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L. M. Cheesman—Measurement of Electrie Currents. 121 
axis of the windings of the galvanometer makes an angle of 
45° with the magnetic meridian. For suppose the instrument 
placed so that the axis of the windings makes an angle (a) with 
the magnetic meridian and that the needle has experienced a 
deflection gy from the meridian by the alternating currents; 
the conditions of equilibrium will evidently . 
MT sing=iM’/(R) sin(a—g), 
M denoting the permanent magnetic moment, 
M’ the induced magnetic moment, 
T’ the horizontal intensity of the earth’s magnetism, 
«the intensity of the alternating currents, an 
/(R) a function depending on the number and form of the 
Indings, ete. 
M’ can be replaced by 7/(R) cos(a—g), whence we obtain, 
spa! si _MT 
ak [PR 
differs but 0°2 per 
Pp 
St ee ow Wa ia sas —= 2. 
. sin2(a—@)’ 
; es Ty 
For the special case a=45°, anna=e) 
cent from tan g, when g=3°. 
Delicacy.—The following table gives an idea of the delicacy 
of the above instrument and its variation with the time of 
vibration of the needle as altered by reducing the value of the 
horizontal intensity of the earth’s magnetism. The first col- 
umn gives the time of vibration of the needle, the second the 
quotient obtained by dividing the deflection observed on the 
galvanometer by that of a Weber’s* electro-dynamometer in 
the same circuit, so that the same intensity of current acted in 
each case, both deflections of course being reduced to the same 
scale distance. The time of vibration of the dynamometer 
sec, 
spool was 
Time of vibration. Quotient of the deflections. 
8:3" O-7 
10° ; Eis § 
16° 2°6 
22° 43 
So that for equal times of vibration the galvanometer had 
considerably greater delicacy, although the Weber instrument 
had over 1800 more turns of wire than the galvanometer. : 
_4n conclusion, I should state that a number of determina- 
tions of resistances by the method of substitution with alter- - 
nating currents were made with the above instrument with 
very satisfactory results. 
* Instrument made by Leyser. Number of windings of the stationary spool, 
1860; resistance, 152 ohms; number of windings of the moyable spool, 4380; 
resistance, 205 ohms : : 
