320 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



shows these new members. They are numbered from VI. to XL; series 

 IV. and V. of Deslandres' are included in the table for the sake of com- 

 parison. The first two bands in the fifth series were measured by the 

 writer. When it is remembered that the errors of observation make 

 the fifth place in the frequencies very doubtful, it will be seen that the 

 law of constant second differences is fairly well obeyed. 



TABLE III. 

 Fifth Group. 



Table II., which gives the first differences for each series, is arranged 

 to show the similarity which exists among the members. It will be 

 observed that the second rule is obeyed, for the series resemble each 

 other. An exact similarity is not demanded by the rule as has been 

 recently pointed out by Deslandres himself. 9 The arrangement of the 

 series, however, does not permit of the "second progression " 10 men- 

 tioned by Olmsted and others. 



In addition to the series VI. to XL there appear to exist two others, 

 in the region near A. 1800. These show larger second differences than 

 the first type. They have not been included in the tables. 



9 Comptes Rendus, 1904, 138, 317. 



10 Comptes Rendus, 1902, 134, 748; Zeits. f. Wiss. Photographic, 1906; 4, 

 255. 



