32 
The Light from the Stars [ch. ii 
If m denotes the actual observed magnitude of the star, and M the mag 
nitude the same star would have if moved to a distance of 10 parsecs from 
us, then formula (36T) provides the relation 
M ~ m “ - 2 ' 5 >°8 (f ) = " 2 ' 5 lo « (&) 
= 5 — 5 log p.. 
If vs is the parallax of the star in seconds of arc, p = — so that 
M = m + 5 + 5 log vs (38’2). 
The magnitude M, which would be the observed magnitude of the star if 
it were moved to a distance of 10 parsecs* from us, is called the absolute 
magnitude of the star, while m is called its apparent magnitude. 
The absolute magnitude M gives a measure of the total light emitted by 
a star, and again of course a drop of five magnitudes must represent a light 
ratio of 100. Of stars whose absolute magnitude is known with fair certainty, 
the most luminous is the bright companion of the binary star B.D. 6° 1309 
recently investigated by Plaskett, which has an absolute magnitude of about 
— 6'4. The star S Doradus, in the greater Magellanic cloud, is almost 
certainly brighter, its absolute magnitude being estimated at — 9‘0. 
At the other end of the scale come Proxima Centauri, our nearest neigh 
bour in the sky, with an absolute magnitude of 14‘9, the companion to Procyon, 
with absolute magnitude about 16, and the faint star Wolf 359, whose absolute 
magnitude is 165. 
Between the two extremes of absolute magnitude just mentioned, — 64 
and 16*5, is a range of 22‘9 magnitudes representing a light ratio of 1500 
millions. The sun with an absolute magnitude of 49 comes not far from the 
middle of this range. Plaskett’s star, B.D. 6° 1309, with an absolute magnitude 
of — 6‘4, emits about 30,000 times as much light as the sun, while Wolf 359 
emits only 000002 times as much light. It is usual to speak of the light emitted 
in terms of “luminosities,” that of the sun being taken to be unity. Thus the 
luminosities of the two stars just discussed are 30,000 and 000002 respectively. 
39 . We can obtain some idea of the way in which the luminosities of the 
stars are distributed by considering the luminosities of our nearest neighbours. 
If we go far afield, our results at once become vitiated, because the fainter 
stars at great distances are unknown to us. But our previous discussion (§ 8) 
has made it probable that all fairly bright stars within a distance of 4 parsecs 
are known, so that if we limit ourselves to the fairly bright stars within a 
distance of 4 parsecs from the sun, this complication is not likely to enter 
* If M^r denotes the absolute magnitude when the Siriometer is taken as standard distance 
in place of 10 parsecs,