416 AUGUST WITKOWSKI ON EFFECTS OF STRAIN 
7 the radius of the circle C (=5-2 cm.), then we have the following equations of 
equilibrium :— 
Qarra i 
and 
Qarr4 ; 
G=+Dpe tt 
hence 
K { 1 dsctres) 
Ga FE AD. 0/ PSE TS 
@ L@?+D2)? (7 +D73 § 
where 
for. a7r(R3—R?) 
Ries LR AN eile GN 
Jn+(g) Je) 
a constant depending on the dimensions of the apparatus. For the apparatus 
described above we have— 
K=1515'9655. 
The mode of experimenting is now obvious. The magnet, attached to the 
light mirror, is maintained in a plane perpendicular to the axis of the tube, and 
this position ascertained by observing the spot of light reflected on a scale from 
a lamp placed in the prolongation of the axis. 
A few further remarks appear necessary. Although the proceeding 
described is a true “zero method,” the exact positions of the compensating 
circle C cannot be easily determined by simply shifting it along the scale, and 
even the deflections of the spot of light caused by twisting the tube are so 
small as to be scarcely visible. The circuit contained for that reason a 
reversing-key K, and after the approximate position of the circle had been 
found, more exact readings were taken by comparing the vibrations of the 
magnet, produced by reversing the current, while the circle C occupied two 
positions on both sides of the presumed zero position. 
Another remark that should be made is this. The effects of permanent 
strain are well known to interfere in all experiments concerned with elastic 
bodies. They do so in the present case more than in others, inasmuch as the 
constant o for permanent strains seems to exceed considerably the value found 
for elastic strains. Thus the distances D, and D, were found variable to a 
considerable extent, and the positions of the compensating coil, corresponding 
to equilibrium, were successively shifted, the shifting coinciding in direction 
with the quasi-elastic shifting, when the tube was twisted again and again in 
the same way. Several trials were necessary to bring the apparatus into such 
a condition that both the tube and the compensating coil should return to their 
initial positions when the weights were removed, with the precision that might 
