TRANSACTIONS OF THE SECTIONS. 29 
circuit with a tangent-galvanometer and set of resistance-coils, causes the galvano- 
meter-needle to be deflected from the magnetic meridian through an angle a; on 
adding to the circuit an additional resistance R, the deflection of the needle 
diminishes to the value a’. From these observations it is required to deduce the 
original resistance 7 and the electromotive force e of the circuit, 
A B DB 
From any point B in the straight line AB draw BC, so that angle ABC=q; take 
BD, in AB produced, to represent the added resistance R, and draw DE so that 
angle ADE=a’. Since the angle at B (=a) is greater than the angle at D (=a’), 
the straight lines BC and DE must intersect (both being drawn on the same side of 
AB). Let F be the point of intersection, and draw FA perpendicular to AB: then 
the distance AB, between the point B and the foot of the perpendicular from F, will 
represent the original resistance of the circuit 7, on the same scale as that on which 
BD represents the added resistance R; and the perpendicular AF will represent the 
electromotive force e, in terms of that electromotive force taken as unity which, if 
it acted in a circuit of unit resistance, would produce a current capable of causing 
a deflection of 45° on the galvanometer employed. 
If the strength of the current in the first experiment be denoted by c, and in the 
second experiment by c', we have, by experiment, 
F AF 
inet i e 
e=tana=—_ ay and c’=tana —At ————— 
also, by Ohm’s law, 
c= and c’'=—°_ 
7? rth 
Therefore 
r AB a 7+R AB+BD, 
or REY AO bene mA 
whence 
ens sae 
AB” AF BD’ 
which proves the construction. 
II. Observations with a sine-galvanometer.—In this case let the first angle of 
deflection be denoted by 8, and that obtained after adding to the circuit a resistance 
