PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 65 



its truth. When, however, his values are contrasted with actual measurements (see 

 below), it would appear rather to show that if the law is correct his formula is wrong, 

 or if his formula is correct the law is not exact. 



(H) The value of N is the same for all series and for all elements. 



There can be little doubt but that N is very nearly the same for all known series, 

 and it is a tempting hypothesis that it is actually so. We have no evidence, however, 

 to prove that it is either the same for all series, or has different values for the different 

 types of series, which may well be the case. If it be found that all observed lines 

 come into the formula with the same value of N, and further if thereby the validity 

 of (F) and (G) can be established, or if other relationships which present themselves 

 are more clearly brought out, then the evidence that N is a constant of nature (as 

 RYDBERG calls it) will be very strong. We shall start, therefore, by taking N to be 

 the same for all series, and the same which RYDBERG assigns to it, viz., 109675, when 

 referred to vacuum. 



This value, however, may require redetermination. It was determined by RYDBERG 

 from hydrogen by least squares applied to BALMER'S formula for HD and using the 

 observations of AMES. It was BALMER'S form which led to RYDBERG'S modification, 

 putting m + n in place of m, where p. depends in some way on the properties of the 

 substance. To suppose, therefore, that BALMER'S formula is exact, i.e., p 0, seems 

 like saying that hydrogen has no individual properties. In any case, it would seem 

 extremely unlikely that, as every other substance has a finite value of /*, H should 

 have /A = 0. It is to be expected that its p. would be small. All the low atomic 

 weight elements have /u, small (or very nearly unity) for a D series, and we should 

 expect the lightest element of all to have a very small one (or nearly = l). To find 

 N, then, the series of RYDBERG should be used as a basis, and N and /* both determined. 

 Unfortunately the HD spectrum is not known with great exactness of measurement. 

 The most accurately measured spectra as wholes are without doubt those of He by 

 RUNGE and PASCHEN, and it would seem preferable to use these to determine N. At 

 first sight, then, it might appear more logical to consider this point of the value of N 

 as determined from H and He spectra before going further. It is preferable, however, 

 to postpone this until the alkali spectra have been discussed, and some information 

 obtained as to the connection of the different types of series. Moreover, by keeping 

 at present to RYDBERG'S value, it will be possible to directly compare the results from 

 the formula adopted in this paper with those from that of RITZ, which is the only 

 other comparable in accuracy. 



The Spectra of the Alkali Metals. 



As SAUNDERS has given very complete tables of the observed spectra of the 

 alkalies/' it will be sufficient to refer to them for the material at disposal at that date. 



* 'Astro. Jour.,' xx., p. 188. 

 VOL. CCX. A K 



