168 REPORT—1863. 
coils 1, 2, 4, &c. had amalgamated copper terminals which simply dropped 
into mercury-cups on the copper bars. The observations could be made very 
rapidly and accurately, as the galvanometer was sensitive enough with four 
Daniell’s cells to indicate the addition or subtraction of the 512 coil with per- 
fect distinctness. The reduction of the observations to find the ratio seems 
somewhat complicated at first, but with the aid of a table of reciprocals it 
takes but little time. No improvement seems necessary in this part of the 
apparatus. The idea of using large coils combined with small ones in mul- 
tiple are to obtain extremely minute differences of resistance, was suggested 
to the writer by Professor W. Thomson, and will be found useful in very 
many ways. 
Part I17.—Maruemarican THEORY oF THE EXPERIMENT. 
A circular coil of copper wire is made to revolve with uniform velocity 
about a vertical diameter. A small magnet is suspended by a silken fibre in 
the middle of the coil. Its position is observed when the coil is at rest, and 
when the coil revolves with velocity w the magnet is deflected through an 
angle g, Currents are induced in the coil by the action of the earth’s mag- 
netism, and these act on the magnet and deflect it from the magnetic meri- 
dian. By observing the deflection and the velocity of rotation, we can deter- 
mine the resistance of the coil in electromagnetic units. 
In determining the strength of the current we may neglect the motion of 
the suspended magnet, as it is found, both by theory and by experiment, to 
be insensible. We have therefore, in the first place, to determine the elec- 
tromagnetic potential of the coil with respect to the earth’s magnetism, with 
respect to the suspended magnet, and with respect to itself. 
1st. Let H be the horizontal component of the earth’s magnetism. 
y the strength of the current in the coil. 
G the total area enclosed by all the windings of the wire. 
@ the angle between the plane of the coil and the magnetic meri- 
dian. 
Then the potential of the coil with respect to the earth is 
—HyG sin 0. 
2nd. Let M be the magnetic moment of the suspended magnet. 
@ the angle between the axis of the magnet and the magnetic 
meridian. 
K the magnetic force at the centre of the coil due to unit current 
in the wire. 
Then the potential of the coil with respect to the magnet is 
—MyK sin (0—¢). 
3rd. Let 1L be the potential of the coil on itself for unit current. 
Then the potential due to a current y is 
ALy? 
ral 9 
Let P be the electromotive force, and R the resistance, then the work 
spent in keeping up the current is Py in unit of time; or, since P=Ry, the 
work spent in keeping up the current for a time 6¢ is 
Ry’ ot. 
If the current is at the same time increased from y to y+6y, the work 
spent in increasing the current will be 
Ly dy. 
