210 On the Formula for the Dispersion of Light. 
By My #, 
Medium, Calculated Calculated 
fedinm Observed by by theexact | by the approxi- 
Fraunhofer. Formula. mate Formula. 
——— el — eee eee —EEEEEE——EES 
Flint-glass 13. 1°6350 1°63492 1°6355 
Do. 93. 1°6337 1°63350 1°6335 
Do. 30. 1°6306 1°63051 1°6305 
Do. 3. 1:6085 1°60825 1°6079 
Crown-glass M. 1°5591 1°55901 1°5593 
Do. 13. 1°5281 1°52788 1°5279 
Do. 9. 1°5296 1°52945 1°5296 
Oil of turpentine.| 1°4'744 1°47444 | 1°4746 
Solution of potash. 1°4028 1°40270 1°4029 
Water. 1°3336 1°33346 1°3333 
I shall not here enter on any detailed remarks or compari- 
sons of the results exhibited in this table. From it the reader 
will be enabled to form a correct judgement of the degree in 
which the approximate method is comparable with the exact ; 
at least for media of no higher dispersive power than those 
examined by Fraunhofer. Meanwhile we may just observe, 
that the results here given by the exact formula are invariably 
a little in defect compared with those of observation; whereas 
the approximate numbers are sometimes in defect and some- 
times in excess. To this circumstance, and some further 
investigations connected with it, I shall recur in a future 
communication. 
—<—<_—_—=— 
In the last Number (p. 113) 1 alluded to the calculations of 
M. Rudberg. It may be worth while to observe that such a 
formula as that which he adopted empirically, may give results 
nearly coinciding with those of the formula derived from 
theory which I have used, as will appear by the following con- 
siderations. 
M. Rudberg’s formula, in my notation, becomes 
ie = a ae), 
be 
1 
Now (writing @ gaan a'), let us suppose a quantity H! so 
assumed that we have 
or; atx = H'(1-=5); 
