36 Dr. Wentwortu Erck on the Satellites of Mars. 
been removed to the distance of Vesta, his light would have been enfeebled 40 
times; and therefore his limiting aperture would require to be increased to V40, or 
6.4 times, and so would have become 0.032 inches. 
But the limiting aperture for Vesta is 0.25 inches, or only 8 times that of Mars 
at her distance. 
Therefore, on the assumption of equal reflecting powers, the diameter of Vesta 
should be an eighth of that of Mars, or 520 miles; butit is highly improbable that 
her diameter is more than half that quantity, and therefore her reflectng power 
must be more than 4 times that of Mars; and if we assume the received value of 
the diameter of Vesta, 230 miles, to be correct, then it will appear that her 
reflecting power is 5.2 times that of Mars, whose diameter is 4150 miles; for 
(230 x 8)?x 5.2=4150°. 
Now applying this correction to the diameter of the Satellite, as determined by 
comparison with Vesta, we must increase the area of the disc of the Satellite 5.2 
times, or multiply the diameter by .75.2 which is 2.2; but 6X2.2=13.2, so that com- 
parison with Vesta gives the diameter of the Satellite as 13.2 miles. 
Great as the disparity between the reflecting powers of Mars and Vesta may 
thus appear to be, still it is corroborated by other observations. 
In the first place, Vesta is known to be the brightest of the minor planets 
(Chambers) ; that is to say, her light is more intense than that of any other. 
In the next place, the light of Mars is well known to be less intense than that 
of Jupiter or Saturn; and for the purpose of getting some idea of the relative 
reflecting power of the surfaces of these planets, I endeavoured to compare their 
actual apparent brightness with their calculated brightness on the assumption of 
equal reflection. ; 
On several occasions, about the 5th of this month, I measured, as care- 
fully as my means would admit, the relative brightness of Mars, Jupiter, 
and Saturn. I noted the time at which the two former became visible in 
the twilight at nearly equal altitudes ; also, I employed the neutral tint sun glasses 
with limiting apertures, and also reflexion from the first surface of a prism. After 
many trials I came to the conclusion that Mars and Jupiter were, as nearly as I 
could judge, of equal brightness, and 10 times as bright as Saturn. 
-Of course it is necessary to make some allowance for the superior illumination 
of the western sky wherein Jupiter was. Suppose we assume this to have reduced 
his brightness one-tenth, the comparison of actual apparent brightness would then 
stand nearly thus— 
Jupiter 100: Mars 90: Saturn 9. 
It is easy to calculate the amount of light received by us from any planet at 
any distance— 
The light is equal to x N where— 
A? 
