It must not be supposed from this that such estimates are of no value for scientific purposes. Very important conclusions, based on great numbers of stars, may be drawn even from these uncertain quantities. Yet, it can hardly be doubted that if the light of a star could be measured from time to time to its thousandth part, conclusions of yet greater value and interest might be drawn from the measures.
We have said that in our modern system the aim has been to so designate the magnitudes of the stars that a series of magnitudes in arithmetical progression shall correspond to quantities of light ranging in geometrical progression. We have also said that a change of one unit of magnitude corresponds to a multiplication or division of the light by about 2.5. On any scale of magnitude this factor of multiplication constitutes the light-ratio of the scale. In recent times, after much discussion of the subject and many comparisons of photometric measures with estimates made in the old-fashioned way, there is a general agreement among observers to fix the light ratio at the number whose logarithm is 0.4. This is such that an increase of five units in the number expressing the magnitude corresponds to a division of the light by 100. If, for example, we take a standard star of magnitude one and another of magnitude six, the first would be 100 times as bright as the second. This corresponds to a light ratio slightly greater than 2.5.
When this scale is adopted, the series of magnitudes may extend indefinitely in both directions so that to every apparent brightness there will be a certain magnitude. For example, if we assign the magnitude 1.0 to a certain star, taken as a standard, which would formerly have been called a star of the first magnitude, then a star a little more than 2.5 times as bright would be of magnitude one less in number, that is, of magnitude 0. The one next brighter in the series would be of magnitude -1. So great is the diversity in the brightness of the stars formerly called of the first magnitude that Sirius is still brighter than 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. |