322 PROCEEDINGS OF THE AMERICAN ACADEMY. 



On the more refrangible side of A 1600 matters are not very satis- 

 factory. The bands must be arranged into series showing very large 

 second differences which are only approximately constant. These 

 series, which are numbered from 1 to 7 go to make up the Fifth Group. 

 Their frequencies together with the second differences are given in 

 Table III. No attempt has been made to adopt an arrangement which 

 would show the similarity between the members of the group. In fact 

 these series fall in with the second rule only to a limited degree ; 1 and 

 5 resemble each other, as do 2 and 6, and 3 and 7, but the relations 

 are not exact. 



The writer makes no claim that the arrangements given in this Fifth 

 Group are the best possible, they are only the most obvious. 



The spectrum contains a great many bands which are either too 

 feeble to measure or whose positions are made uncertain by the tails 

 of stronger bands ; if these could be included in the series a better 

 system would probably result. 



It is to be remembered that although relations similar to Deslandres' 

 laws have been proved to hold within the limit of error of observation 

 for the distribution of lines within a band, 11 no such accuracy of agree- 

 ment has been found when the laws of the distribution of the heads of 

 the bands themselves have been tested. In fact, the rule of constant 

 second differences as applied to the heads of bands must be looked 

 upon as a first approximation only. The work which has just been 

 described indicates that the approximation holds even in the region of 

 extremely short wave-lengths. 



In conclusion the writer wishes to point out that the important re- 

 sults of the investigation are the values of the wave-lengths contained 

 in Table IV. 



Jeffeeson Physical Laboratory, 

 Cambridge, Mass., 

 December, 1909. 



11 v. Carlheim-Gyllenskold, K. Svensk. Vetenskaps-Akad., Handl., 1907, 

 42, No. 8. 



