238 POPULAR SCIENCE MONTHLY. 



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 differ- 

 ence 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 quan- 

 tities. 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 multipli- 

 cation 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 in- 

 definitely 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 



