775 
ishes and the curve approaches asymptotically to the axis of X 
as the distance from the point X — X* increases. 
The maximum value cp * can be found from the following (ap¬ 
proximate) equation 
— log 10 tg (45° — <P*)_2\D\ . 
log, 0 e _ ' 
§ 11. We now proceed to examine to what extent the foregoing 
results are corroborated by experimental evidence. It will be con¬ 
venient first to consider the variation of the rotation ty with the 
wave-length; in this discussion the further question of the ellipti- 
city of the light transmitted through the substance will not, at first» 
be involved. 
A. In the case of a 10% solution of what he calls «double 
tartarate of chromium and potassium», M. Cotton gives, on page 
401 of the paper alluded to, the rotations tp, these observations 
covering a range which extends from wave-length 4,75.10 -5 cm 
to 6,57.10 5 cm. From the graphical representation, given l. c. on 
page 408, we infer that 
X ml — 5,13.10 -5 cm ; X m2 == 6,09.10 -5 cm (1) 
and from (3) in § 9. we obtain by use of (1) • 
X 0 = 5,63.10“ 5 cm. (2) 
The wave-length corresponding to / ip=0 on the curve is 5,65.10 -5 cm 
or nearly so; with this the result just obtained agrees fairly well. 
Applying equation (4) of Art. 9. we find 
r= 0.956.10" 5 cm (3) 
whence 
& = 2,84.10 14 sec -1 . (4) 
The quantity 1/2^ may be called «the time of relaxation» of the 
vibration. Its magnitude in the case considered seems thus to be 
about 2.10“ 15 sec; that, it may be observed, is the order of magni¬ 
tude of the period of the natural vibration. 
From (6), § 9., we obtain 
WU ; tym2 — lj!8:1 : • (5); 
X 0 and T having the values assigned to them in (2) and (3). This 
result may appear to conflict with M. Cotton’s diagram on page 
