358 1>R- W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



first denominators = 181557 = 653x278'03. It is possible the real errors attached 

 to D (2) by RANDALL may be greater and the difference slightly less ; but if we 

 suppose 278-03 to be the real value of S it makes $ = 361'82t^, and, therefore, very 

 close to the adopted value. It would appear that D 12 (4) has been displaced from its 

 normal value, judging from the irregularity introduced into the separations. If so 

 the separations might be 14<5 in place of 15S. 



Ba. 



Starting with the uncertain value of S(<) = 28642'63, as given in [II.], the value 

 of S as calculated from A, + A 3 is 68270, and from A a is 684'34, both being near the 

 most probable values but on opposite sides. The value 683 is taken at first as a rough 

 approximation. Apparently, the first set of lines have not been observed. RANDALL* 

 has observed two lines, 29223'4, 23254'8, which give a separation 878'27, which is v lt 

 but no signs of satellites or, rather, if there are satellites, the separation observed 

 should be much smaller. If, however, the satellites have gone here, and this pair 

 denote the first two lines of the first triplet, they depend on VD 13 , and the value of 

 the denominator is 2'085331,t which would range well with those of Ca and Sr, viz., 

 1'946, 1'987, but the second lines of these give 3'082, 3'169, and of Ba 3'093, which 

 would rather point to a less value than 2'085 for the first line. But if VD (2) is 

 larger than D(oo), the lines would be -23254'8 for the first and -29223'4 for the 

 second, giving a denominator for the first of 1 '825551. The differences of the 

 denominators of the D 13 lines for m = 2, 3, 4, will then be 267632, 38612 instead of 

 6528, 38612, and are therefore more in agreement with the type of the other elements 

 of this group. Moreover, the former, as we shall see, is a multiple of S, whilst the 

 other (6528) is as far out as it can be. Both values, however, are inserted in the 

 tables (see also p. 389). 



The satellite differences for D (3) are 949232 and 751640. The values of US 

 and US are respectively 95625 and 75134, and hence the first cannot be 14<S within 

 limits of error, although it is so close as to produce a conviction that it really is so. 

 Now for small variations of the limit D ( oo ) the separation differences are scarcely 

 affected, but, as we saw in [II.], there was evidence to show that the limit S ( oo ) was 

 considerably less than that found, and, in that case, the separation differences would 

 be slightly changed. A decrease of D ( oo ) would increase those differences. If, 

 however, it is so large as to bring up the first to 14<$, the second is increased so much 

 that it is not IIS within limits. Consequently, the two conditions confine the choice 

 of D(oo) within very narrow limits. It is found to be close to a decrease of 32, 

 i.e. t D() = 28610'63. This again changes the values of A 1} A 2 , with the given 

 values of Vl and v, to 29379 and 11997, giving from A,, S = 683'2. The table is 



* 'Ann. der Phys.,' 33 (1910), p. 745. 



t The values in this and in the table are calculated from the limit as modified below. 



