Livers J 
fpherical furface, and y the femi-aperture of the lens, Newton has 
demonftrated, that when parallel rays fall on the plane fide of 
a plano-convex Jens, the lateral aberration at the focus, arifing 
2 w3 
from the pert eas of the figure, will be equal to pat 
RD 
which divided by Ru) the diftance of the focus from the 
R?—RI. 3 
centre of the lens, gives 
TE pe AL for the angle which the 
lateral aberration at the focus fubtends at the centre of the 
furface. Now when the ray pafles from the glafs into the 
included water, and from the water into the glafs, it is. evi- 
dent that the refraétions, and confequently the fpherical aber- 
rations, are contrary to thofe at the firft and laft furface ; and 
therefore, that all aberration fhould vanith, the lateral aberra- 
tions from glafs into air and from glafs into water (as being 
the principal, and wearly equal to thofe from air into glafs, 
and from water into glafs) fhould fubtend equal angles at 
the common centre of the fpherical furfaces. The fine of 
incidence out of water into air is to the fine of refrac- 
tion as K to R, and by confequence out of glafs into water 
as J to K; therefore if we fuppofe the rays, in pafling from 
the glafs into the water, to fall parallel on the water, the 
angle which the lateral aberration of the rays atthe focus fub- 
tends at the centre of the refracting furface will be equal to 
K*—KTI1 93 > i R?—RTx 7 
oe ee which being made equal to ae ae 
have d3 to D? as KK—KIto RR—RF Though the rays 
do not fall parallel on the water, yet the error caufed by their 
> we 
divergence 
