brush in degrees, so that 60 on this scale corresponds
with a complete cycle. Three degrees are thus -^-^
. Oo.o X <v(J
of a second. The second column of Table IX. is the cur-
rent in the thick coil of No. 1 transformer, as determined
by the difference of potential at the two ends of a non-
inductive resistance in which the current passes. The
third column is the potential difference of No. 2 trans-
former, a direct determination. The fourth column is
solely for the purpose of determining the square root of
the mean of the squares of the third column. This column
is a direct determination of the difference of potential of
No. 1 and No. 2, obtained in the manner explained with
reference to Fig. 63.
The sixth column is the deduced potential difference of
the terminals of the thick wire of No. 1 transformer, being
the sum of the third and fifth columns. The seventh col-
umn, like the fourth, is merely for the purpose of deter-
mining the square root of the mean of the squares of col-
umn six, while the eighth gives the rate at which power is
given out or received by the pair of transformers.
If the transformers had been exactly equal, the poten-
tials for the two given by Table IX. would have been equal,
though they would have differed a little in phase owing to
the lines of magnetic induction which pass through the
non-magnetic space between the two coils of the trans-
former.* The difference shows that No. 1 transformer has
*Prof. Perry has already pointed out that the effect of such an induction
cannot be entirely neglected, even in endless circuit transformers.
TEST OF WESTINGHOUSE TRANSFORMERS. 195
a ratio of transformation slightly greater than No. 2. If
we correct the potential of either No. 1 or No. 2, there
196 DYNAMO MACHINEKY AND ALLIED SUBJECTS.
still remains a difference between them, but this difference
will be greatest about when the potentials are nil. This
is due to the lost induction just referred to. In order to
check the conclusion that the two transformers are not
KHOM WAyHTNCtERMINXtB
NAAA/WV \^A/Wv*
ywvwvwvww /WW.VWWM
TO CONTACT MAMER iEl.ECTROME.1ER,
Fio.70
precisely equal, they were directly compared, as in Fig. 70.
The transformers were coupled parallel, as in Fig. 70, and
TEST OF WESTINGHOUSE TRANSFORMERS. 197
the difference of potential of the two high potential coils
was measured : the value of its square root of mean square
was 12.5 volts, the potential of the transformer being 2,400.
This does not necessarily imply that the potentials of the
two transformers differ by one half per cent.; it maybe
largely due to a difference of phase between the two.
The current supplied to the No. 1 transformer is to be
accounted for by the currents necessary to magnetize the
Z
FIG. 71.
two transformers, and by the local currents in their cores.
To ascertain the former, the curve of magnetization of one
of the transformers was determined by the ballistic galva-
nometer for nearly the same induction as in Table IX., the
changes of current supplied by a battery being made by a
reversing switch, or by suddenly introducing resistance
198 DYNAMO MACHINERY AND ALLIED SUBJECTS.
into the primary circuit, and the consequent changes of
induction being measured by the galvanometer. The
tardiness of change of current in the transformer due to
its self induction was sufficiently reduced by using many
cells and a considerable resistance. The results are shown
in Fig. 71 for a single transformer. In this curve the
abscissae are the currents in the thin coil of the trans-
former, divided by 24 to reduce it to the same effect as it
would have had if it had been in the thick coil. The
ordinates are the inductions as measured by the kick on
the galvanometer, but reduced to a scale to make them
directly comparable with the volts when the transformer is
used with an alternating current. These results are not
TEST OF WESTINGHOUSE TRANSFORMERS. 199
given in absolute units. The procedure to determine
points on the curve was: first, pass the maximum current
corresponding to the point C\ next, suddenly diminish the
current by inserting suitable resistance in the thin coil
circuit, and observe the kick the drop of ordinate from
C to A corresponds to the kick, and the abscissa of A is
the current after it has been reduced; next, reverse the
current, and observe the kick the kick corresponds to the
further drop of ordinates from A to B. In this manner a
series of points are determined on the curve. Fig. 72
shows the relation between induction and magnetizing
current for the pair of transformers, as deduced from the
experiments with alternating currents set forth in Table IX.
The ordinates in this curve are the area of the curve of
potentials of Fig. 66, for the ordinates of this latter curve
are the rates at which the induction is changing, while the
abscissae are the currents in the thick wire at corresponding
times. The points marked in Fig. 73 give the remainder
after deducting the magnetizing current as estimates in
Fig. 71 from the currents of Fig. 72 that is to say, Fig.
71 is corrected first for the small difference in maximum
induction; then, corresponding to any induction, the cur-
rent is taken from the curve, it is doubled, as there is only
one transformer, and the result is deduced from the cor-
responding current of Fig. 72. The differences are, the
magnetizing current equivalent and opposite in effect to
the local currents in the cores. If the local currents were
equivalent to a current in a single secondary circuit, the
points of Fig. 73 ought to have had the form of the full
line of Fig. 73, drawn through the points -f, in which the
abscissae are proportional to the potential difference, and
200 DYNAMO MACHINERY AND ALLIED SUBJECTS.
the ordinates to the induction. Returning to Table IX., we
find that the fall of potential difference on open circuit in
the whole combination is 0.8 volt, and that the loss of
power in magnetizing the cores and in local currents is
222.86 watts, that is, a loss for each transformer of 114.13
watts. The total loss of 228 watts maybe divided into 126
watts accounted for by hysteresis and 102 watts due to
local currents.
Referring now to Table XI. and Fig. 68, the earlier col-
umns explain themselves, but a word is necessary about
the last six columns. The watts supplied to No. 1 are
simply the products at each time of the volts at its termi-
TEST OF WESTINGHOUSE TRANSFORMERS. 201
nals and the amperes passing through, similarly to the
watts given out by No. 2. We see first that the efficiency
of the whole combination with this load is 93.73 per cent.,
and hence the efficiency of one transformer, if the losses
in the two are equal, may be taken as 96.9 per cent. The
fall of potential in the whole combination is 6.1 volts, but
the fall with no load is 0.8 volt; hence the variation due to
the load with constant potential on the thin coil of No. 1
is 5.3 volts, or, if the fall of potential in the two transform-
ers were equal, which it is not, for a single transformer
2.65 volts. Assuming that the transformers are equal, the
power lost in resistance would be expected to be the mean
of mean current X the difference of potential difference,
or 215.4 watts. It is, in fact, 150 watts, as given by multi-
plying the square of currents by resistances. But the
transformers are not exactly equal, and there is the waste
magnetic field, both of which will have a small effect on
the distribution of loss between the two classes of loss,
viz., that by hysteresis and local currents, and that by re-
sistance, but none upon the gross efficiency.
The other tables, X. and XII., are arranged in exactly the
same way as Table XL, but the number of observations
on Table XII. is insufficient to bring out all the peculiari-
ties of the transformers.
