31 
34-38] Stellar Magnitudes 
36 . Thus, if i? x and R 2 are the amounts of light received from any two 
stars, their magnitudes m 1 , m 2 are connected by 
m 1 — m 2 = — 2 5 (log- log R 2 ) (36T), 
and as a conventional standard has been selected to fix what is meant by zero 
magnitude, this relation determines the magnitude of every star in the sky. 
The star from which we receive most light is of course the sun, whose 
magnitude is — 26'72. Apart from it, the apparently brightest star is Sirius, 
of magnitude — 157, and then Canopus, far down in the southern sky, with 
magnitude — 0'86. The magnitudes of all other stars are expressed by positive 
numbers, Vega of magnitude 0T4 coming next, then Capella (0‘21), Arcturus 
(024), and the bright component of a Centauri (033). At the other extreme 
we may place the faintest stars which are accessible photographically in the 
100 -inch Mount Wilson telescope, of which the magnitude is about 21 . The 
difference of about 47£ magnitudes between these and our sun represents a 
light ratio of 10 19 . 
For comparison with these figures of stellar magnitudes, it may be added 
that the “magnitude” of the full moon is about — 125, and that of Venus at 
its brightest is about — 4'0. The magnitude of a standard candle 100 yards 
distant is also — 4’0, and that of a standard candle 6000 miles away is 211. 
Absolute Magnitudes. 
37 . So long as the stars were deemed to be all at the same distance, 
the relative brightnesses of various stars gave appropriate measures not 
only of the amount of light we received from them, but also of the amounts 
of light they emitted; a first magnitude star not only sent two and a half 
times as much light to the earth as a second magnitude star, but also 
was supposed to emit two and a half times as much light in all—it might 
fairly be said to be two and a half times as luminous. We now know that 
the differences in the amounts of light received from different stars arises 
largely from their being at different distances, and before w r e can make any 
progress with our physical knowledge of the stars we must eliminate this 
distance effect; in other words, we must consider what would be the amounts 
of light we should receive from the various stars if they were all placed at the 
same distance away. The standard distance used for this purpose is generally 
10 parsecs, although some continental writers prefer to use the Siriometer (§ 4 ). 
38. Suppose that an amount R x of radiation is received from a star whose 
distance is p parsecs. If the same star were placed at a distance of 10 parsecs, 
the radiation received, R 2) would be given by 
( 88 - 1 ), 
since the intensity of light falls off inversely as the square of the distance.