C 2 9o ] 
lb long ago has been demonftrated impoffible. But, 
as fo great a mathematician as Mr. Euler has lately 
pubiifhed a theorem * * for making objedt-glafies, that 
lhould be free from the aberration arifing from the dif- 
erent refrangibility of light, the fubjedt deferves a par- 
ticular confideration. I have therefore carefully exa- 
mined every hep of his algebraic reafoning, which X 
have found ftridtly true in every part. But a certain 
hypothecs in page 2 8 f. appears to be deftitute of fup- 
port either from reafon or experiment, though it be 
there laid down as the foundation of the whole fabrick. 
This gentleman puts m: 1 for the ratio of refradticn out 
of air into glals of the mean refrangible rays, and M: 1 
for that of the lead; refrangible. Alfo for the ratio of 
refradtion out of air into water of the mean refrangi- 
ble rays he puts n : 1 , and for the lead refrangible 
N\\. As to the numbers, he makes >// = —£, M— 
-J ~, and ^=7; which fo far anfwer well enough to 
experiments. But the difficulty confifts in finding the 
value of N in a true proportion to the reft. 
Here the author introduces the fuppofition above- 
mention’d ; which is, that m is the fame power of M, 
as n is of N-, and therefore puts n = m *, and N=M*. 
Whereas, by all the experiments that have hitherto 
been made, the proportion will come out thus, m — 1 : 
n — 1 : : m — M : n — N. 
The leters fixed upon by Mr. Euler to reprefent the 
radii of the four refradting furfaces of his compound 
objedt-glafs, are fg h and and the diftance of the 
objedt he expreftcs by a ; then will the focal diftance 
be = — t ; rr-T — 7—- : 7-7— . . No W, 
■t) 4 ntf-i+t-t) -7—}+ f 
fays 
* Vide Memoiresof the Royal Academy of Berlin for the Year 1747. 
