On the Spectra of the Alkalies. 77 



Li = -96; Na = l-2; K=l-44; Rb=l-57and 1-61; Cs (probably) 

 = 1-75. 



Mr. William Sutherland, who most kindly volunteered to assist 

 me in drawing up my report, and has also kept me informed of 

 the latest intelligence bearing on this paper, has discovered the 

 following remarkable relation, communicated to me in these 

 words : — 



" If you take your series of numbers 



•96 1-2 1-44 1-57 and 1-61 ITo 



and write their differences you get 



•24 -24 -13 or -17 -18 or -14 



while the diifei*ences of atomic weights are 



16 16 46 48 



whose square x^oots are nearly inversely proportional to the 

 previous numbers." 



My second proposition leads to a considerable simplification in 

 the process of evolving the constants. After first having ascer- 

 tained which of the series is the normal, i.e., yields precise results 

 with three constants only according to equation No. 3, the roots 

 thus obtained lead to the determination of the moduli of the 

 co-ordinated abnormal series. If a, b and c are three successive 

 wave lengths with their roots subtracted, the modulus is found 

 by the equation — • 



My constants have been obtained from three wave lengths only 

 for the normal series, excepting the series b^ of Sodium, where 

 discrepancies exceeding the probable limit of error of observation 

 induced me to harmonise my results by rejecting the third wave 

 length and employing in its stead a mean value derived from the 

 other members of the series. 



For the ultrai^ed rays of Lithium and Sodium I have adopted 

 the very accurate numbers found by E. P. Lewis, in preference 

 to those of Kaiser and Runge. Swan's numbers for the same 

 part of the spectrum in regard to Potassium, Rubidium and 

 Caesium can only be considered as widely approximative. The 

 spectra of the two last named metals are, in my opinion, incom- 

 plete ; Rubidium wanting another pair of abnormal series for 



