134 
DE. T. E. EOBINSON AND ME. T. GKBUBB’S DESCEIPTION OF 
those of the second and third images from the first lens, and z that of the fourth (a 
virtual one) from the second lens, then the fourth image is seen directly by the eye 
placed at the eyestop : this stop must be at the image of the small speculum formed by 
the second lens, and of the same diameter as that image, to exclude all light except 
what comes from the specula. The distance of the stop from the lens r being 
a small quantity, this distance + 2 — V the distance of distinct vision. Hence we obtain 
in succession 
and hence 
2V — 2r -f" /"(2V-2r + 3/") ^ ,/"(2V — 2r + 3/") 
2 ; u — 2V-2t +/" ; Q— * V-r ’ 
magnifying-power M=^X 
F_2F d'Y t\ 
r/4 v 
As the small speculum should receive all the light from the large one, and as 
in these eyepieces f bears a given ratio to a'— a, we have a=nf ; and substituting these 
in M, 
M= 
2A d' 
w 
M nf* 
But we have a second value of d', 
d! =F — cZ — ^ — f- 
1 being the distance of the great speculum from the first lens ; and equating the two, 
which, when A, F, n and V are known, gives f\ and thence the other elements of the 
telescope. In this case F=366 inches, 5=11, A=48 ; opticians generally make n— 0’5. 
About Y there is doubt ; it has been estimated from 10 to 5 inches, but I will take 8 
inches, that adopted by Sir W. ITerschel, and several others. M=240*, hence 
1-21675 N 
-vj 
As r is small, omitting it, we get an approximate value off', and thence of d', from 
~\~f 1 X 3 '3125 — 3/7. 
* M is nearly inversely as f ; for though ^ changes with the adjustment of focus, the change is trifling. 
It may also he remarked that the common mode of getting M, dividing A by x, the diameter of the image of 
the large speculum at the stop is not correct unless/' is small; the expression is 
x 
^4 
