with a fluid concave lens. 221 



secondary spectrum, either to zero or to a very inconsiderable 

 amount. In order to examine the practicability of this object, 

 let us first consider the two lenses in contact, and inquire into 

 the conditions requisite for uniting the violet, the red, and the 

 mean ray, which latter may be accounted that on the confine 

 of the violet and red sides of the spectrum. Let the focal 

 length of the mean ray in the plate lens be^ and the length of 

 the focus beyond /, viz. the red side of the spectrum, be r, its 

 whole focus being/ + r ; tetf, t& and of course f'+r' de- 

 note the same in the correcting fluid lens : then, in order that 

 the red ray may coincide with the mean ray, we must have 



1 __!__! tt< 



f ff+r f' + r 



1 1 r 



Now fT^ = f-f'{f+r) 



1 1 r' 



and 



f+r'-f-fU'+r') 

 therefore, when j —j, = jzf r — f + r ' 

 we must have jtf^ = jr^r+ 7) 



T t' 



and therefore, /'•/''■: JZI7 : f + y 



That is, the mean focal lengths must be to each other as the 

 red part of the focus divided by the whole focal length of the 

 red ray, or, as the dispersive powers for this side of the spec- 

 trum, in each lens. 



" In the same way, if we denote by v and if the length of 

 the violet part of each focus ; then to have the violet and the 

 mean ray coincide, we must have 

 1 1 _J_ 1 



and as before, we shall find that this can only take place when 



hence, in order to unite these, three colours, the conditions 

 must be that 



r v r' v 



/+ r : /--i> ' 'f+r' 'J" — V 

 " But as /, r and v, in one case, and /', r and if, in the 



VOL. IX. NO. II. OCTOBER 1828. P 



