A^HiOF THE SUN WITH THAT OF THE FIXED STARS. 23 



paring the candle with the star, -b" X -^ X y X j wilr bfe the aistSnce 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 pD x8 X A xJ' V j^jit js 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 Appendixi'" 



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 ax-e 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 roth 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 M. might be compared at places having different latitudes, or even in different 

 hemispheres, whereby the unec[ual influence of the atmosphere at different altitudes might be wholly 

 eliminated. 