It has already been stated that, if the loss of potential
due to load in the two transformers be equal, it will amount
to 2.65 per cent. The following experiment was tried to
ascertain if this loss was equal: The transformers were
coupled in series as before. The mean potential difference
of the thick wire was measured by Thomson's multicellu-
lar, and of the thin wire by Thomson's electrostatic volt-
202 DYNAMO MACHINERY AND ALLIED SUBJECTS.
meter. The mean of a considerable number of experiments
is given in the following table, the load being the same as
in Table XL, and the results being corrected to the same
potential of the thin wire :
Number.
Full Load.
Open Circuit.
Thomson's
Multicellular.
Thomson's
Electrostatic.
Thomson's
Multicellular.
Thomson's
Electrostatic.
1
2
2,380
2,380
99.8
94.2
2,380
2,380
97.0
96.2
This shows that of a total drop of 4.8 volts, 2.8 volts oc-
curred in No. 1, and 2 volts in No. 2. There is no doubt
of the fact that the drop is greater in No. 1 than in No. 2,
which is connected with the waste field between the two
coils. Of course these transformers are intended to work
exactly as No. 2 is working, in which case the drop from
no load to nearly full load, as shown by this experiment, is
2.0 volts. The way in which this waste field causes ine-
quality of drop of potential in the two transformers, coupled
as in my experiments, is well worthy of careful considera-
tion. The waste field is proportional to the current in the
transformers, or, better, to the mean of the two currents in
ampere turns. The electromotive force due to this waste
field will be proportional to the rate of change of the cur-
rent. If the current were expressed by a simple harmonic
curve, the electromotive force due to the waste field would
jyr
also be a simple harmonic curve differing in phase by .
The curve of potentials is roughly in the same phase as the
TEST OF WESTINGHOUSE TRANSFORMERS. 203
curve of current. Let A be the amplitude of potential
difference of No. 2 transformer, B be the amplitude of
difference of potential difference in No. 2, or the potential
difference of the thin wire divided by 24. 2 b will be very
nearly the amplitude of difference between the thick wires
o'f Nos. 1 and 2. The ratios of potentials in No. 1 and
No. 2 will then be
Va? + b 9
and
2 a
a and 1
or the drop in the first from this cause is three times as
great as in the second transformer. We shall return to the
waste field immediately. Putting aside harmonic curves,
and returning to the facts as they are, the following table
gives: first, half the difference of potential difference
Half Difference of Potential
Difference.
Volts of High Potential
Coil Divided by 24.
Squares of Volts.
| 15.6
-5.0
25.0
148
41.3
1,706.0
11.3
74.3
5,520.0
10.8
102.6
10,530.0
11.1
131.3
17,240.0
5.5
147.1
21,640.0
1.1
137.0
18,770.0
- 3.1
119.3
14,230.0
- 5.9
95.1
9,040.0'
-12.1
53.4
2,850.0
Square root of mean square = 100.8.
taken from Table XI., that is, at each instant the drop of
potential in No. 2; secondly, the volts of the thin wire of
No, 2 reduced for number of convolutions this is of course
204 DYNAMO MACHINERY AND ALLIED SUBJECTS.
the mean of potential difference between 1 and 2 ; lastly,
the squares of these volts. From this we see a mean square
100.8 showing the drop in No. 2 to be 2.6 volts out of a
total drop of 6.1, and the remainder 2.5, the drop in No. 1.
Diminishing these results by 0.4, the half of 0.8, the fall
observed with no load, the actual losses from no load to
nearly full load will be 2.2 and 3.1.
Turn now to the last column of Table XI. This gives
the difference of potential differences corrected for the loss
of volts by resistance. It is shown dotted on Fig. 68; this
curve presents one or two peculiar features. It should be
possible to infer the form of this curve from the curve of
current. The rates at which the mean current is changing
are as follows :
268* 271* 274* 277* 280* 283* 286* 289* 292* ....
30.7 24.2 19.2 18.5 18.9 1.7 -9.8 -12.7 -21.7 -28.1
which happens to come to a scale which can be at once
plotted. The points marked are the points of the curve
corresponding with the above rates. The agreement of
the points with the curve is remarkably close. This ex-
hibits very completely the effect of waste magnetic field in
this transformer.
For half power, as taken from Table X., the rates are as
follows :
268*6 271* 274* 277* 280* 283* 286* 289* 291>* 295*
14.6 11.5 9.4 10.6 4.4 -4.6 -7.2 -7.5 -13.6 -17.6
and in the same way in Fig. G7 the dotted curve represents
the difference of electromotive force corrected for resist-
ance, and the points correspond with the above rates.
TEST OF WESTINGHOTJSE TRANSFORMERS. 205
Fig. 74 gives the efficiencies for the combined transform-
ers in terms of the load. This curve is the hyperbole :
Efficiency = 100 .
where A = 228, the loss by hysteresis;
B = 0.005, and mainly depends upon the waste
field;
C = 0.0000035, and is mainly the loss by resist-
ance;
X = load in watts.
To sum up, I find that the efficiency of the transformer
at full load would be 96.9 per cent. ; at half load, 96 per
JOOi
Load in 103 watte.
Fio. 74.
cent.; and at quarter load, over 92 per cent. The magnet-
izing current of the transformer amounts to 114 watts, or
1.75 per cent. The drop of potential from no load to full
load is between 2 per cent, and 2.2 per cent.
In conclusion, I wish to express my thanks to Mr. Wil-
son, of King's College; this gentleman carried out the
experiments under my direction, and made nearly all the
numerical calculations and drew most of the curves for me.
DYNAMO MACIIINEKY AND ALLIED SUBJECTS.
x
ential No.
Thick Coil.
Pot
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t- CO I- OS C OC
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ST OF WESTINGilOUSE TRANSFORMERS. C J07
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DYNAMO MACHINERY AND ALLIED SUBJECT*
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ance and
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pinunooovun
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TEST OF WESTINGHOUSE TRANSFORMERS. 209
Potential No. 2.
Thick Coil.
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210 DYNAMO MACHINKRY AND ALLIED SUBJECTS.
s s
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THEORY OF THE ALTERNATE CURRENT DYNAMO.
\
THEORY OF THE ALTERNATE CURRENT
DYNAMO.
ACCORDING to the accepted theory of the alternate current
dynamo, the equation of electric current in the armature
is y y + R y periodic function of t, where y is a constant
coefficient of self induction. This equation is not strictly
true, inasmuch as y is not in general constant,* but it is a
most useful approximation. My present purpose is to in-
dicate how the values of y and of the periodic function
representing the electromotive force can be calculated in a
machine of given configuration.
To fix ideas, we will suppose the machine considered to
have its magnet cores arranged parallel to the axis of rota-
tion, that the cores are of uniform section, also that the
armature bobbins have iron cores, so that we regard all the
lines of induction as passing either through an armature
coil or else between adjacent poles entirely outside the
armature. The sketch, Fig. 75, shows a development of
the machine considered. The iron is supposed to be so
arranged that the currents induced therein may be neg-
lected. We further suppose for simplicity that the line
integral of magnetic force within the armature core may
be neglected.
* See chapter on the " Theory of Alternating Currents" in this volume.
212 DYNAMO MACHINERY AND ALLIED SUBJECTS.
i
Let A t be the effective area of the space between the pole
piece and armature core when the cores are in line, J, the
distance from iron to iron.
