28 Prof. W. M. Hicks on the 



The mean limits are both in defect by about 2-5, and the 

 •allocation of R : seems rather arbitrary. R 2 is much weaker 

 than Hi and can be accounted for by the presence of the 

 displaced lines, thus : 



(2)38127-63 



6436 oc x on limit gives 64--30 



(2)38191-99 



1298 c, „ • 12-90 



(4/038204-9 



From the sets for m = 3, 4 and the given S(x), the 

 following formula is found : 



n=29469-85— n/4 m + '715861 + '°' Mm ' 2 I \ 

 I I m J 



The positive term in 1/m points to the series being of the 

 D or F tvpe. With this the set for ni = 5 is found to be 

 (0-C=--3). 



(2) 261 1 2-25 (-45) =..19-84 ) 

 (^)(8)26130-61 = . . 19-85 f - 6119 ' 8i *>W** (2)32822-40 



351613 



(1)36338-53 



For m = 2, 'R l comes into the ultra red, but the others are. 

 indicated, viz. : 



[14815-91] 29469-60 (44123-29)=(1%)44130'82(25 1 ) 



381556 381420 



(2?i)18638-98(-2^)=(18631-47) 83284'48 (1)47937-49 



Any combination lines from these would fall in the ultra 

 red region. There are thus considerable indications in favour 

 of this second explanation, although perhaps not very con- 

 vincing. Both cannot be correct and one, at least, is there- 

 fore spurious. 1 have inserted the second because it affords 

 warning against relying on a few numerical coincidences, 

 especially where, as in this case, so many of the lines are in 

 crowded positions. At the same time, the second may be 

 possibly the real solution, and the question may be left for 

 solution in the future. 



We may make the direct attempt to determine the P series 

 without regard to the 41172, which, as we have seen, cannot 



