OF THE SUN WITH THAT OF THE FIXED STARS. 
23 
paring the candle with the star, X -j X ~j X -j- will be the distance at 
which the little sun would appear of equal brightness with the star ; and the 
brightness of the little sun would then be to the brightness of the sun itself as 
1 to [" -VP X j X / X X /r l ; and it is according to the latter formula that the obser- 
vations, made with bulbs of different diameter and with lenses of different focal 
length, have been reduced so as to be compared in No IV. of the Appendix. 
The first star that I compared with the sun, was Sirius ; and the observations 
were made at times when, the altitudes of the two bodies being not very 
widely different, their powers of illumination might be presumed to be 
affected, on the average, in almost an equal degree by the atmosphere. The 
table of reduced observations [No. IV. of the Appendix], in which each of 
seven observations of the sun is compared with each of seven observations of 
Sirius, will be found to exhibit discordances, which are referrible, probably, 
to our variable climate, and to the smoky atmosphere of London. Uniformly 
transparent skies are requisite to give uniformity to such experiments ; and in 
our climate, therefore, though the mean of very many comparisons would, 
probably, give a result not very remote from the mean of a much smaller 
number of trials made under a less variable atmosphere, we must expect the 
greatest and least results to differ widely from one another*. 
The mean of the various trials seems to show, that the light of Sirius is 
equal to that of the sun reflected from the surface of a sphere Toth of an inch 
in diameter, and seen at the distance of about 210 feet. The diameter of such 
an image of the sun, is to that of the sun itself as 1 to 100,000 ; and, conse- 
quently, the brightness of the image would be to the brightness of the sun 
itself as 1 to 10,000,000,000 ; but as nearly half of the light must be lost during 
reflection, we are not warranted by these experiments in supposing that the light 
of Sirius exceeds a 20,000,000,000th part of the sun’s light. 
* An observer, intending to pursue this inquiry, would do well, therefore, to choose a favourable 
climate ; and, further, he ought to select such stars for comparing with the sun, as have, severally, at 
the times of observation, nearly the same altitude with the sun. The accuracy of these comparisons 
with the sun would admit of rigorous investigation, by comparing the same stars with one another. 
Stars having the same .31 might be compared at places having different latitudes, or even in different 
hemispheres, whereby the unequal influence of the atmosphere at different altitudes might be wholly 
eliminated. 
