FORCE OF THE WESTON NORMAL CELL IN SEMI-ABSOLUTE VOLTS. 177 
Now the amplitudes for successive transits are in geometrical progression such that 
ai /a 2 = e (n ~ 1)x where X is the logarithmic decrement; hence we have 
T — T' J1 — / l —e 4NA 
0 1 32N \ \ —e~ 2K 
and therefore approximately 
T _ T' J 1 a l 2 —a 2N 2 1 
1 64NX ^ 
If a n is the distance between extreme scale readings for the n th period or 2 n th 
transit and D is the distance from the axis of rotation to the scale we have 
tan 2a = a/ 2D or approximately, a = aj 4D and therefore 
«i 2 -«n 2 l 
1024N\D 2 j 
• ( 10 ) 
If the correction due to the resistance of the air had not been neglected there would 
have been a further factor, (1 — 6). It can be shown that 6 < (k\) 2 where k is a 
constant less than unity, and since X 2 is quite negligible in our case we need not 
consider 6. 
Since the value of the correction in (10) was usually less than 2 parts in 100,000, 
the various figures recorded below for T x and T 2 have already been corrected when 
necessary. 
In the case when the cylindrical weights were in the exterior position it was found 
experimentally that X = 0‘00090. It was convenient to start observations with an 
oscillation of about 5 cm. on the scale. If the observations extended over 1500 
periods the correction for T would be less than 1 part in 1,000,000. Starting at 5 cm. 
it took over 3000 periods before the oscillations were too small to be observed. 
When the weights were at the internal position X = 0‘0016, and if desired it was 
again possible conveniently to choose a x and N so that the correction for T would be 
negligible. 
The elastic fatigue produced by the continuous torsional oscillations was not of a 
sufficient magnitude appreciably to affect these observations in any way. 
The transits were observed through a telescope and recorded electrically on the 
chronograph with the aid of a tapping key. With a little practice the time between 
transits could be repeated to within a tenth of a second, but the period as deduced 
from a full set of oscillations could be repeated to within 1 part in 100,000. 
( e) The Masses of the Cylinders. 
The weighings were made on a Troemner balance sensitive to O'OOOl gr. with the 
given mass of the cylinders, and using a set of standardized weights with corrections 
obtained at the Bureau of Standards in Washington. The readings were taken by 
the usual method of oscillations, and repeated with the weights and cylinders 
VOL. CCXIV.—A. 2 A 
