474 Prof. W. M. Hicks on 



are given as possibilities to show how the theory of! dis- 

 placement can explain them. The limit found by the high 

 orders 59150 should be expected to deviate by only a few 

 units from the truth and 59174 would seem too large. It 

 is, however, the only value for which a succession of corre- 

 sponding lines can be found. It could be explained by 

 supposing the summation series to have the limit 59150 + 

 and the difference series about 59200 + . For the sake of 

 brevity we will refer to the series by the letter Q, but this 

 is not to suggest a new kind of series. It is probably only 

 one of several P series (or possibly F or D). The order of 

 intensities in the & lines can easily be explained as due 

 to weakening at the red end because of increase of order 

 and an apparent weakening at the other as being close 

 on the limits of Handke's region. But this explanation 

 will not hold for the Q where the order of intensities is 

 quite anomalous. The explanation offered is that the 

 configurations giving lines of lower order are excessively 

 broken up and only a small number subsist to give weak 

 normal lines. This weakening in the low orders points to an 

 F type, rather than P. 



For Q(6) no line is observed but the two strong lines 

 shown in the table are numerically + 7 8 displacements on 

 the limit and are probably really so. Their separation from 

 their mean is 89*06 and this requires a mantissa difference of 

 1024 whilst 78 = 1024. The numerical coincidence is thus 

 exact. Again there is no representative for Q(4). The 

 two lines given in the table lie on either side of it and the 

 displacements shown produce a Q lf Q 2 with separation 14*6 

 which will go with combination lines as will be shown 

 immediately. Q (3) would lie in the unobserved region 

 between the shortest of K. H. and the longest of Handke. 

 The two strong lines given for Q (2) are certainly of the P 

 type and give the same separations for m = 2 as in the P series 

 considered above. There is no strong and definite repre- 

 sentative for Q (1). All the lines in the region suitable for 

 it are nebulous. We should expect a doublet with separation 

 of the order 248 such that it should be produced by the A 

 displacement on 51 974*8 — Q (1). There are several doublets 

 but none quite satisfactory. For instance, that given in the 

 table for Q^l)— 275~ 3*46— gives q (1) =31591*3 or 63 

 greater than p(l) and equivalent to ( — 135)^(1). But 

 this would mean with A a separation 248*44 + 13 x *06 

 = 249*22 instead of 245*50 as shown. There are so many 

 possible explanations that nothing is to be gained in 



