Prism on Newton's Rings. 351 
Corresponding expressions are required for the dispersive 
instruments. In any particular case they could o£ course be 
determined ; but no very simple rules are available in 
general. If the intrinsic dispersion be small — the necessary 
effect being arrived at by increasing D, we may make the 
comparison more easily. Thus in the case of the grating 
the variable part of f is proportional to 8k simply, so that the 
ratio of the second and third terms, corresponding to (16), is 
zero. And in the case of the prism if we assume Cauchy's 
law of dispersion, viz. /j, = A + BX -2 , we get in correspondence 
with (16) 
-I®!: (19) 
So far as these expressions apply, it appears that the dis- 
persion required is between that of a grating and of a prism, 
and that especially when a = the grating gives the better 
approximation. It would be possible to combine a grating 
and a prism in such a way as to secure an intermediate 
law, the dispersions cooperating although the deviations 
(in the case of a simple prism) would be in opposite 
directions. 
I have made observations with a grating, using for the 
purpose a photographic reproduction upon bitumen *. This 
contains lines at the rate of 6000 to the inch and gives very 
brilliant spectra of the first order. I thought that I could 
observe the superior achromatism of the most nearly achro- 
matic bands as compared with those given by the prism, 
but the conditions were not very favourable. The dispersive 
power was so high that the grating had to be held very close, 
and the multiplicity of spectra was an embarrassment. If it 
were possible to prepare a grating with not more than 3000 
lines to the inch, and yet of such a character that most of 
the light was thrown into one of the spectra of the first 
order, it might be worth while to resume the experiment 
and, as suggested, to try for a more complete achromatism 
by combining with the grating a suitable prism. 
Terling Place, Witham, 
Jan. 30, 1908. 
* < Nature/ liv. p. 332, 1896 ; < Scientific Papers/ iv. p. 226. 
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