DETERMINING THE CONSTANTS OF A VOLTAIC CIRCUIT. 
319 
If r' = g, that is if the resistance of the galvanometer wire be equal to that of the 
wire which diverts a portion of the current from it, then R = r. 
Third Method. — Bring the needle to any determined point, and ascertain by means 
of the instrument described at § 1 8. what degree corresponds to one-half the intensity 
thus indicated. Since, when the electro-motive force remains the same, the force of 
the current is simply inversely as the total resistance, to reduce the needle from a to 
a resistance exactly equal to that previously existing in the circuit must be added ; 
therefore the number of turns of the rheostat required to reduce the needle from a to 
— will be the measure of the total resistance of the circuit when the needle stood at a. 
The total resistance being thus measured, that of the rheomotor is determined by 
subtracting from it the other known resistances, including that of the galvanometer. 
More generally, if the forces of two currents, a and h, corresponding to two sta- 
tionary positions of the needle, are known (§ 19.), the total resistance of the circuit 
b t 
will be R = a _ jp r being the resistance added to reduce the current from a to h. If 
a = 2 Z>, then R = r as before. 
Fourth Method. — For this and the following process two exactly equal rheomotors 
must be employed ; their equality may be tested by successively interposing them in 
the same circuit, when one and the other should deflect the needle of the galvanometer 
precisely to the same degree. 
Place one rheomotor in the circuit and adjust the rheostat until the needle points 
to any degree arbitrarily fixed upon ; then add the second element by the side of the 
first, and increase the reduced length of the circuit by turning the rheostat until the 
needle again points to the same division. The known quantity, measured by the 
number of turns of the rheostat, by which the reduced length of the circuit is in- 
creased, is equal to one-half the resistance of a single rheomotor. By placing the 
second rheomotor by the side of the first, the resistance of that portion of the circuit 
is reduced one-half; therefore, to restore the former condition of the circuit, a resist- 
ance equal to one-half that of the rheomotor must be added. For 
E _ E . _ R 
R being the resistance of the rheomotor, and r the other resistances in the first circuit. 
Fifth Method. — Place both the rheomotors in series, and vary the resistance until 
the needle stands at any determined degree. Then place them side by side, and in- 
crease the resistance, by turning the rheostat until the needle again stands as before. 
The resistance of a single rheomotor is equal to twice the resistance required to 
be added, plus all the resistances in the first circuit except that of the rheomotor, 
2 E E 
2 R -f r R 
y + r + A 
.’. R — r -f" 2 X, 