Let A 9 be the section of magnet core, 7, the effective
length of a pair of magnet limbs, so that /, may be re-
Fro. 76.
garded as the length of the lines of force as measured from
one pole face to the next.
Let m be the number of convolutions in a pair of magnet
limbs, and
n the convolutions in one armature section;
T the periodic time.
The time is measured from an epoch when the armature
coil we shall consider is in a symmetrical position in a field
which we shall regard as positive.
x and y are the currents in the magnet and armature
coils, the positive direction being that which produces the
positive field at time zero.
At time t the armature coil considered has area Af,
= ft + ft, cos (2 n t/T) + ft, cos (4 it t/T) + etc.,
THEORY OF THE ALTERNATE CURRENT DYNAMO. 213
in a positive field; and area A" 9
= b -b, cos (2 n t/T) + b, cos (4 n t/T) - etc.,
in a negative field, where
and
&o ~ &, + t>, + - - - = 0.
The coefficients b , b } , etc., are deducible by Fourier's
theorem from a drawing of the machine under considera-
tion.
Let / be the total induction in the magnet core, and let,
at time t, /be distributed into /' through A' 9 I" through
A" and /'" as a waste field to the neighboring poles.
The line integral of magnetic force from the pole to
either adjacent pole is /'"/&, where k is a constant.
We have first to determine /', 1", /'", in terms of x
and y.
Take the line integral of magnetic force in three ways
through the magnets, and respectively through area A',
through area A", and across between the adjacent poles
f + 3 l ' ~' = 4 * m X ~~ 4 * H y
214 DYNAMO MACHINERY AND ALLIED SUBJECTS.
whence
A,' -A
When t, x and y are given, this would suffice to determine
1 by means of the known properties of the material of the
magnets as represented by the function /. We will, how-
ever, consider two extreme cases between which other cases
will lie.
First. Suppose that the intensity of induction in the
magnet cores is small, so that /,/(//^4 a ) may be neglected,
the iron being very far from saturation. We have
= 2T !m (A ' " A ") x + n - (A * + A
7t ( (. 27Tt . 67Tt \
= -y- 1 m \t t cos -y- -f J, cos -^ + ...)
+ n -f b, cos -- + . . .
We see that the coefficient of self induction y in general
contains terms in cos (4 n t/T).
Second, In actual work it would be nearer the truth to
THEORY OF THE ALTERNATE CURRENT DYNAMO. 215
suppose that the magnetizing current x is so great that the
induction / may be regarded as constant, and the quantity
l^f(I/A^ as considerable. But as small changes in /
imply very great changes in l^f(I/A^), its value cannot be
regarded as known. We have then
(A* A
I-- 1 2l
A/ -A"
-
whence
r r , = (A; -A,") i
(A: - A,")'
(A,' - A,") I
~ A^ + AS' + Zkl,
4 A,' A," + 2 k I, (A,' + A,") titny
' "
\
216 DYNAMO MACHINERY AND ALLIED SUBJECTS.
For illustration, consider the simplest possible case: let
b = b. = $A t , and b 9 = ft, = . . . = 0, and let 2 k Z, be
negligible; we have
T/ , 2jrtf, .2 TT t 47rny
I - I = Jcos -y- + A l sin 9 ^- . -y^,
and the equation of current will be
instead of the simple and familiar linear equation.
THE ELECTRIC LIGHTHOUSE OF MACQUAKIE. 217
THE ELECTRIC LIGHTHOUSES OF MACQUARIE
AND OF TINO.
THE subject of the use of the electric light in light-
houses was fully discussed at the Institution in 1879, when
papers by Sir James Douglass, M. Inst. C.E., and by Mr.
James T. Chance, Asso. Inst. C.E., were read.*
The subject has been further elaborately examined by
Mr. E. Allard,f and more recently in practical experi-
ments made at the South Foreland, exhaustively reported
on by a committee of the Trinity House.J The justifica-
tion of the present communication is that, at the light-
houses of Macquarie and of Tino, the optical apparatus is on
a larger scale than has hitherto been used for the electric
arc in .lighthouses, and presents certain novel features in
the details of construction. Further, as regards the elec-
trical apparatus, tests were made upon the machinery for
Macquarie when it was in the hands of Messrs. Chance
Brothers & Company, which still possess some value,
although five years old; and, in the case of Tino, the
machines are practically worked together in a manner
not previously used otherwise than by way of experiment.
* Minutes of Proceedings of the Inst. C.E., vol. LVII., pp. 77 and 168.
t " M6moire sur leg Phares filectriques," 1881.
% " Report into the relative merits of Electricity, Gas, and Oil as Lighthouse
Illuminants." Parts 1 and 2, PP. 1885,
218 DYNAMO MACHINERY AND ALLIED SUBJECTS.
In the case of both lighthouses, Messrs. Chance Brothers
& Company, of Birmingham, entered into a contract for
the supply of all the apparatus required, including engines,
machines, conductors, lamps, optical apparatus, and lan-
terns; and Sir James Douglass, engineer-in-chief of the
Trinity House, acted as inspecting engineer to the respec-
tive colonial and foreign governments.
As these two lighthouses present many features in com-
mon, it may be most convenient to give a full description
of the earlier lighthouse, and then limit the description of
Tino to those points in which it differs from Macquarie.
MACQUARIE.
This lighthouse is situated on South Head, near Sydney, ,
the precise position being shown in a copy from the
chart, Fig. 76. A lighthouse was first placed at this im-
portant landfall in 1817. The focal plane is 346 feet
above the sea, and the distance of the sea horizon is there-
fore 21.6 nautical miles, and the range about 27 nautical
miles for an observer 1 5 feet above the sea.
Optical Apparatus. The light is a revolving one, giv-
ing a single flash of eight seconds' duration every minute.
On account of the considerable altitude of the lighthouse,
it was necessary to secure that a substantial quantity of
light should be directed to the nearer sea; but it was also
essential, on account of the exceptional power of the ap-
paratus, that this dipping light should only be a small
fraction of that sent to the horizon, otherwise its effect
would be excessively dazzling. Many years ago Mr,
THE
ELECTRIC LIGHTHOUSE OF MACQUARIE. 219
EAST MAITLAND JN.
?/ A NEWCASTLE
FIG. 7<J.
220 DYNAMO MACHINERY AND ALLIED SUBJECTS.
James T. Chance urged that it was not wise to make use
of very small apparatus for the electric arc, because a
larger apparatus renders it possible for the optical engineer
to effect with greater precision the distribution of light
which is most desirable, and because any trifling error
which may occur in the position of the electric arc lias,
with the larger apparatus, a less marked effect on the light
as seen from the sea. In the lighthouses of Souter Point,
the South Foreland, and the Lizard, the third order ap-
paratus of 500 millimetre focal length was adopted.
