SCIENCE. 
103 
ELECTRO-MOTORS. 
THEIR POWER AND RETURN. 
J. Hospitalier. 
The transmission of force from a distance, electric 
ploughing, the electric railroad, etc., have made electric 
motors and the conditions of maximum work and maxi- 
mum return, quite the order of the day. In a previous art- 
icle on the available force in batteries, we have determined, 
for the most usual forms, the quantity of energy that could 
be furnished by a certain number of elements in an external 
circuit of proper resistance, supposing no polarization and 
without variation of the internal resistance. 
Is this maximum of available work entirely convertible 
into effective work ? It is not, and we will show how this 
maximum should be reduced when a given electric energy is 
to be transformed into mechanical force. 
Let us suppose, for instance, in numbers, which always 
strike the attention more than formulas, that we have a 
source of electricity of 100 volts, with an internal resistance 
of 1 ohm. It would be easy to realize the conditions by 
employing an electro-dynamic machine, separately excited, 
or 100 very large Bunsen cups, arranged for tension in 2 
parallel series of 50 each. Putting into the circuit an ex- 
ternal resistance equal to the internal, and supposing no 
polarization to exist and no change in the internal resist- 
ance, we obtain as elements for the electric circulation : 
E. — Electro motive force = 100 volts. 
r. — Internal resistance = 1 ohm. 
R. — Exterior resistance = 1 ohm. 
(r + R) — Total resistance = 2 ohms. 
Q. — Quantity — — - = — = 50 webers. 
v V ' 3 r + R 1 4 - 1 
In these conditions we know that we have in the external 
circuit the maximum of available work, as deduced from 
the formula of Joule : 
W = 10 Q 2 R meg-ergs (a) 
or W = kilogram-meters (b) 
q.8i 
In the case before us we have : 
W = 10 X 50 2 X 1 = 25,000 meg-ergs (1) 
What can we do with this available electric work ? If we 
make it traverse an inert wire it will heat it. All the elec- 
tric energy will be transformed into heat, and in this wire 
will be developed a certain number of calorics C, per sec- 
ond : 
c = Sr x t- M 
9.81 A 
A being the mechanical equivalent of heat 424. 
Let us substitute for the inert resistance of a wire, an 
electro-motor of equal resistance with the wire, say 1 ohm 
in this particular case. Let us suppose this motor to 
be one of Gramme’s magneto-electric machines, and that 
the resistance of the armature is equal to 1 ohm. If we 
put a break on the armature to prevent it turning under 
the influence of the passing current, we will not have any 
of the original conditions changed ; the wire of the armature 
will be heated by the current, and a number of calorics C 
will be produced equal to that developed in the wire. Now 
let us make the armature turn under the action of the elec- 
tric current. The rotary motion of this armature will de- 
velop a certain electro-motive force E', inverse to that 
emanating from the source of electricity E, varying with 
the speed of the motor. It results in a diminution of the 
current, and can be expressed at each instant by the form- 
ula : 
qi = e-e; > {d) 
r + R 
Hence the rotation of the motor diminishes the intensity 
of the current (and consequently the work of the motor) if 
a machine is employed as a source of electricity, or the 
consumption of zinc, if you employ a battery. The diagram 
shows how the different elements vary when the speed of 
the motor varies from zero (where the work developed is 
null) to a velocity such that the opposing electro-motive 
force E, which it develops, becomes equal to the electro- 
motive force of the source. It is seen that the energy ex- 
pended by the source of electricity diminishes from the 
time the motor begins to turn (curve I.) ; similarly, the in- 
tensity of the current (curve V.) diminishes to zero when 
E and E' become equal. Curve II. represents the work 
developed by the motor at different speeds. Let us sup- 
pose these speeds are proportional to the electro-motive 
forces — a hypothesis easily verified in a well constructed 
magneto-electric machine — then we see, by the diagram, an 
augmentation of the work produced, up to a point where 
the speed of the motor becomes 50. At this moment the 
work done is at a maximum, and represents but 50 per 
cent, of the work expended by the source of electricity. 
The energy converted into work (curve III.) is equal to 
what is unconverted (curve II.). If the speed augments 
beyond this point the work produced (curve II.) dimin- 
ishes, but the return augments (curve IV.). 
O IO 20 30 40 50 60 70 80 90 ICO 
The work produced and the return are hence perfect- 
ly distinct things which are too often confounded. 
There is no impossibility in making the motor return 80 
per cent, of the work expended by the source of electricity, 
on condition you do not make this source produce all the 
work which it can furnish. When, at the limit, the work 
produced becomes null, the return becomes equal to 1. 
The same conclusion is arrived at on comparing curves I. 
and II. It is thus seen that energy not converted into 
work, diminishes more rapidly than the total energy ex- 
pended by the source of electricity. When the motor is at 
rest, the work is zero, all energy being transformed into 
E 
heat. When E = — , the diagram shows that the work is 
2 
equal to the loss ; curves II. and III. cut each other at B 
and the return is 50 per cent. Several consequences re- 
sult from this. If you wish to obtain the greatest results 
from any given source of electricity, the electro-motor, 
turning at normal speed, must be so arranged as to de- 
velop a counter electro-motive force equal to the half of the 
original source. If the best results are wanted greater 
speed is required, by which a return in work is gained 
with a corresponding loss in the quantity of work pro- 
duced. 
Curves III. and IV. show why an electro-motor heats 
more when stopped than when turning at a certain speed ; 
the intensity of the current is greater in the first case than 
