40 REPORT — 1871. 



achromatize each other so as to exhibit no secondary spectrum, or a single glass 

 which would achromatize in that manner a combination of crown and flint. 



This inquiry presented considerable difficulties. The dispersion of a medium is 

 small compared with its refraction ; and if the dispersive power be regarded as a 

 small quantity of the first order, the irrationality between two media must be 

 regarded as depending on small quantities of the second order. If striae and 

 imperfections of the kind present an obstacle to a very accurate determination of 

 dispersive power, it wiU readily be understood that the errors of observation 

 which they occasion go far to swallow up the small quantities on the observation 

 of which the determination of irrationality depends. According^, little success 

 attended the attempts to draw conclusions as to irrationality from the direct obser- 

 vation of refractive indices ; but by a particular method of compensation, in 

 which the experimental prism was achromatized by a prism built up of slender 

 prisms of cro^vn and flint, I was enabled to draw ti'ustworthy conclusions as to 

 the character in this respect of those prisms which were sufliciently good to show 

 a few of the principal dark lines of the solar spectrum. 



Theoretically amj three difi"erent kinds of glass may be made to form a combi- 

 nation achromatic as to secondary as well as primary colour, but practically the 

 character of dispersion is usually connected with its amount, in such a manner 

 that the _ determinant of the system of three simple equations which must be 

 satisfied is very small, and the curvatures of the three lenses required to form an 

 achromatic combination are very gi'eat. 



For a lon^ time little hope of a practical solution of the problem seemed to 

 present itself, in consequence of the general prevalence of the approximate law 

 referred to above. A prism containing molybdic acid was the fiirst to give fair 

 hopes of success. Mr. Hai'court warmly entered into this subject, and prosecuted 

 his experiments with unwearied zeal. The earlier molybdic glasses prepared were 

 many of them rather deeply coloured, and most of them of a perishable nature. 

 At last, after numerous experiments, molybdic glasses were obtained pretty free 

 from colour and permanent. Titanium had not yet been tried, and about this time 

 a glass containing titanic acid was prepared and cut into a prism. Titanic acid 

 proved to be equal or superior to molybdic in its power of extending the blue end 

 of the spectrum more than corresponds to the dispersive power of the glass ; while 

 in every other respect (freedom from colour, permanence of the glass, greater abun- 

 dance of the element) it had a decided advantage ; and a great variety of titanic 

 glasses were prepared, cut into prisms, and measured. One of these ^led to the 

 suspicion that boracic acid had an opposite effect, to test which Mr. Harcom-t 

 formed some simple borates of lead, vrith varying proportions of boracic acid. 

 These fuUy bore out the expectation ; the terborate for instance, which in dispersive 

 power nearly agrees with flint glass, agi-ees on the other hand, in the relative 

 extension of the blue and red ends of the spectrum, with a combination of about 

 one part, by volume, of flint glass with two of crown. 



By combining a negative or concave lens of terborate of lead with positive 

 lenses of crown and flint, or else a positive lens of titanic glass with negative 

 lenses of crown and flint, or even with a negative of very low flint and a positive 

 of crown, achi-omatic triple combinations free from secondary colour may be formed 

 without encounteriag (at least in the case of the titanic glass) formidable cm-vatures ; 

 and by substituting at the same time a titanic glass for crown, and a borate of lead 

 for flint, the curvatures may be a little ftu-ther reduced. 



There is no advantage in using three different kinds of glass rather than two to 

 form a fully achromatic combination, except that the latter course might require 

 the two kinds of glass to be made expressly, whereas with three we may employ 

 for two the crown and flint of commerce. Enough titanium might, however, be 

 introduced into a glass to render it capable of being perfectly achromatized by 

 Chance's " light flint." t> f j j 



In a triple objective the middle lens may be made to fit both the others, and be 

 cemented. Terborate of lead, which is somewhat liable to tarnish, might thus be 

 protected by being placed in the middle. Even if two kinds only of glass are 

 used, it is desirable to divide the convex lens into two, for the sake of diminish- 

 ing the curvatm-es. On calculating the curvatui-es so as to destroy spherical as 



