62 PROF. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SERIES. 



observed give A = 21963'38, p, = '825786, = '047604. The variations due to 

 the errors are found to be 



SA = - -673p + '520<7 -l'988r, 

 Sp = '001646p-'000969g + '002540?% 

 Sa = - '005216j9+-002514g- '006116r. 



If, then, the constants calculated from three observed lines give a formula which 

 brings a particular line outside the limits, it is possible to determine whether a 

 permissible change in the original wave-lengths can bring it within. It is used also 

 to test the validity of EYDBERG'S law as to the limits of S. and P. A further valuable 

 result is that it enables us to give the limits of possible variation of A, /n, a, e.g., in 

 the example above cited by putting p = q = r = 1. The utmost possible, thougli 

 unlikely, variations are then 3'18 for A, +'005155 for fj., and '013846 for . 

 When in the following pages limits of this kind are given, it will be \mderstood that 

 they have been arrived at in the above manner. 



We shall have to apply certain laws and relationships already known, and it is 

 necessary to have some clear idea of the degree of exactness with which they represent 

 facts. Some of these depend on direct observation, others on relationships arising 

 from the formula?. Of the former the most important relate to the doublet (v) and 

 triplet (v lt ZAJ) separations of the various series. They are : 



(A) The value of v (or of v l , v^ is the same for all the members of either the 

 sharp or diffuse series the separation in the diffuse series being taken 

 between the satellite of the first and the second, and in the case of triplets 

 for v 2 between the satellite of the second and the third. 



(B) The values of v for sharp and diffuse are the same. 



(C) The value of v for the first line of the principal series is the same as for the 

 sharp or diffuse. 



It may be said at once that these statements are true within the limits of 

 observational errors, the only exceptions that I have met with are in the case of the 

 sharp series of oxygen and the diffuse of sodium. O.S (4) gives v as lying between 

 3'52 and 372, and O.S (5) as between 2'82 and 3'46, or say v > 3'52 by the former 

 and < 3 '46 by the latter. One is naturally tempted to put this down to a larger 

 observational error than the estimated one. There are cases, however, in which a 

 doubt may arise as to whether these statements are absolutely exact. For instance, 

 NaD gives the following values for v (the observational errors are given in 

 brackets): D (3) 16'60 ('5); D (4) 17'04 ('8); D (5) 19'28 (2'3) ; D (6) 28'1S (5). 

 It is to be noticed the least possible v from D (6) is 18 '18, and the greatest from 

 D (3) is 17'60. If it is real, (A), (B) are not true, but D t (6) and D 2 (6) are bad 

 measurements, and the limit of accuracy (5) given for each is probably a rough way 

 of saying very large. On the other hand the gradual rise with increasing order 



