() Prof. W. M. Hicks on the 



recourse to the existence of summation series if they show 

 themselves. This type of series has been shown to exist in 

 [V.]. If the wave-number of a given series of the hitherto 

 recogDized type is written as the difference of two sequents 

 A — <p(m). it is there shown that in many cases at least a 

 summation type A + </>(»*) also exists. When this occurs the 

 mean of two corresponding wave-numbers gives the exact 

 value of the limit. Unfortunately, it is also shown that dis- 

 placements sometimes appear concurrently, especially in the 

 summation type which require some care in applying the 

 condition. In this particular case a displacement of one oun 

 in the limit produces a change in it of 10" 76, and in the 

 sequent a change which depends on the order m. For m = 2, 

 the lines just considered, it produces 2*90 in <Zi(2) and 2" 93 

 in d,(2). 



With the given D(2), the region in which D(3) is to be 

 expected is narrowed down. The lines chosen were 



[22496-77] 381556 (2n) 26312-33+-34 

 32*55±*5 



(T) 22529-32 ±'25, 



in which the D 12 line is, as before, too faint to be seen, and 

 is interpolated as 26312 — v. Its possible error is the same 

 as that of 26312. The oun displacement on the sequent 

 produces 1*228. Consequently 2$ B 1 produces 32*13, which 

 not only reproduces the observed satellite separation but 

 gives the same oun multiple as in m=2, and lends additional 

 support to the allocations. With D n (2) = 17125 and 

 D n (3) =22529 with the limit 29465 the formula for D M 

 was determined and the wave-numbers up to m = 10 calcu- 

 lated and compared with the observed lines. The result is 

 given on the left hand of Table I. in which under any order 

 the lines in succession correspond to D 12 , D 11; D 22 . A search 

 was then made for the corresponding summation or D lines 

 which was successful. The results are entered on the 

 right hand. The middle column gives the means of the 

 corresponding D and D* lines, which in the absence of 

 displacement effects should be the true limits and the same 

 in each order. They form the raw material for a closer 

 discussion which follows. In the table calculated values are 

 given in [ ], deduced values in italics. 



* Summation series are denoted by clarendon type. The author lias 

 found it convenient in writing to use capitals reversed right and left, as. 

 in a looking-glass. 



