490 Mr. H. Bell on the 



Re-writing (1) in the form 



N..=^^-(^)} 



4(m' 2 — p 2 ) \ \p' 



fm 2 ^ i( 1 -u 1 \ 



4(m 2 — p 2 ) \jr mV 



(2) 



we see that if the formula is to hold the second or relativity 

 term must be just large enough at each value to reduce the 

 corresponding first one to a constant. Both terms are given 

 in the table, and their difference is under Nse* 



For the series p = '6 a constant value is reached, average 

 109722'31 ; but such is not the case for the unresolved series 

 p = 4. Now this series is according to the theory one of 

 quadruplets I, II, III, IV, each bordered towards the red 

 by fainter lines as before ; but I, II, III were not resolved, 

 and it is most likely that Paschen's readings apply to some 

 kind of a mean among them, and consequently the wave- 

 numbers are all too high for I to which the formula applies. 

 Theoretically, IV-iII = '730 cm." 1 , ]II-II = -243 cm" 1 , 

 II-I = -123cn-.- 1 . 



If we assume the wave-numbers to be all too high by oV,, 

 then by (2) we need to apply a correction : 



fm 2 . ;> 4 /l 1 p 2 \ 



772 27 ° v — 7 ° v \ ~~2 + ~2 + 4 I • 



4:(m z — p> ) 4 \p z m z nv ) 



It is rather surprising * that this should so exactly, as far 

 as present accuracy in measurements goes, be the relativity 

 correction. To equal it we require Si/ — N« 2 4/p 4 = "091 cm. -1 . 

 However, it is readily seen that we cannot correct these 

 terms by subtracting a suitable multiple of the relativity 

 correction, for although a multiple 4 or 5 would do away 

 with the diminishing trend the resultant Nu e would be 

 much lower than that from the other series. It will 

 be seen from the following that this difficulty is due to 

 systematic error among unresolved lines. 



The components III of the triplet series and 1Y of the 



quadruplets stand farthest out, differing from I by 2'31 ci 



am 



1*09 cm. l respectively. Their corresponding N values 

 have therefore to be corrected by these differences multiplied 



* If the differences in "wave-n timber among the standard iron lines 

 are all counted correctly (by interference methods) but the reference 

 Cadmium line is in error by 8v, we should have a spurious relativity 

 effect d\=—\ 2 cv throughout the spectrum. This error "09 cm. -1, 

 would, however, represent a miscount by about one part in 200,000 for 

 a red line. An accuracy of one part in ten million is claimed. 



