*of ascertaining the Magnitude of small celestial Bodies.*

The night is so clear, that I cannot suppose vision at this altitude to be less perfect on the stars, than it is on day objects at the distance of 800 feet in a direction almost horizontal.

Oct. 11. By comparing the asteroid alternately and often with equal stars, its disk, if it be a real one, cannot exceed 2, or at most 3-tenths of a second. This estimation is founded on the comparative readiness with which every fine day I have seen globules subtending such angles in the same telescope, and with the samp magnifying power.

"The asteroid is in the meridian, and in high perfection. I perceive a well defined disk that may amount to 2 or 3-tenths of a second; but an equal star shows exactly the same appearance, and has a disk as well defined and as large as that of the asteroid."

RESULT AND APPLICATION OF THE EXPERIMENTS AND OBSERVATIONS.

We may now proceed to draw a few very useful conclusions from the experiments that have been given, and apply them to the observations of the star discovered by Mr. Harding; and also to the similar stars of Mr. Piazzi and Dr. Olbers. These kind of corollaries may be expressed as follows.

(1.) A 10-feet reflector will show the spurious or real disks, of celestial and terrestrial objects, when their diameter is 14 of a second of a degree; and when every circumstance is favourable, such a diameter may be perceived so distinctly, that it can be divided by estimation into two or three parts,

(2.) A disk of 14 of a second in diameter, whether spurious or real, in order to be seen as a round, well defined body,