350 Lord Rayleigh : Effect of a 
by a region where the bands are fringed with colour. This 
feature becomes more distinct as the interval is still further 
increased, so that without the prism only faint rings or none 
at all can be perceived. For the greater intervals the inter- 
position of a piece of mica at one edge is convenient. In 
judging of the degree of achromatism, I found that narrow 
coloured borders could be recognized as such much more 
easily by one of my eyes than by the other, and the difference 
did not seem to depend on any matter of focussing. 
In observing bands of rather high order, the question 
obtruded itself as to whether the achromatism was anywhere 
complete. It will have been remarked that the theoretical 
discussion, as hitherto given, relates only to a small range 
of wave-length and that no account is taken of what in the 
telescope is called secondary colour. So long as this limita- 
tion is observed, the character of the dispersive instrument 
does not come into play. It appeared, however, not at all 
unlikely that even with gaslight the range of wave-length 
included might be too great to allow of this treatment being- 
adequate ; and with daylight, of course, the case would be 
aggravated. It is thus of interest to examine what law of 
dispersion is best adapted to secure compensation and in 
particular to compare the operation of a prism and a 
grating. 
As to the law of dispersion to be aimed at, we have from 
(4), if X=X + 8X, 
If f be the displacement due to the instrument, f should be 
a similar function of 8X. In this matter the constant terms 
(independent of 8\) are of no account, and the terms in 8X 
may be adjusted to one another, as already explained, by 
suitably choosing the distance D. In pursuing the approxi- 
mation, what we are concerned with is the ratio of the term 
in (8X) 2 to that in 8X. And in (15) this ratio is 
1 nBX (16) 
8 inX Q — a 
thus in the particular cases 
ISA- .-,-, 
a = 0, -j-; .... (17) 
a = ±nX , — 9 .- ( 18 ) 
