722 
DR. ARTHUR SCHUSTER ON THE EORCE PRODUCING THE 
If the time t for the elongations is only given approximately, the elongations will 
determine A. 
For the first elongation y x we have, if the time is t ls 
y x — aJj? - ** 1 sin ( 7 ^+ a) — sin (12) 
In this equation — A sin a is put for B. 
Differentiating (5) we have for the first elongation, as the velocity is zero, 
0=e~ Ml {ncos(nt l -i~a)—?iSm(nt 1 +a.)}+smaje jtl . . . . (13) 
The equations (12) and (13) will determine t x and a. They can, however, be brought 
into a more convenient form. 
Eliminating e~ 1<: out of (12) and (13), and introducing a new variable (3 , such that 
u 
tan j3=-, we get 
sin (a— B)= 7 ===; sin nt x e~ Kh (14) 
We also get easily 
cos (*-P)=^~=^(cos nt, (!-«■+<)' <'*) (15) 
Knowing a, we shall be able to determine ^ from (11), and hence to calculate the 
force L. 
In the experiments actually made, 20 successive elongations were observed. It was 
found that after the third the vessel vibrated round its position of rest. All the elon- 
gations after the third were therefore used to determine the time of vibration and the 
logarithmic decrement. Another set of observations was taken after the light had been 
removed, and the position of rest was determined in this way for the case in which no 
light falls on the mill. 
In the bifilar suspension the distance between the two threads at the top was 0-25, 
between the two threads at the bottom 0 - 08. The vertical distance from the top to the 
bottom of the suspension was 19-6, and the weight of the vessel was 31’2. The units 
used are those of the centimetre-gramme system. We calculate from these data 
H=0-00796. 
We find by experiment the time of half a vibration 11*03, and the logarithmic decre- 
ment 0-02978. Hence we calculate 
a=0-006219, 
w=0-28482. 
Equations (6) and (7) give 
H=I(A 2 -t-<). 
