2i8 Dr . Herschei/s Observations on 
mention this as a measure of Jupiter, for the wall was not per- 
fectly at right angles to the telescope, on which account the 
projected image would be a little larger than it should have 
been, nor was I very attentive to other necessary minute cir- 
cumstances, which would be required for an accurate measure ; 
but we see at once, from the size of this picture, that the power 
of the telescope exerted itself to the full of what has been stated. 
As we generally can judge best of comparative magnitudes, 
when the measures are, as it were, brought home to us ; it will 
not be amiss to reduce them to miles. This, however, cannot 
be done with great precision, till we are more perfectly ac- 
quainted with the elements of the orbits of these stars. But, for 
our present purpose, it will be sufficiently accurate, if we admit 
their mean distances from the sun, as the most recent informa- 
tion at present states them ; for Ceres 2,6024 ; and for Pallas 
2,8. The geocentric longitudes and north latitudes, at the time 
of observation, were, for Ceres, about m qo° 4', 15 0 20'; and for 
Pallas, m 23 0 M', 17 0 30'. With these data, I have calculated 
the distances of the stars from the earth at the time of obser- 
vation, partly by the usual method, and, where the elements 
were wanting, by a graphical process, which is sufficiently 
accurate for our purpose. My computed distances were 1,634 
for Ceres, and 1,8333 for Pallas ; and, by them we find, that the 
diameter of Ceres, at the mean distance of the earth from the 
sun, would subtend an angle of o", 351 27; and that, conse- 
quently, its real diameter is 161,6 miles. 
It also follows, that Pallas would be seen, at the same 
distance from the sun, under an angle of o^giq^; and that its 
real diameter, if the largest measure be taken, is 147 miles ; 
but, if we take the most distinct observation, which gives the 
