PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 105 



The difference for m = 7 in I. is clearly wrong, the mean of G and 8 gives '20, so 

 also is that for m = 9, and beyond this the measurement errors are clearly greater 

 than the differences themselves. It will be seen by inspection that a change in N 

 alone gives too slow a decrease and a change in a alone too quick. A change in /u, 

 gives about the correct average descent with increasing m, but m = 3, 4 are too much 

 out to be due to mere errors of observation. Eow V., term in A/2"" 1 , marches closely 

 with I. On the other hand, VI. is extremely close. It gives the differences as 

 calculated from the formula obtained by least squares, which has met the difficulty 



by increasing N by 17 and diminishing the denominator by '000022 +- . Now 



'014U0 2 for He is '000022, which is evidence that we have here to do with the regular 

 atomic weight term. 



So far nothing has been said as to the true form of the series, but the usual classi- 

 fication has been followed. With our present knowledge, however, a glance at once 

 shows that the third series in each set belongs to the F sequence, and that the sets of 

 series should be classified as follows : 



rvs'(i)-vp(m) rvs"(i)-vi> ( m ) 



Singlet series I yp (I) _ VS , (OT) D bl t series I yD (1) _ w(ro) 



positive type negative type 



LVP (l)-VF (m) LVD (l)-VF (m) 



The sets are apparently independent, except as depending on the same He 

 fundamental sequences. In the singlet series the negative type is wanting ; in the 

 doublet the positive is wanting. They are, as is well known, developed in different 

 ways, and it is not to be expected that the P sequence of the first is also that of the 

 second, and the D sequence of the second the same as that of the first. The singlet 

 series stands out by itself also as having a much larger value of N for the P sequence 

 than in any of the other spectra. In the doublet series, however, it might be 

 expected that similar relations to those found in the other elements might exist. For 

 instance, the D of VF(1) is '998547. The /A of VD is '9294 or '0691 (say '0700) less. 

 If this depends on the atomic volume constitution of the term, as indicated in the 

 alkalies, it should be possible to determine the atomic volume of solid He by 

 comparison with any of the alkali spectra. Now K, with an atomic volume of 44'617, 

 gives for the corresponding difference about '300. On this supposition, therefore, the 

 atomic volume of He would be 10 '41. The density of solid He should, therefore, be 

 "38. KAMERLINGH ONNES gives that of liquid He at its condensing point as '154. 

 The density of the solid would probably be considerably greater, but scarcely so large 

 as '38. The deduction, of course, is not reliable, but is interesting as deducing a 

 value of the right order of magnitude. It may be noticed that the /* of S' differs 

 from that of S" by '1560 = 2 x '0780 ; /x of V'-fj. of S' by '1534 = 2 x '0767 ; and //, of 

 D"-/A of S" by '2243 = 3 x '0748, all approximately multiples of the '075 which go 



VOL. COX. A. P 