Optically, the larger the apparatus used the better, but
there might be some question whether, on purely optical
grounds, the advantage of going beyond the third order is
sufficient to justify the additional expense; but in the case
of a revolving apparatus the third order is a very incon-
venient size for the service of the lamp it is too large to
be conveniently served from the outside, and too small to
admit the attendant within it with comfort. With the
large currents, which are now easily obtained and are
likely to be used in lighthouses, a first or second order
apparatus has the further advantage that it is less liable to
injury from particles thrown off from the heated carbons.
In the case of Macquarie, it was decided to adopt an ap-
paratus of the first order, 920 millimetre focal length; it
was further decided that the optical apparatus should pro-
duce its condensing effect by means of a single agent that
is to say, the vertical straight prisms which were used in
Souter Point and other revolving electric lighthouses
should be dispensed with. The condensation and dis-
tribution of light necessary may be obtained by means of
a single agent, with apparatus such as has been pro-
THE ELECTRIC LIGHTHOUSE OF MACQCJARLE.
posed by Mr. Alan Brebner, Jr., Asso. M. Inst. O.E.;*
but this construction is open to the objections that it
is somewhat costly, and that it increases the length of
the path of the rays through the glass, and consequent
absorption. A practically better plan is to adopt forms
not differing very greatly from those introduced by
Fresnel; to specially arrange them for the purpose in
hand, and to accept certain consequent minute deviations
from a mathematically accurate solution for the sake of
advantages of greater importance when all the actual con-
ditions are taken into account. Fig. 77 shows the optical
apparatus in vertical section: the upper and the lower
totally reflecting prisms are, as is usual in revolving lights,
forms of revolutions about a horizontal axis; they direct
the light incident upon them to the horizon and the dis-
tant sea from 10' above the horizon to 30' below; they are
specially adjusted to distribute the light in azimuth over
the arc of 3 necessary for a proper duration of flash.
The refracting portion of the apparatus has the profile
so calculated that the central lens and the three rings
next to the lens above and below direct their light to the
horizon without vertical divergence, except what is due to
the size of the arc. The light for the nearer sea is obtained
from the remaining ten lens segments, Nos. 5 to 9 in-
clusive, above and below the centre, counting the centre as
No. 1, the distribution being according to the following
table, in which the first column gives the denomination* of
the elements of the lens in accordance with the numbers
marked upon the section ; the second, the angle between
* Minutes of Proceedings of the Inst. C.E., vol. LXX., p. 386.
222 DYNAMO MACHINERY AND ALLIED SUBJECTS.
L II. HI.
O I It O t II
gtop 10 2 30 59
8 2 30 59 5 8 52
7 " 10 2 87 30
6 10 1 30
5 " .... 10 100
Sbottom.. 10 100
6 " 10 1 30
7 " 1 80 3 44 27
8 3 44 27 5 50 41
9 " 5 50 41 7 46 57
the direction of the sea horizon and the ray emerging from
the upper limit of the element; the third, the angle be-
tween the direction of the sea horizon and the ray from
the lower limit of the element, the negative sign denoting
that the emerging ray is above the horizon. This practice
of appropriating certain elements of the apparatus to dif-
ferent distances on the sea was first introduced by Mr.
James T. Chance, in the lights of the South Foreland ex-
hibited in January, 1872.
The ray, dipping at an angle of 7 46' 57' below the
horizon, will strike the sea at mile, while 5 8' 52' cor-
responds to } mile, 2 37' 30' to 1 mile, 1 30' to 2 miles,
1 to 2i miles, and 30' to about 4 miles. Thus the direct
light begins at about i mile from the lighthouse. From |
mile to | mile the sea receives light from one element of
the apparatus, from J to 1 mile from two elements, from
1J mile to 2 miles from three elements, from 2 to 2 miles
from four elements, and beyond 2 miles from six
elements; the upper and lower totally reflecting prisms
come in aid at about 5 miles. The main power of the ap-
paratus is hardly attained till a distance of 8 or 10 miles.
Fig. 78 is a sectional plan of the apparatus by a horizontal
THE ELECTRIC LIGHTHOUSE OF MACQITARIE.
Fio. 77. Fia. 79.
FIG. 78.
FIG. 80.
224 DYNAMO MACHINERY AND ALLIED SUBJECTS.
plane through the focus. It will be seen that a dioptric
mirror is placed on the landward side of the arc. This
mirror is arranged to form the image of the arc at one
side of the carbons, so avoiding the interception of light
which would result if the mirror were used in the ordinary
way, and contributing to the horizontal divergence neces-
sary. Further horizontal divergence is given by the form
of the lens. In the ordinary revolving light the inner face
of the lens is plane; here it is cylindrical, the axis of the
cylinder being vertical. This method of obtaining hori-
zontal divergence is a modification of a proposal of Mr.
Thomas Stevenson,* M. Insl. C.E.; it is not mathemati-
cally accurate, inasmuch as the cylindrical form of the
inner face of the lens not only displaces the emergent ray
horizontally, but also, in the case of rays not in the verti-
cal nor horizontal plane through the focus, to a small ex-
tent vertically; but the error is easily calculable, and is
unimportant, provided the lens is narrow, and the hori-
zontal divergence of the beam moderate. Fig. 79 shows a
complete panel in elevation with revolving carriage. Fig.
80 shows the plan of the service table of the pedestal and
lamp table. A new construction was adopted for the gnn-
metal framework of the optical apparatus to reduce the
interception of light by the frame to a minimum. The
metal segment A, Fig. 81, forms part of the lower prism
frame, B part of the upper frame, while C and D are parts
of the frame for the refracting portion of the apparatus;
uprights E support the upper prism frames without throw-
ing weight on the lens frames. With the ordinary con-
*" Lighthouse Construction and Illumination," p. 186.
THE ELECTRIC LIGHTHOUSE OF MACQUARIE. 225
structions of frame, Figs. 82 and 83, the equivalent of these
ring segments A and B would intercept about double as
much light as in this new construction.
E
Fio. 81.
FIG 82.
Fio. 83.
Mechanism for Rotation. The pedestal is similar to
those designed by Sir James Douglass to permit the light
keeper to obtain access from below to the interior of the
apparatus without in any way interfering with its rotation.
The clockwork is fitted with the governor, and maintain-
ing poweV used by Messrs. Chance Brothers & Company
for the last twelve years. The roller ring may be men-
tioned as of an improved type, for although it has been
used for some years in all Messrs. Chance's lights, it has
not been described before. The rollers and roller paths
which carry the whole weight of the optical apparatus
have long been made conical, so that the surfaces roll
226 DYNAMO MACHINERY AND ALLIED SUfeJECTS.
upon each other without twisting. There is consequently
a very considerable radial force on each roller tending to
force it outwards; the reaction against this force causes a
very important part of the total frictional resistance. Fig.
84 shows a portion of the roller ring and one of the conical
Fio. 84. Fio. 86. FIG. 86.
rollers, according to the old construction; Figs. 85, 86, ac-
cording to the improved construction; in the former it
will be observed that the thrust of the roller is received on
a collar; in the latter, on the end of a pin. The reduction
of friction is practically very considerable, and although of
small importance in a slow-moving apparatus like Mac-
quarie, is of great importance in heavier and quicker ap-
paratus; for example, the triple flashing light at Bull
Point, in Devonshire.
