made quite an extensive photometric survey, using an instrument by which the light of one star was cut down by a wedge-shaped dark glass, whereby any gradation of light could be produced. A comparison shows that the results of Pritchard agree substantially with those of Pickering. It is quite possible that the Purkinje phenomenon may be the cause of the difference, the source of which is eminently worthy of investigation.
This fact simply emphasizes the lack of mathematical precision in photometric measurements of star light. Even apart from this difference of color, the estimates of two observers will frequently differ by 0.2 and sometimes by even 0.3 of a magnitude. These differences correspond roughly to 20 or 30 per cent in the amount of light.
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