550 SCIENCE PROGRESS 



the forecast. In 1899, when 600 plates had been measured, an 

 examination was made of the accumulated measures {Mon. Not. 

 Ix. p. 3), the stars being grouped in half-magnitudes ; and it 

 was found that the fainter stars had been " observed late " by 

 Mr. Graham as follows, taking as standard those of magni- 

 tude 6'o : 



Determination of Mr. Graham's Magnitude Equation in 1899. 



s. 



Magnitudes 6"5 to 6'9, 147 stars, o"oi6 late. 

 7-0 to 7'4, 320 „ 0-025 „ 

 „ 7'5 to 7"9. 504 » 0-038 „ 



It will be noticed that there are roughly twice as many 

 stars in the second group as in the first, and in the third twice 

 as many again, this being the natural increase of stars in the 

 sky as we go to fainter magnitudes. But at the fourth group 

 there is a discontinuity, owing to the fact that only half the 

 available material was discussed beyond this point. The labour 

 was considerable and it was thought that the examination, 

 which was in any case only preliminary, need not be carried 

 further at that time. In the fifth and sixth groups the increase 

 is resumed. The discontinuity should not, of course, affect the 

 averages in the last column, and we see that there is an increase 

 of " lateness " which seems to be rapidly growing, since not 

 only the quantities themselves, but their differences, get larger 

 and larger. There is no suggestion of a sudden jump, such as 

 we shall notice in a moment : the smoothness of the growth 

 was considered to be satisfactorily established and the matter 

 was left there until the present time. The measures are now 

 printed and a final examination can be made, using the whole 

 material and classifying the stars in smaller subdivisions, 

 especially where they are numerous, as is the case for the 

 fainter magnitudes. The work is only in its early stages but 

 already an important new fact has come to light, as will be seen 

 from the following figures, from which the brighter stars have 

 been omitted, because hitherto only a few observations of them 

 have been collected definitively: 



