268 Mr. M. Ponton on certain Laws 
how far the peculiarities observed in some of the media, as 
respects the number and position of the nodes of the extrusions, 
may be traceable to errors of observation. 
In the case of sulphuric acid, these peculiarities are removed 
by the entire extinction of the extrusions, under the operation of 
the exponential law. But the extrusions are brought to assume, 
by virtue of this law, the regular type in the following cases, in 
which the observed indices cause them to appear quite irregular, 
namely, muriatic acid, alcohol, solution of soda, pyroligneous 
acid, and oil of anise, temp. 15°. See end of Table IV., where 
the extrusions of these media are given as they appear after the 
indices have been corrected by the exponential law. 
The removal of the irregularity in the extrusions, by the ope- 
ration of this law, is particularly noticeable in the case of oil of 
anise; for there is thus made to disappear from this medium the 
apparent anomaly of its having its extrusions regular at temp. 
13°25 and temp. 20°-9, but irregular at temp. 151, they being 
thus rendered regular at all the three temperatures. 
It is interesting to note in this particular case the effect of the 
exponential law on the values of ¢, the index of elasticity, as 
viewed in relation to the temperature. These values become— 
Diff. 
Temp. 13°-25 « = 1478427. . 1044 
La PUL OME 1:477383 . . 3898 
»  20°9 1473485 . . 4942 
These differences are not far from being proportional to the 
differences of temperature, but they may be brought into that 
precise ratio by a further slight alteration on the indices of refrac- 
tion, while these latter may be at the same time preserved obe- 
dient to the exponential law. This end may be attained by 
making the values of log e, and a, stand thus :— 
Temp. 13°-25 log e, 0°1857298 a, 0006160, 
Temp. 15° 1 log e,,0°1857412 a, 0:006303, 
and Temp. 20°9 log €, 0°1847219 a, 0:006350. 
The values of ¢ then become 
Diff. 
Temp. 18°25 ¢1:478482 . . 1181 
v.01. Lav7S0l... ose 
» 20°9 1478568 . . 4914 
These differences are in exact proportion to the differences of 
temperature, while the values of ¢ themselves are in the inverse 
order of the temperature, thus strictly fulfilling the law. 
The indices of refraction thus corrected will be found at the 
