on the local arrangement of the celestial bodies in space. 3 1 9 
the formula ^ x • A *~ 1 ^ gives the whole quantity of the space 
a 
penetrating power, a reduction to any inferior power p, may 
be made by the expression -f- & e = A ; when the aper- 
ture is then limited to the calculated value of A, the tele- 
scopes will have the required gaging power. Or we may 
prepare a regular set of apertures to serve for trials, and 
find the gaging powers they give to the telescope by the 
original formula. 
In the formula by which the required apertures for the 
gaging powers were calculated, a has been put equal to two 
tenths of an inch, and to show that this assumption is founded 
upon observation, I give the following extract from my 
astronomical Journal. 
- Dec. 27, 1801. I looked at « Lyrae with one eye shut and 
the other guarded by a slip of brass with holes of various 
sizes in it. Through the hole which was o 28 inch in 
diameter, I saw the star just as well as without the limiting 
diaphragm, which shows that the opening of the pupil of the 
eye does not exceed 0.28 inch. 
I tried the same star through 0.24 and still saw it equally 
well. I tried next 0.21 and still saw it as well. 
The slip of brass was held as close to the eye as possible. 
The next I tried was 0.17 in diameter, and through this I 
could perceive a small deficiency of light, so that the opening 
of the pupil exceeds 0.17 inch. The night is hardly dark 
enough yet for great accuracy. 
Having been out long in the dark, and trying the same 
* See Phil. Trans, for x8oo, page 66. 
Tt 
MDCCCXVII. 
