226 Mr. J. F. W. Herschel on the aberrations of 
its developement than was required for its application to the 
theory of thin lenses placed in contact, and especially to 
that of double object-glasses, reserving the theory of eye- 
pieces, microscopes, &c. as well as that of thick lenses, for 
a second communication, should the Society honour this 
with a place in their Transactions. 
The problem of the destruction of the spherical aberration 
in a double or multiple lens, is well known to be indetermi- 
nate, the algebraic conditions requisite for that purpose fur- 
nishing but a single equation (at least when the mean rays 
only are considered). To fix on the best possible condition 
for limiting the problem, is a matter of considerable delicacy ; 
D’Alembert has proposed, among others (Opusc. Tom. 3, 
Art. 742), to annihilate the spherical aberration for rays of 
all colours , a refinement which might almost be termed puerile, 
were it not for the respect due to so great a name.* It has, 
besides, the inconvenience of leading to equations of the fourth 
degree. A much better condition, in every point of view, 
is another proposed by the same profound geometer, in Art. 
758, viz : the destruction of the aberration for an object 
situated out of the axis of the telescope ; or in other words, 
the rendering the whole field of view equally perfect so far 
as the object-glass is concerned. But even this is perhaps car- 
rying refinement too far. The difference of the aberrations 
of an object-glass in and out of the centre of the field, is so 
small in ordinary telescopes, as to have escaped (so far as my 
enquiries have gone), the notice of the best practical opticians 
* I pass over the construction proposed by D’Alembert, in Art. 746, as having 
no recommendation but that of avoiding a biquadratic equation ; though, it is true, 
the radii resulting from it might be used. 
