116 J. Trowbridge on Ohm's law. 
tical with the equation S= ee which is our original expression 
for Ohm’s law. 2. 
If we construct the various 
curves represented by the \ \ 
equation S= R taking X as 
the axis of resistance, E be- 
ing constant for each curve, 
we shall have a series of hy- 
perbolas. 
The series of curves repre- 
sented in fig. 2 may be called 
isoelectric curves, and present 
some remarkable analogies to 
the isothermal curves of ther- 
mo-dynamics. 
Let m=F (Sk) be the equation of the curve ab. The curve 
ab will represent the relation between the increase in resist- 
ance and the decrease inten- y 3. 
sion. The curve a’b’ will 
represent this relation for 
m+dm. The twocurves a 
and a’b’ differ from each oth- 
er by a constant; the same 
is true of the curves a’ a and 
b’b, which are similar to the 
adiabatic curves of thermo- 
dynamics. Perhaps the sub- 
ject is best exemplified by 
an application to the electro- ~2 
magnetic engine. 
“The performance of external work by an electro circuit pro- 
duces a counteractive force whose magnitude is equal to the 
external work performed in an unit of time divided by the 
strength of the current. ; 
“ Let W be the external work performed in any unit of time 
by the engine. This gives rise to a counteractive force which 
causes the current to be of less strength than that which the 
battery produces when idle. Let 7 be the strength of the cur- 
rent in the idle circuit, and 7’ the strength when the work VW 
is performed per unit of time; then the counteractive force 18 
—, and the strength of the current 7’ is the same as if the 
electromotive force instead of being E were H— Sate | 
<——R— 
