TRANSACTIONS OF THE SECTIONS. 



21 



(W'-HGW}-* 



It is then shown that the following relations subsist, with sufficient accuracy to 

 admit of their being fairly assumed : viz. B~' = D" and 13 7 D = E", — the E being that of 

 the first series. Another advantage, presented by the first series, is then pointed 

 out. The whole of the wave-lengths being formed into an equicentral series of 



fractions, thus, — , -, -, -, -' -, -» -, -, in which each greater is divided by 

 nulbJ^i/run 



each less; and these being arranged in the order of their magnitude, the following 

 relations are traced : viz., 



The series based on these relations stands thus : 



Logs. 

 B 

 jj 0-2436268 



C 



£ 0-1847346 



H 0-1270422 



t; 0-1165846 



C 



£ 0-0960845 



F 



^ 0-0886501 



^,0-0848012 

 r 



D 



g 0-0490882 



E 



^ 0-0357130 



r 



Numbers. Differences. 



1-752374 



1-530152 0-222222' 



1-339807 0-190345] 



1-307930 0-031877 



r 



222222' 



1-247626 0-060304 



1-226451 0-021175 



1-215630 0-010821 



1-119665 0-095965 



1-085708 0-033957 ) 



r 0-222222' 



0-666666' 



The differences between this series and the corresponding series deduced from the 

 observed values, are shown to be so trifling that they may be fairly attributed to 

 errors of observation. 



The wave-lengths, as calculated from this series, are then compared with the 

 observed wave-lengths, as in the following Table : — 



The differences here presented being smaller than the least of the differences 

 between the corresponding members of the two observed series, the relations on 

 which the calculated values are based are submitted as being in the highest degree 

 probable. These relations present the advantage of rendering the whole of the wave- 

 lengths deducible from that of either B or D. 



The following Table exhibits the relative wave-lengths, referred to that of B as 

 unity : — 



