412 DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



for these groups until the whole system of D and F series is placed on a secure and 

 comprehensive foundation. The above notation, therefore, is only to be regarded as 

 one which in this communication serves to identify certain of those groups here more 

 specially discussed. 



The material was treated by the same method as in Kr, and search made for the 

 above separations in the region where F (2) lines should be expected. From the lines 

 thus obtained the actual F lines were sought for, bearing in mind the large sequence 

 displacements so common in the low orders. In only three cases those for F 2) 3 , 6 

 were suitable undisplaced lines found for m = 2, and of these only F 3 , F 6 gave 

 observed lines for m = 3. They were separations from F 6 



m. 



2. (8)18812-55 432'46 (8) 18380'09 619'82 (1)1819273 



3. (1)24253-30 432-49 (<l) 23820'81 



5. (2) 28108-52 432'00 (l) 127676'52 



For m = 4, F :i showed no undisplaced line, but in good position for m = 5 there were 

 lines for F 6 , F 3 . From the three lines for F ;i the following formula was found 



We can at once apply two tests to this as to fulfilling the conditions for F series. 

 The limit 30740 must be a d-sequent, i.e., must differ by oun multiple displacement 

 from some other known d-sequent, and the first /-sequent must depend directly on a 

 multiple of A 2 . We already have a very accurate cZ-sequent found as the limit of the 

 1864 series, viz., 30725'30 + f'. On this a <S, displacement produces a change of 4'97 

 so that -3(5, produces 30725'3() + ' + 3 x 4'97 = 30740'21 +', and this condition is 

 accurately satisfied by , = ' + '04 where , belongs to the present case. For the 

 second test the mantissa of /(2) is 



978816-121f, = 89(l0997'93-r3G) = 89 (A a -'27-'36-.x) 



which again is seen to satisfy the test exactly. The satisfaction of these two conditions 

 must give full confidence as to the correctness of the allocation of the F 3 lines. 



From this formula lines were calculated from m = 4 to 27 and the other sets 

 allocated by their corresponding separations. They are not reproduced here, however, 

 beyond m = 15, partly because they are only of importance in a systematic 

 arrangement of the X spectrum, and partly because the lines to be identified are 

 so close that it becomes a matter of extreme difficulty to allocate them correctly. For 

 instance, the calculated values of F 2 (14) and F, (15) are 30064*38 and 64'16 ; of 

 F 4 (l2)and F 3 (l6) are 30360'47 and 60'29 with many other examples. With the 

 high orders successive lines become close, and with the large number of separate 

 series involved the observed spectrum should be expected to be crowded, as indeed 

 in this region it is. 



