omer] 
in the concavity BMZEN. Let the fine of incidence to the fine 
of refraction of glafs into air be as J to R, and out of water 
into air as K to R, and by confequence out of glafs into wa- 
ter as J to K: and let the diameter of the fphere to which 
the convex fides 4G D and CHD are ground be PD; and the 
diameter of the {phere to which the concave fides are ground be 
to D, as the cube root of KA—KTJ to the cube root of RK—RTJ; 
by which means the refractions on the concave fides of the 
glafles will very much correct the errors of the refraCtions 
on the convex fides, fo far as they arife from the fpherical- 
nefs of the figure. 
M. Eurer, improving on this hint, was not without hopes of 
being able, by the fame artifice, to prevent the difperfion which 
is occafioned by the difference of refrangibility; and publifhed a 
memoir ‘on that fubje@t in the Berlin Tranfactions for the year 
1747. . This memoir excited the attention of Mr. Dollond, and 
gave rife to that controverfy, which terminated fo happily in the 
glorious difcovery of the Achromatic Telefcope. 
Ir is fingular that this conftruction of the firft compound objec 
glafs, though fo principal a fubject of enquiry, fhould never have 
been demonftrated in the progrefs of this controverfy. Count 
Redern, in his memoir on “ The influence which the famous 
“ Newton attributes to the different retrangibility of the rays of 
“ light on refraéting Telefcopes,” in the Berlin Tranfadtions for 
the year 1760, obferves, that “ it is to be lamented, that 
«“ Newton has not given us the demonftration of this admi- 
“ rable conftruction, the difcovery of which would not be in- 
“ ferior 
