'174- -A Paper to obviate feme Doubts concerning the 
different methods of afeertaining them are ufed. The varia- 
tion in the two higheff powers is more confiderable than I was 
aware of; but hill may ealily be (hewn to be a neceflary confe- 
quenee of the difference in the methods. However, if upon 
comparing together the methods it fhould be thought, that the 
power 5786 is nearer the truth than 6450, I (hall readily join 
to correct that number. The manner in which I have now 
determined the powers is as follows : I took one of the eye 
lenfes which magnifies leaff, and meafured its folar focus by 
the fun’s rays as exactly as I could five times, which proved to be 
1.01, 1.04, 1.09, 1.01, 1.05, in half-inch meafure, a mean of 
which is 1.04. The fidereal focus of my feven-feet fpeculum 
is 170.4 ’ m the fame meafure. Thence, dividing 170.4 by 
1.04 we find that the telefcope will magnify 163.8 times when 
that lens is ufed. This power being found, I applied the fame 
lens as a fingle microfcope to view with it a certain objeCt, 
which was a drawn brafs wire fattened fo as not to turn upon 
its axis or change its pofition ; for thefe wires are feldom per- 
fectly round, or of an even fize, and it is therefore neceffary to 
ufe this precaution to prevent errors : then, with a fine pair 
rtf compafifes, I took four independent meafures of the image 
of the brafs wire, which was thrown upon a theet of paper 
exadtly inches from the lens, the eye being always as clofe 
to the lens as poffible. I viewed the fame wire, exaCtly in the 
fame manner, with every one of the lenfes, and rneafured the 
pictures upon the paper. When I came to the higher powers 
the wire eyas exchanged for another 4.37 times thinner than 
the former, as determined by comparing the proportion of their 
images 54 to 235 £, taken by the fame lens. 
When the images of thefe wires are obtained, the power of 
the telefcope, with every one of the lenfes, becomes known 
by 
