THE MASS-LUMINOSITY RELATION 
149 
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Still higher mass has with some plausibility been assigned to v Sagittarii 
(M x sin 3 i = 260, M 2 sin 3 i = 54), but the determination seems uncertain*. 
(4) The Sun. 
Mass 1-985.10 33 gm.; radius 6-951.10 10 cm. 
Although we are no longer dealing with material of low density we 
suppose tentatively that the theory of a perfect gas applies. The methods 
of calculation have been shown by the previous examples. The results are— 
1 - j8 = -0499, 
Pm ~ 1*411, 
Pc = 76-5, 
T c = 3-95.10 7 , 
k c = 177-0, 
L = 5-62.10 33 . 
The value of L found by direct measurement of the solar radiation is 
3-78.10 33 . The difference of calculated and observed values is equivalent 
to 0 m -43, the sun being fainter than predicted from its mass and radius. 
Although this is in the direction corresponding to the deviation of terrestrial 
gases from the perfect gas laws there is no reason to attribute it to such a 
cause, since it is within the margin of error. For example, it might be due 
to a slightly lower molecular weight in the sun than in Capella due to the 
very much higher temperature. Many other sources of small deviations 
can be suggested. 
It may be remarked that by using in our calculations the radius of the 
sun and the effective temperature of Capella we have magnified any 
discrepancy. All our results are differential with respect to Capella which 
was used to determine k x . A more direct method of comparison, using 
the spectral type instead of the radius of the sun, is as follows. Since 
Capella and the sun are of the same spectral type we neglect at first any 
difference of effective temperature. Then, using Lee M k (1 — /?)-' we find 
that the ratio of the U s is exactly 100 or 5-00 magnitudes. Hence the 
sun’s bolometric magnitude is — 0-40 + 5-00 = + 4-60. To allow for the 
more diffuse condition of Capella we have assigned it an effective tempera 
ture 9 per cent, lowerf. The change in the factor gives a correction 
0 m -08, raising the sun’s bolometric brightness to + 4 m -52 as compared 
with the observed value + 4 m -85. The discrepancy is 0 m -33. 
* H. Ludendorff, Berlin Sitzungsberichte, 1924, p. 67. [According to later in 
formation the determination must be rejected altogether. Another massive system 
(Boss 46) with masses 35 and 32 has been found by J. A. Pearce; this is the second 
largest mass known.] 
f It is better not to refer to the actual effective temperatures here—to avoid 
suspicion of a vicious circle. The effective temperature of the sum is derived from the 
observed L which we are holding in reserve for the final test.