[ r 7 ] 
IV. A "Letter from the Rev. Nevil Mafke- 
lyne, A. M. Fellow of Trinity College , 
in the Univerfity of Cambridge, and 
F. R. S. to the Rev. Dr. Birch, Secretary 
to the Royal Society ; containing a Fheorem 
of the Aberration of the Rays of Light 
refracled through a Lens , o?i account of 
the ImperfeSlion of the fpherical Figure. 
Reverend Sir, 
Read Jan. 2z, BOUT two years ago, becoming 
y \ acquainted with Mr. Doilond’s cu- 
rious difcovery in optics, of correcting the aberration 
of the rays of light arifing from the different refran- 
gibility of the different forts of rays, by a combina- 
tion of two different kinds of glafs ; and learning 
from him, in converfation, that he had invented a 
theorem, fhewing the quantity of the aberration of 
the rays refraCted through a lens, on account of the 
imperfection of the fpherical figure ; by the applica- 
tion of which, he was able to make the aberrations 
of the combined concave and convex objeCt lenfes 
perfectly equal to, and confequently to correCt one 
another ; I was defirous of being more minutely 
acquainted with this farther great improvement in 
optics j and Mr. Dollond accordingly readily offered 
to gratify my curiofity. But in the mean while that 
he was looking over his papers, in order to lay them 
before me, having leilure, I fet about the investiga- 
tion of a Similar theorem myfelf ; which having 
Vol. LIJ. D completed, 
