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



All are easily zero within limits of observational error. It will be further necessary 

 to discuss whether the alterations called for will affect the permissible exactness of 

 the formula for all the lines. Its discussion is bound up with that of the next 

 relation. 



Relation (G). Viz. : P ( oo ) = VS (1). As before, write P ( oo ) = N/D /2 . The 

 table gives the following values of D D' : 



Na . . . -002772 -008390 Rb . . . -010696 + '016119l 



K . . . -009150-00871G - '003210 J 



Cs . . . -016712 ? 



This at first sight appears distinctly against the truth of (G). Taking the actual 

 errors of observation in the three lines used to calculate the constants of P to be 

 respectively p, q, r times the possible amounts, and p', q f , r' to be the corresponding 

 ratios for the S series, the constants of the formulae were determined in terms of them 

 as explained before. Then the conditions (F) and (G) were imposed, and the question 

 discussed whether it was possible to satisfy the equation by values of the p's, 

 numerically less than unity. Starting with Na, the result was that it was impossible. 

 As, however, this might be due to the fact that another term was required in the 

 denominator, the work was repeated, using the formula D = m+/x + a/?n + /S/7n 2 . As 

 we have seen above, NaS (G) is in all probability a bad reading. If this be put aside, 

 it was found that it would be possible to satisfy the conditions and still bring in all 

 the other lines within observational errors. For instance, putting r = / = p' '5 and 

 q' = (p, q have inappreciable effect) gives 



v AT /I 10* '033851 , -0013521 2 



For P, n = 4144G"44 N/ < m + T149427 - +- -V , 



/ [ in m' J 



/f\-\ A Af> A .Al 1 OK 



\ni+ -652800- 



m m 



These satisfy both (F) and (G) exactly, and reproduce all the lines (S (6), of course, 

 excepted) well within the limits of error. In S it is to be noted that the a, ft are 

 practically equal, and that /3 for P is negligible, i.e., so small that a very small error 

 in one of the determining lines would wipe it out. 



The case of K was then discussed. Again, the relations could not be satisfied with 

 the form /A + a/m, and the work was repeated with a/m+/3/m 2 . As in the previous 

 case, it was found possible indeed, but it was now necessary to take P(l) close to 

 K.R's value instead of that of L. It could be done, for instance, by putting p = '11, 

 p' = - q' = r' = - -35, and q = r = 0. This gives 



For P, n = 35006-05-Nm + 1-296929 - ' 064312 + 



m mr 



8 n = 21965-21-N/{ + -820947 - ^5714 _ ;025656l' < 



I [ m m* J 



