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



by. a permissible change in D 2 (2.3), thus leaving T>i(G) outside, which must neces- 

 sarily be the case with v so large as 28. We may regard, therefore, the formula as 

 satisfying the conditions for NaD. EITZ gives no constants for his formula for this 

 series. 



KP. The observations for P(l) are very bad. K.R. give 7665'6 and 7699'3 

 (possible errors 5). L. gives 7668'54 and 7701/92, R. 7664, and S. 7664'91 and 

 7699-08. HERMANN* 7665-29, 7699'32. The votes carry it for the lower value of P, 

 and one gets an almost superstitious belief in K.R.'s measurements after long use of 

 them in this kind of work. On the contrary, L.'s result appears to agree better with 

 those computed from K.R.'s values of P (2.3.4), the case here adopted. RITZ' 

 constants are calculated from L.'s result for P(l) and K.R.'s for P(2.3). In the 

 table, then, L.'s result is used. It will be seen that the formula adopted here gives 

 excellent agreement except in P(5), where the deviation is twice that allowable. 

 The order from m = 2 to 7 is 0, 0, 0, '21, 0, "01, a striking agreement with a sudden 

 jump at m = 5, pointing to observational error, but there is no further evidence as in 

 the case of NaS (6). RITZ' are all outside, except for m = 8, 9. 



The S are corrected to constant v = 57 '93. The agreement is very good except for 

 S (2), which is far out. RITZ has all outside. In his paper he must have given 

 S 2 ( co) for Sj ( oo ). I have calculated his S (2.8.9) on this supposition. 



The numbers for KD are calculated from a form p = f. It appears p. = 1 + f is not 

 possible. As is seen, there is good agreement. In this case, in order to bring D (2) 

 within limits, errors have been allowed to D (3) and D (5). This is the only diffuse 

 series for which RITZ has given constants, and I have calculated from them the values 

 for m = 2.3.8.9. The formula in this case is quite out. 



RbP. The only accurate measurements for this series are those of K.R. for P (2.3.4). 

 P(l) is as uncertain as in the case of KP(l). K.R. give 7950, 7811 (observational 

 error = 5) with v 223 '85 ; at least one, therefore, is certainly wrong. L. gives 

 7950-46 and 7805'98 (i; = 23276) ; S. gives 7947'6 and 7800'2 (v = 23773) ; whilst 

 R. has 7799 for P l (I). Using Pj (2.3.4) for constants gives P a (l) close to L.'s 

 value and PI (5) close to observed value, pointing to L.'s value for P (1) as being very 

 close to the truth and that K.R.'s error is almost wholly in P l (l). K.R. and L. 

 agree practically for P 2 (l). S. gives a line at 31587 which is closer to P 2 (6) than 

 P! (6) ; it has been taken for both lines in the table. For P 2 the limit has been made 

 the same as for P 1; and the lines P 2 (2.3) used for calculation. P 2 (4) is just outside, 

 but a slight permissible alteration will bring it inside. 



RbS. The text for this series is very corrupt. K.R. only observed Sj (4.5) and 

 S 2 (4) with possible errors '2 for m = 4 and '15' for m = 5. For S (3) L.'s measure- 

 ments give v = 239-62 and S.'s 237'60. For the constants I have used S (4.5.6) 

 corrected to v = 236 70. The formula gives S.'s result for S (3) as against L.'s. 

 S (7.8) are given both by R. and by S. : for lack of any other guidance I have taken 



* 'Ann. d. Phys.,' 16, p. 684. 



