DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SEKIIX 



it is possible there may be this difference and VD S1 (4) is not VD,,(4) as in the typical 

 cases. The real difference may be any multiple between 52<J and 55i. In fact 3 is so 

 small that there is not absolute certainty. 



AID has proved itself the most intractable series to bring into any simple formula 

 of the ordinary kind. It was, in fact, the difficulty with this element which first led 

 mi- to seek another solution on the lines now being considered. 



It will be seen that it lends strong support to the theory suggested. The table is 

 arranged with = 2 '66. The exactness of the relations there shown is very 

 remarkable, and when it is remembered that A is a large number like 1754, the 

 practically exact multiples referring to the first five lines must carry very great 

 weight in the argument that AID at least is subject to a modification of successive 

 denominators by multiples of certain units. The objections to the arrangement are 

 two : (l) that = 2'66 is outside the error limits of S ( o), and (2) the denominators 

 appear to go on diminishing without reaching a limit. A slight alteration, however, 

 in A will get over the first. For instance, if A = 1754 '5, would be about '5 less, 

 D(oo) would be within limits of 8(00), and the same arrangement would also hold, 

 but it could not be much more diminished because with m = 5 and 6 the changes 

 introduced into the denominators by would upset the multiples 54 and 29. A 

 change of A by '5 would change the ratio to w* from 361'88 to 36178. D(oo) is, 

 therefore, probably very close to 48163'62. 



If = 10, the denominators tend to a limit about '107 for m = 7 and beyond. 

 But this is far outside permissible limits of D(oo), and, moreover, the striking 

 arrangement with multiples of A is quite upset. We must therefore conclude either 

 that the limit is not reached until an order m = 10, or beyond, or collaterals enter. 

 If the former, multiples of A can enter, but the observation errors are too large to 

 give certainty. If collaterals based on (9<5)D(oo) are used with = 2' 16 or 

 D(oo) = 48163'62 the mantissas for 7, 8, 9 come respectively to '11:3569, '113590, 

 '113956, and for 10 for a VD U = VTX,,, 113700. The separation observed for m - 10 

 is 107'96 instead of 1 12'15, 'either an observation error or a displacement of D n or D a ,. 

 A displacement of D,, by + 2$ on D(o) brings the separation very nearly correct, 

 although the observation error in the wave number of these two lines is as large as 

 4 '4, it is probable their difference is much more exact and that the defect shown by 

 v = 107 is real. (For m = 10, D n is practically = D ia .) The results therefore go to 

 show that the D, and D a lines for m = 7, 8, 9, 10 are collaterals, (9c$)D(oo), except 

 that for D(lO) an extra displacement of 2<5 is added. Although the numbers above 

 are so nearly equal we must not place too much reliance on them, as the observation 

 errors have a very large effect on the denominators for such high orders. If the 

 suggested arrangement is correct it must mean that K. and B.'s measurements must 

 have been of a very high order of exactness, which would further mean that the 

 measures for the D., lines would not be so exact since the observed values of the v for 

 m = 7, 8, 9 are respectively '68 (possibly real on D a ), '7, '13 in error. 



3 A 2 