Lamp*. These are of the Serrin type, and were supplied
by Baron De Meritens.
Lamp Table. The arrangements for rapidly changing
electric lamps, and for substituting gas or oil when de-
sired, are shown in Figs. 87, 88, 89, and 90.
The intention was to use a gas lamp in clear weather,
and half power or full power electric light in thick
weather, according to the opacity of the atmosphere; but
the author understands that in practice the electric arc is
THE ELECTRIC LIGHTHOUSE OF MACQUARIE. 227
always used. The paraffin oil lamp is intended as a re-
source in case of failure of the supply of gas.
FIG. 87.
Fio. 88.
FIG. 89.
ARRANGEMENT FOR OIL LAMP.
FIG. 90.
ARRANGEMENT FOR GAS BURNER.
Focussing the Arc. Two approximately rectangular
prisms are fixed upon the mirrcr frame at about 90 from
228 DYNAMO MACHINERY AND ALLIED SUBJECTS.
each other, the longer face of each is plane, the other two
faces convex, of such curvature as to form a good image
of the arc upon the service table, as shown in Fig. 91.
Fio. 91.
During daylight, a pointed sight or focimeter is placed at
the position of the image formed by the lens of an object
on the horizon; this then is the position which the arc
should occupy. A sight is next taken over the focimeter
into one of the adjusting prisms, and a bright object such
as a threepenny piece placed on the service table, is moved
about until its centre is seen in the prism, exactly upon
the point of the focimeter; a mark is made in the then
position of the object. When the arc is corrootly adjusted,
its image on the service table will be at the point where
the mark is made. Two prisms are used in order to secure
that the arc shall be in the centre of the apparatus as well
as at the correct level.
Lantern. The lantern is of the well known Douglass
type.*
* Minutes of Proceedings of the List. C.E., vol. LVI., p. 77.
THE ELECTRIC LIGHTHOUSE OF MACQUAKIE. 229
Dynamo-Electric Machines. Two alternate current ma-
chines, with permanent magnets manufactured by De
Meritens, were supplied. Each machine has five rings in
its armature, and in each ring there are sixteen segments.
In supplying one arc for a lighthouse the machine runs
about 830 revolutions per minute, and gives a current of
55 amperes when half the coils are used, and of 110 when
the whole of the machine is in action, the internal resist-
ance in the two cases being 0.062 and 0.031 ohm. It is
unnecessary to give a description of the machine as its
general construction and dimensions are well known, but
some numerical details are given below.
Engines. Each machine is driven by an 8 h. p. Crossley
gas engine through a belt without countershafting.
Tests. Whilst the dynamo machines were at the works
of Messrs. Chance Brothers & Company, a series of ex-
periments was made in March, 1881, to determine their
properties. The time is long passed when it would be
profitable to give the details of these experiments, but the
general conclusions drawn at the time are still interesting.
When the external resistance was a metallic conductor
with small self induction, it was found that with varying
resistance and speed the currents observed agreed fairly
well with calculation from the formula
in which R is the total resistance of the circuit, y the self
induction, and T the periodic time. When the machine
* Lectures on the "Practical Application of Electricity. 1 ' Session 1883-83.
Paper on " Some Points in Electric Lighting," reprinted in this volume.
230 DYNAMO MACHINERY AND ALLIED SUBJECTS.
was running 830 revolutions per minute A = 67 volts and
= -1 9 ? i 11 onm s<i"aivl, hence y = 6.4 x 10*
centimetres. The eighty sections of the machine ;t it-
arranged four in series, twenty parallel. For a single sec-
tion the value of y would be 32 x 10* centimetres. The
maximum induction in the core, which has an area of 5
square centimetres, is 24,600 or 4,920 per square centi-
metre. The loss of power was greater when the machine
was doing little or no external work than when that work
was great. This is clearly seen in the following table :
Current amperes ............................... ........ 7.70 73. GO
Electrical work h. p ................................... 0.69 5.66
Mechanical work applied ............................... 8.09 6.56
Loss ................................................. 2.40 0.89
Photometric experiments were made upon the arc, and
simultaneous measurements of effective power applied and
of current passing. The red light was measured through
bright copper ruby glass, and the blue through a solution
of sulphate of copper and ammonia. The h. p. was meas-
ured by a transmission dynamometer; but the results must
be accepted with some reserve, on account of the difficulty
of ascertaining the mean tension in a strap which is con-
stantly varying. The oscillations of the dynamometer
were damped by a dashpot containing tar.
Half Power. Full Power.
Redcandles ........................................ 1,988 I.'"*
Blue " .......................................... 4,079 11,382
Current (amperes) .................................... 54.5 105
Mechanical power applied (h. p.) .................. 4.5 6.9
Power expended in heating conducting wires (h, p.) 0.34 0.95
THE ELECTRIC LIGHTHOUSE OF TINO. 231
The results illustrate the fact that, as the current in-
creases, the total light increases in a higher ratio, red
light in a slightly higher ratio, and blue in a considerably
higher.
The machinery for this lighthouse was sent out to New
South Wales in November, 1881, and was put up and
started under the superintendence of Mr. J. Burnett, the
architect of the colony, to whom is mainly due the success
of the whole from the first start. The glare of the light
upon the sky is said to have been seen at a distance of
over GO miles, far beyond the distance at which it would
cease to be directly visible. The only criticism from
mariners has been that when somewhat near the light-
house the flashes are so bright as to dazzle the eye. This
is an excellent proof of the power of the light, as a much
smaller proportion of the light is directed upon the nearer
sea than in any previous lighthouse. The lesson is that
with powerful electric lighthouses almost all the light
should, in ordinary weather at least, be directed to the
horizon, and that the quantity thrown upon the nearer sea
must be strictly limited. This is only possible when the
focal length of the apparatus is large.
TINO.
This station is on a small island at the mouth of the
Gulf of Spezia. Fig. 92 is copied from the chart of the
neighborhood. The focus is 386 feet above sea level. The
distance of the sea horizon is 22.7 nautical miles, and
the range practically 28 miles. The conditions, therefore,
232 DYNAMO MACHINERY AND ALLIED SUBJECTS.
were very similar to those of Macquarie, with the excep-
tion that it was required to throw some light dowii into
the channel between Palmaria and Tino. The lighthouse
itself presents some interesting historical features. The
buildings were originally a place of defence against the
pirates who occasionally made descents upon the coast.
Fio. 92.-(Scale t 22 miles - j i nc h.)
Subsequently a coal fire lighthouse was established, and in
the spring of 1885 part of the stock of lignite was still
found to be in some of the buildings, where it had been
lying for fifty years. In 1839 a dioptric light was estab-
lished, one of the earliest of Fresnel's types, the lens ring
being replaced by short straight prisms, which formed by
no means a bad approximation, and could be ground with-
out special machinery. The present electric lighthouse has
been in contemplation for several years.
