32 DR. WOLLASTON'S METHOD OF COMPARING THE LIGHT 



two lights, I might obtain a nearer approximation to the ti-uth*. Tlie measure 

 taken in each experiment was the distance of the two candles from the bulb ; 

 and every distance that I have reported amongst the observations, was the 

 mean result of several trials. 



In reducing these observations we have to consider that though the image 

 of the sun, which is half the radius distant from the centre of the bulb, sub- 

 tends at its surface the same angle, of half a degree, as the sun itself, and there- 

 fore to an eye placed at the surface would appear equally brilliant with the 

 sun itself ; yet the apparent diameter of this little sun will decrease in pro- 

 portion as the eye recedes from the bulb, so that at the distance of D inches, 

 the apparent diameter of the image will be reduced in the ratio of ^ih of the 



diameter of the bulb, or of -^, to D, and consequently the brightness of the 



4 D 

 image will be reduced in the ratio of 1 to the square of -g-. 



If the distance of the eye from the bulb be so chosen, that, on comparing the 

 little sun and the star, separately, with the candle's image, the candle in the two 

 cases is at unequal distances from its bulb, d being made to represent the can- 

 die's distance from the bulb in comparing it with the sun, and 5 the candle's 



4 D 8 

 distance from the bulb in comparing it with the star, -g- X -j will be the di- 

 stance 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 



itselfasl to[^^]. 



If, in two comparisons made, the one between the candle and the sun, the 

 other between the candle and a star, the candle be reflected by bulbs of dif- 

 ferent diameters, and viewed with lenses of unequal focal length, the apparent 

 diameter of the candle's image will be as tlie diameter of the bulb directly, and 

 as the focal length of the lens inversely ; and hence, if b be the diameter of the 

 bulb and / the focal length of the lens in comparing the candle with the sun, 

 and |8 be the diameter of the bulb and K the focal length of the lens in com- 



• If any other artificial light could be found, which would at all times be of uniform brilliancy, and 

 of so white a colour as to supersede the necessity of using yellow glasses, it would of course be pre- 

 ferable, as a standard, to tlie light of a candle. 



