20 
DR. WOLLASTON’S METHOD OF COMPARING THE LIGHT 
From a comparison which I made in the year 1799 (by a method described 
in the note subjoined) of the light of the sun with that of the moon, I should 
estimate the direct light of the sun as being nearly one million times greater 
than that of the moon* ; and consequently the direct light of the sun as very 
many millions times greater than that afforded us by all the fixed stars, taken 
collectively. Such then being, to our visual organs, the vast disproportion in 
radiance between the sun and the whole starry firmament, it is not to be ex- 
pected that we should assign very accurately how much greater the light of 
* The observations on which this estimate is founded, are given in detail at the end of the Ap- 
pendix to this paper. The mode of making the observations was the following. 
The sun’s light was compared with that of a candle, by admitting a beam of it into a room through 
a small circular hole in a plate of metal, fastened in a window-shutter ; and a small cylinder of any 
opaque material being placed in the beam, so as to cast a shadow upon a screen, the distance of a 
candle from the same cylinder (or an equal one placed at the same distance from the screen) was 
varied, until the shadow in the line of the candle became equally intense w T ith the shadow in the line 
of the sun. The direct light of the moon was compared with the light of a candle in the same manner. 
This method of comparing lights by the intensity of the shadows which they occasion, was pursued 
also by Count Rumford. 
It appears from the mean of the observations given in No. V. of the Appendix, that the light of the 
sun is equal to that of 5563 candles placed at the distance of one foot; a result which accords very 
nearly with that of Bouguer. For he states the light of the sun to be equal to that of 11,664 wax 
candles at the distance of 16 inches French, which is equivalent to 5774 wax candles at the distance 
of one foot English. It appears also from my experiments, that the light of the full moon is equal to 
j^th part of the light of a candle, placed at the distance of a foot ; and hence, that the sun’s light is 
equal to 5563 X 144 X moon’s light = 801,072. X moon’s light. Bouguer, who differs greatly 
from me in the comparison of the moon with a candle, states the light of the sun to be = 300,000 
X moon’s light. The proportion which the light of the full moon ought to bear to the light of the 
sun, on the supposition that the moon gives off’ again all the solar light that falls upon it, has been 
differently estimated by several mathematicians who have computed it. The light of the sun at the 
earth being represented by unity, Mr. Miciieel expresses that of the full moon by sin 2 1 ([ dia- 
meter = 4 j 0 ^qqq . Euler, in the Transactions of the Berlin Academy for 1750, represents the light of 
the full moon by \ sin 2 ^ 1 diameter, which is only |th of the former expression of Mr. Michele. 
Neither of these expressions, however, appears to be correct. For if we consider that the 
quantity of solar light which falls upon any point in the moon’s surface, must vary, if we regard 
the sun’s rays as parallel, as the cosine of the angular distance of that point from the point in the 
moon over which the sun is vertical, we shall obtain, by following Euler’s own method, the formula 
1 4- 2 sin 3 (f semidiametcr — cos 3 (T semidiameter . ... r.,. , , , .. . 
-Z - , to express the quantity of light, which, on the given sup- 
position, we ought to receive from the moon ; and this expression reduced to numbers = ioo^ooo * ^ ie 
moon therefore appears to give off’ only about |th of the light which she receives. 