THE ELECTRIC LIGHTHOUSE OF TINO. 233
Optical Apparatus. The distinctive character of the
light is a triple flash every half minute. The apparatus for
producing this effect is of the general form introduced by
the author in 1874. In October of that year he issued a
pamphlet pointing out the several advantages of group
flashing lights, showing for the first time a simple dioptric
apparatus suitable to their production, and also pointing
out how easy it is to give the group flashing effect with
catoptric apparatus. Since that time a large number of
dioptric group flashing lights have been made by Messrs.
Chance Brothers & Company, and some also in France,
and Mr. Allard has incorporated group flashing lights in
the system of distinctions he recommends ; also a consider-
able proportion of the light vessels on the English coasts
have been converted into group flashing lights of the
catoptric system. On the ground of economy the second
order apparatus of 700 millimetre focus was adopted in the
case of Tino. It is just large enough for tolerably con-
venient service of the lamp by an attendant entering with-
in the apparatus. The apparatus, shown in vertical
section in Fig. 93, and in horizontal section through the
focus in Fig. 94, has twenty-four sides, eight groups of
three; one group of three is shown in elevation in Fig. 95.
The horizontal divergence is obtained in exactly the same
way as at Macquarie, excepting that no mirror is used.
The metal framework, however, approximates to the
ordinary type, as the type used at Macquarie would have
been costly when applied to a triple flash light. The dis-
tribution of light vertically is as follows : upper and lower
prisms, and the central lens, with the two lens rings next
adjoining it, all to the horizon and most distant sea. The
234 DYNAMO MACHINERY AND ALLIED* SUBJECTS.
Fio. 94.
FIG. 93.
THE ELECTRIC LIGHTHOUSE OF TINO. 235
lens and lens rings direct their rays according to the fol-
lowing table, which is arranged in exactly the same way as
the table already given for Macquarie:
i. n. in.
7 top 31 35 3 16
6 " .. 200
5 " .. 1 30
4 " .. 100
4 bottom .. 45
5 " . .. 30
6 " .. 30
7 " all to the horizon.
No. 7 bottom was directed wholly to the horizon, in
order to avoid the horizontal bar of the lantern. It will
be observed that the quantity of light thrown upon the
nearer sea is much less in the case of Tino than in that of
Macquarie, and that greater reliance is placed upon the
accuracy with which the arc can be kept in focus; ex-
perience has justified these changes, as improvements of a
perfectly safe nature.
A small part of each flash is bent downwards and dis-
tributed over the channel between Tino and Palmaria, by
means of subsidiary prisms fixed upon the lantern, shown
at X, Fig. 93. These subsidiary prisms are really super-
fluous, as the scattered light from the beams overhead is
found to be as effective at this short distance. Fig. 90
shows the plan of lamp shunting table and service table.
Engines. As there is no water upon the island, the
practice of the Trinity House was followed, and two of
the Brown hot air engines were supplied, each driving
through a countershaft one of the machines. The
countershafts could be connected by means of a Mather
236 DYNAMO MACHINERY AND ALLIED SUBJECTS.
and Platt friction coupling, so that the two machines
could be driven together, or either machine from either
engine. Drawings of the Brown engines are given in Sir
Fio. 96.
James Douglass's Paper.* The accompanying indicator
diagrams Figs. 97 and 98.were taken from the compressing
and working cylinders. Whilst these diagrams were taken,
the effective power developed was measured by a friction
brake on the driving pulley, and was found to be 9.1 h. p.
Thus of 33.1 h. p. indicated in the working cylinder, 17.7
h. p. is employed in compressing the air, 6.3 h. p. is wasted
in friction in various parts of the machine, and only 9.1
h. p. is effective upon the brake. The engines consume
about 4 Ibs. of coke per effective h. p. per hour. In future
lighthouses, when a steam engine cannot be employed, it
would be preferable on every ground to use gas engines,
and manufacture on the spot either Dowson gas or
* Minutes of Proceedings of the Inst. C.E., vol. LVII., Plate 6.
THE ELECTRIC LIGHTHOUSE OF TINO.
237
ordinary gas, according to the character of the fuel avail-
able.
Dynamo Machines. There are two machines of exactly
FIG. 97. Compressor- pump cylinder, 24 inches in diameter. Stroke, 22 inches.
Indicated H. P., 17.7.
Fm. 98.-Workinpr cylinder. 3'.' inches in diameter. Stroke, 20 inches. Indicated
H. P., 33.1. Revolutions per minute, 64. Power on brake of fly-wheel, 9.12 H.P.
Pressure in reservoir, 19 to 24 Ibs.
the same type as those supplied for Macquarie, the only
novelty lying in the method of using them. In 1868 Mr.
Wilde discovered, by experiment, that two alternate
238 DYNAMO MACHINERY AND ALLIED SUBJECTS.
current dynamos, independently driven at the same speed,
would, if electrically connected, so control each other's
motions that they would add their currents. The author
subsequently arrived at the same conclusion independently,
on theoretical grounds, and gave a thorough explanation of
the fact.* The result has been put to a practical applica-
tion at Tino. The machines are connected to a single
switchboard, so that each half of the two machines can at
pleasure be connected to, or disconnected from, the main
conductors. Thus a current can be supplied from either
machine at half power, 55 amperes, or full power, 110
amperes, or from the two machines of double power, or
about 200 amperes. Further, a change can be made with-
out extinction of the light from one dynamo and engine to
the other. Thus, suppose one machine is working full
power, clutch the countershafts gradually together, so
starting the second engine; throw on the band of the
second machine, cut out half the first machine, and con-
nect half the second machine at the switchboard; the two
machines at once synchronize, without affecting the light.
Disconnect the remaining half of the first machine, and
connect the remaining half of the second, unclutch the
countershafts, and stop the first engine. One man can
effect the change, with no more disturbance of the light
than a change from full to half power for about one
second. A further conclusion, deduced from theoretical
considerations, was that of two alternate current machines
* Lectures on the "Practical Applications of Electricity." Session 1882-88.
Paper on "Some Points in Electric Lighting," reprinted in this volume. By
Dr. John Hopkinson. And Journal of the Society of Telegraph Engineers and
Electricians, vol. xni., p. 496.
THE ELECTKtC LIGHTHOUSE OF TINO.
of equal potential, one coujd be used as a generator of
electricity, the other as a motor converting the current
generated back into mechanical power. It was found
impossible to verify this conclusion with such intermittent
driving as that of a hot air engine. But Professor W. G.
Adams effected the verification without difficulty at the
South Foreland, the motive power being steam.
Lamps. These are the improved Serrin of Mr. Berjot.
One of the three lamps supplied is of larger size, for the
double power current from the two machines. This lamp
was said to be suitable for a still greater current, but with
about 200 amperes it soon became dangerously heated; a
simple modification rendered the lamp equal to the actual
work it had to do. It is, however, probable that for the
occasional circumstances when it is necessary to use so
great a current as 200 amperes in a lighthouse, a lamp
worked partly by hand would be preferable to a regulator
entirely automatic.
