DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 375 



arrangement in the AgD (4) linkage shown in the c, d, e columns of the map for 

 AgPiii [IV.]. The series is in fact continued further than is shown in the present map. 

 Starting from 26727 we find a c + b d+a c + a c (and +d) = 3a + b(3c + d), the 

 actual separations being 770'92-803'607 + 787'51-821'81 + 771'07-803'66 + 770'68 

 803 '16 (and +825 '35). Further, it should be noted that each successive pair is a 

 parallel inequality, one in excess and the other in deficit of normal value. It means 

 an increased displacement 2<J, in each alternate line. But if the observation errors are 

 small, there appear to be indications of simultaneous displacements in the f sequences 

 as'well as on the limit. In fact a similar phenomenon is indicated in the two next 

 orders though naturally some elements are wanting. A precisely similar connection 

 is shown by AgS (3), [IV., p. 382], in a still more striking and regular series of 

 changes. The elucidation of the laws governing displacements is of the first 

 importance and should be one of the immediate objects of investigation. For this 

 purpose examples of continuous series of simultaneous and like displacements will be 

 of the utmost value. For this reason maps of certain near lines (Plates 4, 5), are 

 given for all the orders from 3 up to m = 8, but no attempt has been made to indicate 

 exact displacements involving unity. The parallel series F' about 16 below F exist 

 for m = 5, 6, 7. The sets connected with F' (7) all show the displacement unity. In 

 the lists the true lines are entered as 1 less for m = 6 and 2 less for 7, 8, 9, 10 (i.e., 

 g about 2) than the calculated values. As is seen it makes the observed separations 

 more normal and in so far supports the putting of the limit about 2 less. Later the 

 actual change in the limit is found to be 1'34. 



KrF. During the work of examining the X spectrum a new type of series, 

 associated with the F series, came to light. Whilst the known F type depends on 

 the differences of two sequences d(l)f(m), the new type .has a series of lines whose 

 frequencies are given by d(\)+f(m). We shall denote the lines of these series by F, 

 so that F will denote a difference frequency and F a summation. 



We have already referred to the general properties of these series in the intro- 

 duction. Some of the material from the Kr spectrum bearing on the subject are here 

 collected. In the following lists each order is considered by itself. The examination 

 has not been exhaustive so as to involve displaced values, but it is believed all the 

 direct observed lines have been included. A few abnormal ones, with considerable 

 displacement in the,/ sequence, have also been entered, as they raised questions which 

 require future investigation. The F and F lines are arranged in parallel columns. 

 The mean of the two corresponding lines is entered in thick type between them. 

 That for the first corresponds to the fundamental limit. The succeeding ones are 

 given in the form mean of the first + difference, and the difference only (which settles 

 the denomination of the set) is entered. Thus for m = 2 the first mean is 3067477, 

 that for F 6 , F 6 is 30976'55 = 3067477 + 30178 and 30178 is entered. Also over each 

 line the difference from F, or F, is entered. Notes on detail are appended below the 

 lists. The evidence is clear as to the existence of a series of the form A+/(m). If 



VOL. ooxx. A. 3 F 



