OF ELECTROSTATIC UNITS IN THE ELECTROMAGNETIC UNIT. 
417 
The solution of this equation gives (T= period of vibration of the coil) 
T=-£=2r -v/"* and E=!?5P- 2 
\/a V E T 2 
(3) 
Let y= strength of current which gives a deflection of one scale-division. 
The deflection of the reflected image being twice the deflection of the coil, the elastic 
couple corresponding to a deflection of one scale-division is 
length of 1 scale-division 
twice distance of scale 
Equating (2) and (4), we have 
4 
X 
length of scale-division 
T 2 ^ 2 x distance of scale ( r 2 pi\ 
~[ 27rnr<2 1 F , [ ‘Z'tn'r'z 1 
.1 (r 2 + brfj ~ l " 1 (r 12 + b 2 f J _ 
«Vc 2 y 2 . 
(4) 
( 5 ) 
Equation (5) gives y in terms of units of space, time, and mass. It is seen also from 
this equation that the deflection produced by a current passing through the coils of the 
electrodynamometer is proportional to the square of the strength of the current. 
Accordingly the strength of current indicated by any given deflection is obtained by 
multiplying the value of y given in (5) by the square root of the number of scale- 
divisions in the deflection. 
Results of the Comparison. 
I. The following is a summary of the results obtained by Mr. King, from a comparison 
of measurements with the Electrodynamometer and the (old) Absolute Electrometer : — 
1867. Nov. 18-27 
1868. 
Electrodynamometer compared with Stan-i 
dard Electrometer, which had been pre- 
viously compared with the Absolute 
Electrometer (indirect) 
(Direct Comparison of Electrodynamometen 
( and Absolute Electrometer ) 
Mar. 10-Apr. 7 . Direct Comparison 
(Direct Comparison ; observers and all the 
Dec. 3-20 
Apr. 20-30 
May 1-10 
’ { instruments insulated 
. Direct Comparison 
centime, per second. 
v=297-2xl0 8 
tt=289-2 x 10 8 
u=284-5xl0 8 
^=283-7 x 10 s 
v=285-Q x 10 8 
Mean value of v given by this comparison, leaving out the two first sets (which were 
taken under very unfavourable circumstances), is 284'6xl0 8 centims. per second. 
II. The comparisons which were made during March 1870 in the Laboratory of the 
old College were preceded by some alterations in the electrodynamometer, and a fresh 
determination of several of the quantities connected with it. Resistances were measured 
by a new set of standard coils, and the old absolute electrometer was superseded, in the 
comparison, by the new absolute electrometer already referred to. 
The movable coil was resuspended, and a light mirror, the opposite sides of which had 
been ground parallel, was substituted for the heavier mirror that had been formerly used. 
3 K 
MDCCCLXXIII. 
