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



true within limits of errors of the measurements, but those limits are very wide, and 

 it may well be that exact equality does not hold. There can be little doubt but that 

 the value of v from NaS is very close to 17'10, and 17'21 is certainly exact for NaP (1). 

 The He lines have been measured with great exactness, but unfortunately v is small 

 (1'007) and HeP"(l) is far up in the ultra-red. In O, v is of the order 3 - (>, and OP(l) 

 is a bad observation, whilst in S (v = 18 '04), SP (1) is outside the region of observed 

 lines. The evidence of the exactness of (C) is, therefore, not conclusive, but in spite 

 of the indications of Na to the contrary, it is probably correct. The doubt, however, 

 should be kept in remembrance.* 



Observation also tends to show that : 



(D) The corresponding 8 and D series tend to the same limits. 



(E) The doublet or triplet series of the P'type tend to the same limit. 



The exact truth of (D) and (E) has not been proved from direct observation, for the 

 actual limits have never been seen nor have a sufficiently high order of terms been 

 observed. The HD has been measured up to TO = 31, but HS (star by PICKERING) 

 only a few to compare with it. NaPj has been measured by WOOD! up to TO = 43 as 

 an absorption spectrum, but only two terms of NaP 2 are known. With the exception 

 of these two, no series has yet been observed nearly up to its limits, and the strongest 

 evidence in favour of (D) and (E) is based on the limits as calculated from formulae in 

 which again the actual limits will vary slightly with the form adopted for the 

 formula. 



The lists of values of limits given by E/YDBEEG| show that the approximate truth 

 of (D) is certain. 



Amongst the relationships depending on the formulae, the chief are those which will 

 always be associated with the name of RYDBERG, viz., the remarkable connection 

 between the sharp and principal series, and the constancy of N. The former may be 

 expressed in the form : 



(F) S(oo) = N/D 2 of P(l) = VP(1). 



(G) P ( oo ) = N/D 2 of S (1) = VS (1). 



The discussion of the evidence for or against them will come later. Their 

 approximate truth is so clear that it would require very strong evidence to justify 

 the use of any formula which did not conform to it. RITZ has imposed the law on 

 his formula, using it in calculating the constants, and supposes that the results prove 



* Since the above was written, PASCHEN has published further observations in the ultra-red, giving 

 what he takes to be the principal series for several elements. When discussed, these will probably give 

 considerably more light on the question. ' Ann. d. Phys.,' vol. 29, p. 625. 



t 'Astro. Jour.,' vol. xxix., p. 97. 



t ' Rapports Congres Internat. de Phys.' II., p. 210. 



The expression " N/D 2 of " will have to be employed so frequently that it will be convenient to use a 

 symbol for it. V will stand for the term of the formula in which m varies. 



