Page:Popular Science Monthly Volume 57.djvu/249

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239
CHAPTERS ON THE STARS.

the imaginary star just mentioned, the number expressing its magnitude being  — 1.4.

This suggests what we may regard as one of the capital questions in celestial photometry. There being no limit to the extent of the scale, what would be the stellar magnitude of the sun as we see it when expressed this way on the photometric scale? Such a number is readily derivable when we know the ratio between the light of the sun and that of a star of known magnitude. Many attempts have been made by observers to obtain this ratio; but the problem is one of great difficulty, and the results have been extremely discordant. Amongst them there are three which seem less liable to error than others; those of Wollaston, Bond and Zöllner. Their results for the stellar magnitude of the sun are as follow:

Wollaston —26.6
Bond —25.8
Zöllner —26.6

Of these, Zöllner's seems to be the best, and may, therefore, in taking the mean, be entitled to double weight. The result will then be:

Stellar magnitude of sun  — 26.4

From this number may be readily computed the ratio of sunlight to that of a star of any given magnitude. We thus find:

The sun gives us:

10,000,000,000, the light of Sirius.
91,000,000,000, the light of a star of magnitude 1.
9,100,000,000,000, the light of one of magnitude 6.

The square roots of these numbers show the number of times we should increase the actual distance of the sun in order that it might shine as a star of the corresponding magnitude. These numbers and the corresponding parallax are as follows:

Sirius; Distance = 100,000: Parallax = 2".06
Mag. 1 " 302,000: " 0".68
" 2 " 479,000: " 0".43
" 3 " 759,000: " 0".27
" 4 " 1,202,000: " 0".17
" 5 " 1,906,000: " 0".11
" 6 " 3,020,000: " 0".07

These parallaxes are those that the sun would have if placed at such a distance as to shine with the brightness indicated in the first column. They are generally larger than those of stars of the corresponding magnitudes, from which we conclude that the sun is smaller than the brighter of the stars.