46 W. Gibbs—Miscellaneous Optical Notices. 
be reduced to its two first terms, and if we then eliminate the 
constants a and ) from three equations of the form 
b 
n=at7 
we shall obtain the three following se asi involving ee 
wave lengths and indices of refractio 
a3 _ (m,—%2) ; (1) 
(mss )ig +- (m2~"1)75 
As os (es -;) ; (2) 
(m2 - ")i3 + (”3- M2)y 
e = (m-%,) (3) 
1 1 
(%5 mae + (3 Bag 
Of these equations (1) and (8) serve for extrapolation and (2) 
for mterpolation. To test 5 egree of accuracy attainable in 
etermining wave lengths by these formulas, ] have selected 
the measurements made by Van der Willigen.* The indices of . 
refraction determined by the Dutch physicist are in fact the only 
indices which are at once sufficiently exact and sufiiciently nu- 
merous. In addition they have the great advantage of having 
been made with reference to lines in the solar spectrum the wave 
lengths of which had been measured by the same observer. 
There can therefore be no question of identity. As a first ex- 
ample of the method, I give a determination of the wave length 
of C, ta B as one of the lines exterior to C, an = Sar in 
succession 7 other exterior lines more refran gible n C, to 
combine with B. Formula (2) was therefore ah nae and 
with the following data and results :— 
B 1°61079 687748 
C 1°61252 656°56 
D 161436 628°11 656°70 +014 
11 1°61537 613°96 656°71 +0°15 
13 1°61560 610°52 656°56 0°00 
14. -161728 589°56 656°71 +0°15 
16 161978 561°80 656°76 +0°20 
17 1°62064 553°19 ~ 656°79 +0°23 
19 1°62143 545°83 656°87 +0°31 
Mean of the errors +017 
In this table the first column gives the designation or num- 
ber of the lines, the second its index of refraction, as deter- 
mined by a Steinheil prism of 60°, the third the corresponding 
* Archives du Musée Teyler, vol. i, p. 70. S 
