23 
this form, and to make it desirable that its principles should 
be developed more fully than is done by the existing treatises 
on Optics. Their formule do not include the magnitude of 
the emergent pencil, or the distance of distinct vision, the lat- 
ter of which I noticed in a former communication as an ele- 
ment of magnifying power, and both of which are important 
in this inquiry. 
‘¢ The data are— 
‘“‘(a) The eye must take in the whole pencil of rays which 
the great speculum received from the point which is examined, 
and which I assume to be on its axis. This diameter cannot 
exceed the maximum aperture of the pupil, which Sir W. 
Herschel determined to be two-tenths of an inch, or, taking 
the foot as unit, ¢4. 
© (6) The small mirror must receive the whole of the cen- 
tral pencil: if its magnitude be-only sufficient for this it loses 
a little of the oblique pencils, but not enough to lessen the 
brightness materially. In a field of 10’ the edge will be about 
one-ninth less bright than the centre. 
“‘(c) The eye must be distant from the-last-image, real or 
virtual, by the quantity V, in order to have sharp vision. 
This distance was formerly assumed = 8 inches, but is less: 
the mean of my eyes, of my two assistants, and another indi- 
vidual, gives it = 6:42; Sir David Brewster makes it as low as 
5, but I think it may be taken 6, or 6:5. 
“‘(d) The first lens of the eye-piece (and the aperture in 
the great speculum) should have the same diameter as the 
small speculum for the lowest power; if less, it-contracts the 
field of view; if larger, it lessens the effective surface of the 
' great speculum. Hence the last ray is parallel to the axis. 
*‘(e) The last image must be near the hinder surface of 
the great speculum box, in order to apply a micrometer. The 
distance between this and the surface of the speculum is about 
one-fifth of its aperture. | 
* Let Ff’, J” be the focal lengths of the specula, and 
