W. Harkness—Color Correction of Achromatic Telescopes. 115 
fp Bits (47) 
in which dy is the difference, and yz the mean, of the refractive 
indices for the rays D-and F. For a law of dispersion involvy- 
ing at least two different powers of the wave-length, these 
equations will hold; but for a law involving only a single 
power of the wave-length, they may be satisfied, and yet the 
system of lenses will not be achromatic. Instead of embodying, 
these equations are actually independent of, the essential con- 
dition of achromatism; which is that at least two rays of 
pee different wave-length must be brought to a common 
ocus. 
I have not had leisure to examine my critic’s figures ; nor 
does it seem worth while to do so. My equation (2) represents 
Written in equation (2), has hitherto been most used ; but when 
compared with the best observations, the residuals, although 
small, show some constancy of sign. It has recently been | 
claimed* that Briot’s formula, which is ' 
fab? +4 cl + kM (48) 
represents the best observations, throughout the whole space 
om the extreme ultra-red to the extreme ultra-violet, within 
the limits of accidental error. If such is the case, a triple 
objective may possibly be better than a double one; but my 
critic's figures certainly do not suffice to prove this. They are 
pendent variable other than the wave-length, is likely to pro- 
uce erroneous results, and certainly does not tend to elucidate 
the subject. 
* By M. Mouton, in the Comptes Rendus, 1879, vol. xxviii, p. 1190. 