The apparatus was delivered in November, 1884, and
was put up by workmen from Messrs. Chance's workshops,
under the supervision of Mr. L. Luiggi, of Genoa, to whose
ability and energy the complete success of the lighthouse
is largely due. A complete test of the performance of the
light, as seen from the sea in all grades of its power, was
made in April, 1885, by a commission, consisting of Profes-
sor Garibaldi, of Genoa; Mr. Giaccone, engineer-in-chief
for Italian lighthouses; Captain Sartoris, and Mr. Luiggi,
the author attending on behalf of Messrs. Chance. The
light was well observed through rain, when distant 32
nautical miles, and although below the horizon, the posi-
tion was precisely localized, and the triple flash distinction
240 DYNAMO MACHINERY AND ALLIED SUBJECTS.
unmistakable. At 18 miles distant the illumination of the
flash upon white paper was sufficient to make out letters
marked in pencil l inch high, and when 14 miles distant
it was easy to ascertain the time from a watch. The light
is frequently seen at a distance of 50 miles, near to Genoa.
A review of work which has been carried out naturally
suggests many questions as to what conclusions experience
has established, and what indications it gives of the prob-
able direction for future developments. In the use of
electric light in lighthouses, there are many questions
upon which there is wide difference of opinion, questions
both as to when and where electric light should be
adopted, and questions as to the best way of employing it.
It may not be unprofitable to allude to some of them.
Although English engineers are now well agreed that a
large optical apparatus should be used for the electric
light, this opinion is not universally accepted. The
advantages of a large apparatus have already been men-
tioned. To balance them, there is nothing on the other
side but the less prime cost of the smaller apparatus.
Although the difference of cost appears considerable when
attention is confined to the optical apparatus, it is un-
important when the whole outlay on the lighthouse is
brought into account. Cases are, however, conceivable in
which a small optical apparatus such as a fourth order,
having a focal distance of 250 millimetres, would be prop-
erly preferred ; such, for example, as a harbor light which
could be supplied with current from machinery also used
for other purposes, but such cases are likely to be excep-
tional.
THE ELECTRIC LIGHTHOUSE OF TINO. 241
When a flame from oil or gas is the source of light, there
is of necessity a considerable divergence vertically ; and the
distribution of the light through the angle of vertical
divergence is not at disposal, except to a very limited
extent in some cases, but is determined by the size and
character of the flame. With the electric arc and a large
optical apparatus it can be determined in considerable
measure how the light shall be distributed how much
shall be sent to the distant sea, how much to the various
distances between the foot of the tower and a distance
of some miles. It becomes then a question what use is to
be made of this facility. The experience at Macquarie
and at Tino is emphatic, that it is in every way advant
ous to direct much the greater part of the light to
horizon with a very small divergence, and to distribute the \^^
comparatively small remainder over the nearer sea with in-
tensity increasing with the distance.
A question allied to the last is this: Whether it be de-
sirable to provide means of directing the strongest light
downwards on to the nearer sea in time of fog? The
answer must depend upon the circumstances of the par-
ticular locality. Take the case of a lighthouse on an
isolated rock, the purpose of which is primarily to be a
beacon to keep ships off that rock; a lighthouse which
would not exist were it not more practical or cheaper to
build and maintain the lighthouse rather than remove the
rock. Here surely it is of the greatest use to provide
means whereby, if the light cannot penetrate 2 miles, it
shall if possible be visible at 1 mile. But other cases
occur in which the lighthouse has to cover a long length
of coast, and has almost as much to do with points of the
242 DYNAMO MACHINERY AND ALLIED SUBJECTS.
coast 10 miles distant as with the point upon which it is
placed, cases in which the lighthouse is far more useful in
guiding the regular traffic passing within a radius of 20
miles or more than in preventing vessels running ashore
within a mile of the tower. Such a light fails of its pur-
pose if it can only be seen at a distance of a mile, covering
less than ^^ part of its normal area of illumination; it
becomes comparatively useless unless it penetrates, to
something like its normal range, and its efficiency must be
measured by the fewness of the occasions when it fails to
do this. It is a grave question whether it be prudent in
such cases to place upon the light keeper the responsibility
of judging when the light should be dipped on to the
nearer sea, the fact being that, if his judgment errs, he
may actually diminish the range of the light, and cause
unnecessarily the lighthouse to fail of fulfilling its most
important function. It is easy for him to be misled if the
fog is local and does not extend to any great distance from
the lighthouse. Another element enters into the con-
sideration the height above the sea. If the focus be 100
feet above the sea level, the dip of the sea horizon is 9'
45", and a ray dipping 9' 45" below the sea horizon will
meet the sea at a distance of 3.1 nautical miles from the
tower. Even with a first order apparatus, if the arc be a
powerful one, it is very difficult to render the light
directed to the horizon from an elevation of 100 feet more
powerful than that directed to a point distant 4 miles from
the tower. Unavoidable divergence will render the two
intensities practically equal.
Passing to questions of another class, what are the rela-
tive advantages in an electric lighthouse of continuous and
THE ELECTRIC LIGHTHOUSE OF TINO. 243
alternating currents? Present practice tends altogether
in favor of alternate currents, but this practice largely
results from unfavorable experience of the older continu-
ous current machines. These machines have in many
respects been greatly improved in the last two or three
years. The continuous current presents the advantage of
greater economy of power in producing the current, less
floor space required by the machine, and a smaller prime
cost. The alternate current magneto machine, on the
other hand, has the advantage that it may be driven with
a defectively governed prime mover, with an indifferent
lamp, and may suffer neglect with impunity; whereas the
more compact and efficient continuous current machine
would be in serious peril of destruction. Optical apparatus
can be constructed suitable to make the most of either
form of arc. Hot air engines have found favor for electric
lighthouses, because in many cases there is no available
supply of fresh water. The engines of which the author
has experience are open to the objection that they take a
great deal of room, are not economical of fuel, and do not
govern so quickly as is desirable; the wear and tear also,
when they are worked to anything like their full power, is
very serious. A gas engine, with Dowson or other gas
made on the spot, could be used with greater advantage,
Antecedent to all considerations as to the best apparatus
and machinery to be used is the question under what cir-
cumstances, if at all, should electric light be used in a
lighthouse ? The Trinity House experiments at the South
Foreland showed to demonstration that, where the issue to
oe decided was how to produce a light which should be ca-
pable of penetrating the furthest in all weathers, electric
244 DYNAMO MACHINERY AND ALLIED SUBJECTS.
light could do that which could be done in no other way,
and that it was the cheapest light of all when the price is
estimated per unit of light. But the conclusion was also
reached that an electric light must inevitably cost a large
sum, both in first outlay and in maintenance; therefore
that electric light is extravagant unless very extraordinary
power is a necessity. This conclusion is doubtless a fair
consequence of experience, but it is not an inherent prop-
erty of electric light. Both the capital outlay and the cost
of maintenance are greatly increased by the practice of so
arranging the machinery as to provide, at all times, a light
of very great power : whence it follows that the machinery
must be placed at some distance from the lantern, and two
men must always be on duty; one man in the lantern, and
another with the machinery.
