48 W. Gibbs—Miscellaneous Optical Notices. 
In the case of the first prism the mean of the errors is +021, 
while for the second the mean of the errors is +035. From 
this it appears that in the more refrangible portion of the spec- 
; tne a 
ing the higher dispersive power. As the probable ee of the 
measurements of the indices of refraction are not given, it is 
ossible to determine to what extent the errors in the ag 
wat wave lengths are due solely to want of precision in the 
dices. It is also to be remarked that, while with the sete 
prism the errors in the less retrangible portion of the spectrum 
are affected with the ele es more refrangible portion they 
= a positive. amy ge in the value of the 
e length of 37, as cant he der Willigen, with the 
waves as found by aechainer and Angstrom—438-27 and 
438-28—proves that the source of error is not an erroneous de- 
termination of this quantity. It seems therefore certain that the 
nearly constant errors noted above are due in part to the fact 
‘that the indices of refraction are determined only to five places 
of decimals, and in part to the high dispersive powers of the 
prisms employed, which would render it necessary to employ more 
= hg terms in Cauchy’s formula to obtain a closer approxi- 
s the formulas for interpolation would in this way be 
Sader Bons complicated, it is better, in the case of any 
series of observations embracing a particular part of the scale, 
simply to determine the mean of the errors, and to apply this 
mean with its proper sign to the computed values of the par- 
ticular wave length to be determined by the measurement of 
indices of refraction. If we apply such a correction in the 
cases of the four series of data and results given above, we find 
for the corrected idee: of the wave-lengths the following nu- 
merical results 
(1) (2) (3) (4) 
656°53 656°49 438°67 438°72 
656°54 . 656°61 438°55 438°54 
656°38 656°59 -438°61 438°57 
656°54 656°66 438°55 -438°65 
656°59 656°75 438°54 —438°54 
656°62 438°44 438°49 
The true values being respectively 65656 aiid 438°56. These 
results: are, It ey, sufficient to show that a valuable control 
