370 A. W. Ewell — Rotatory Polarization. 



III. Aug. 5. Same tube. Twist = 60. (All rotations negative.) 



Change in length 2 3*1 -4 — •] —1 —4 — *3 



Rotation.. 4 9 22 4 2 1 1 2" 



I. Aug. 5. Jelly tube D 1. Original length = 3*70. Twist = 

 • 120. (All rotations negative.) 



Change in length 1-6 3 2-4 1* — -3 —1*2 —2*8 —5 — 1 

 Rotation 9 25 118 75 36 18 10 5 2 9 



II. Aug. 6. Same tube. Twist = — 90. 



Change in length 1*4 2-5 1-2 '5 — 1*6 — 3*5 — 5*4 —2*4 

 Rotation.. 14 35 74 33 14 6 5 1 6 



The results for tube C 5 are plotted in fig. 2, and for D 5 in 

 fig. 3, the abscissa being change of length, a?, and the ordinate, 

 rotation, y. 



Apparently, when x = oo , y = go ; when x = — co , y = 0. 

 This suggests an exponential curve of the general form 



y = c 3 c 2 x or 



log y = A + Bx 



where c 1 and c 2 are empirical constants. In fig. 3a the ordi- 

 nates are logarithms of the rotation and the abscissae are 

 changes of length as before. The closeness of these curves to 

 straight lines indicates that the curves in figs. 2 and 3' are very 

 approximately exponential curves. 



If we let x' represent the actual length, i. e., in figs. 2 and 

 3, cc + a constant ; when x = oo y — 0, when x — y — oo , 

 which is satisfied by an equation of the form 



introducing a few values for x and y from any of the curves 

 shows such an equation to be entirely unsatisfactory. 



The above observations demonstrate that the rotatory polari- 

 zation of a jelly tube, subjected to a given twist, increases with 

 longitudinal compression and decreases ivith longitudinal 

 elongation, the change closely following an exponential law. 



Neglect of this condition was the chief cause of the great 

 irregularities in the. early work. When the lower clamp rested 

 on the platform, e, it made an appreciable difference in the 

 rotation which end of the jelly tube was first clamped, it being 

 clamped in the one case when compressed and in the other 

 when stretched by its own weight. The same tube was quite 

 sure to give different results when taken out and replaced, for 

 it could never be replaced under exactly the same strain. The 

 first attempt to avoid this difficulty was to keep the measured 

 length constant with clamps, but this gave little improvement. 



