472 Scientific Proceedings, Royal Duhlin Society. 



nitude, Q6 ; third magnitude, 190 ; fourth raagnitude, 425 ; fifth 

 magnitude, 1100 ; sixth magnitude, 3200 ; seventh magnitude, 

 13,000; eighth magnitude, 40,000, and ninth magnitude, 142,000. 

 Now, dividing the stars into sets which ought to give equal light 

 on the hypothesis of uniformity, we can easily ascertain to what 

 magnitudes the stars in each set belong; and multiplying the 

 number of stars of any magnitude by the figure which represents 

 the intensity of light for that magnitude, we obtain a result which 

 shows in what direction the deviation from uniformity takes place. 

 Thus the second set consists of 140 stars which will embrace the 

 whole 65 second-magnitude stars, together with 75 stars of the 

 third magnitude. If the average light of a star of the first mag- 

 nitude is represented by 1, that of a second-magnitude star will be 

 represented by 0*4, and of a third-magnitude star by 0'16. Hence 

 the actual light of this second set will be represented by 65 x 0"4 

 + 75 X 0'16 or 38, whereas on the hypothesis of uniformity the 

 value of the total light ought to be 20. There is, therefore, 

 in this instance a very marked deviation in the direction of excess. 

 Carrying on this computation I found that several successive 

 sets will, in many instances, consist altogether of stars of the same 

 magnitude. As the number of stars in each set is greater than 

 in any preceding set, there would in such cases appear to be a con- 

 tinual increase in the light if, in each case, I multiplied the num- 

 ber in the set by the average intensity for that magnitude. But 

 the smaller sets contain the brighter, and the larger sets the 

 fainter stars of any given magnitude, and the apparent increase 

 has therefore, in all probability, no foundation in fact. I have 

 therefore thought it best to strike a general average for all such 

 sets, without attempting to trace whether the total light increases 

 or diminishes as we pass from the earlier to the later. This plan, 

 however, is not available when a set includes stars of two different 

 magnitudes ; and it is evident that if it includes only a few of the 

 fainter stars of one magnitude while it contains a large number 

 of the brighter stars of the following magnitude, its total light will 

 be underrated on the principle of averages. When this state of 

 things is reversed the light will in like manner be overrated. I 

 have applied the principle of averages throughout for want of 

 a better, but I desire to state that the sudden increase of light at 

 the tenth set, and the equally sudden diminution at the fifteenth 