The essentials for a cheap electric lighthouse are, that
for ordinary states of the atmosphere there shall be pro-
vided a plant under the easy control of the light keeper
himself, which shall be precisely adapted to produce that
amount of light which is wanted in ordinary states of the
atmosphere; but for thick weather there shall be provided
a much more powerful engine and dynamo, available also
as a reserve in case the smaller machinery from any cause
breaks down. The occasional machinery may be more
remote from the lantern, as it is a small matter to require
a second man to work on the comparatively rare occasions
when the maximum power is needed. A small gas engine
and a dynamo machine can be placed without any crowd-
ing in the room immediately below the lantern, and arrange-
ments can be made whereby the light keeper, whether he
is in the lantern or in the engine room, can ascertain at a
THE ELECTRIC LIGHTHOUSE OF TINO. 245
glance whether the arc is in its proper position, with an
error of less than 1 millimetre. The attendance on the
lamp, rotating apparatus of, the lens (if a revolving light),
engine and dynamo, would be easy when the whole is
brought together so as to be under observation at once; in
fact the gas engine, dynamo, and lamp constitute together
a gas burner which, though consisting of many parts, is
automatic throughout, and requires nothing but the con-
stant presence of a custodian, exactly as the gas lamp in a
lighthouse requires a custodian as a guarantee against fail-
ure. The same end, viz., the concentration of the whole
mechanical and electrical apparatus under one pair of eyes,
could be attained, of course, in other ways. Accumulators
could be used, or a petroleum engine.
In order to give definiteness and afford facilities for
criticism, the better course will be to describe a suitable
machinery; state what it will do, what attendance it will
require, and what it will cost. The author proposes, then,
for an electric lighthouse where small outlay is essential,
the following: A Dowson gas producing apparatus and gas
holder, the generator and superheater being in duplicate,
each capable of making 1,200 feet of gas per hour, the gas
holder having a capacity of 3,000 cubic feet.
An 8 h. p. nominal Otto gas engine and series wound
dynamo machine, placed in a room near the base of the
tower, and copper conductors to the lantern, the dynamo
having magnet coils, divided 'into sections so as to supply a
small current when required.
A 1 h. p. nominal Otto gas engine and dynamo machine,
placed in the room immediately beneath the lantern floor,
with gas pipe from the gas holder; three electric lamps, to
246 DYNAMO MACHINERY AND ALLIED SUBJECTS.
receive either carbons 25 millimetres in diameter or any
lesser size, with complete adjustments for accurate focus-
sing; one paraffin lamp as a substitute; an optical appara-
tus of the second order of 70 centimetre focal distance.
The cost of this apparatus would depend upon the charac-
ter of the light it was intended to exhibit. To fix ideas,
let it be assumed that the light is to be a half minute
revolving light, showing all round the lighthouse. There
could then be supplied a sixteen sided apparatus with ped-
estal and revolving machinery. Provision would be made
in the optical apparatus for giving the horizontal and ver-
tical divergence desired by the same methods successfully
used in the lighthouses of Macquarie and of Tino.
Two focussing prisms would be fixed to form magnified
images of the arc, on pieces of obscured glass let into the
pedestal floor, so that the keeper, whether in the lantern or
in the engine room, could see at a glance the state of the
arc, and observe whether it is of proper length with the
carbons in line, whether it is exactly at the right height
and in the centre of the apparatus. An error of I millim-
etre would bu glaringly apparent, and call for immediate
adjustment, although its effect would be only a displace-
ment of the beam 5' of angle.
The lantern would be 10 feet diameter, with bent plate
glass.
The cost of the whole above described would be materi-
ally less than the cost of a first order light and lantern
with oil lamp and large burners.
Now what result would be obtained ? In fine weather
the small engine would be used. Its effective power on
the brake is fully 1 h. p.; from this 1J h. p. the dynamo
THE ELECTRIC LIGHTHOUSE OF TINO. 247
machine produces considerably over 800 watts, say 800
watts in the arc itself, or 20 amperes through a fairly long
arc of 40 volts. Of course the value of this in candles de-
pends upon the color in which it is measured, and the
direction in relation to the axis of the carbons. In red
light the mean over the sphere would certainly exceed
1,200 candles. In clear weather or in slight haze or rain,
the beam of this light through the lenses would be much
more powerful at the horizon and on the more distant sea
than any single focus light with oil or gas as the illumi-
nant, and would at least be fairly comparable with any-
thing yet exhibited with oil or gas whether triform or
quadriform. But on the nearer sea the illumination
would be reduced, so that no annoyance would be caused
by dazzling flashes. In thick weather or indeed in any
weather when there was a doubt as to the visibility at the
horizon of the lower power, the large engine would be
used under the superintendence of the second keeper.
This engine will give 10 h. p. on the brake, and there is no
difficulty in obtaining 85 per cent, of this as useful
electrical energy outside the machine, that is, 6,340 watts.
From this deduct 10 per cent, for the leads and the lamp
and for steadying the arc, leaving 5,710 watts in the arc
itself, or 114 amperes, with a difference of potential of CO
volts. Having regard to the fact that the optical appa-
ratus here proposed acts upon a larger portion of the
sphere than that used in the South Foreland experiments,
that the vertical divergence is less, and that the potential
difference is greater and the current continuous, although
less in quantity, it may safely be assumed that the power of
the resulting beam would not be inferior. It hence follows,
248 DYNAMO MACHINERY AND ALLIED SUBJECTS.
from the South Foreland experiments, that in any fog the
flashes would penetrate farther than those of any existing
gas or oil light. The increased size of crater, compared
with that produced by the current of 20 amperes, will give
increased vertical divergence, and so cause the maximum
illumination to be attained at a less distance from the
lighthouse. The attendance of two men would suffice for
all the duties of the lighthouse, because under ordinary
circumstances one man only need be on duty excepting for
two to three hours while gas is being made. The con-
sumption of coal would he 4 Ibs. per hour of lighting, of
water about gallon, of carbons about 4 inches. The
whole cost of maintaining the light would differ little from
that of an ordinary oil light of the first order.
Though it be the fact, that it is possible to exhibit an
electric light at moderate cost, it does not follow that it is
suitable for all ocean lights. There is no room in a rock
lighthouse tower for a gas plant, and few would at present
be prepared to recommend a petroleum engine burning oil
of a low flashing point. The light keeper again must
understand a gas producer, a gas engine, a dynamo, and
an arc lamp, instead of only a paraffin lamp and burner,
and arrangements must exist for repairing the more ex-
tensive machinery. Such considerations will justly weigh
against the use of the electric light in remote stations and
in countries where the labor available is not capable of
much training.
It may possibly be said that in this paper no definite
conclusions are reached as to whether electricity or some
other agent is the best source of light in lighthouses
THE ELECTRIC LIGHTHOUSE OF TINO. 249
generally, nor yet, if electricity be adopted, what is the
best way of producing the light and optically dealing with
it. The answer is that it is impossible on many points to
arrive at general conclusions. Each case must be judged
according to its special circumstances.
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