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



of S ( oo ). If D ( oo ) = ( - J,) S ( oo ), here = - "1 5 of S ( ).] The lines calculated 

 from the formula for the succeeding lines are all outside the observed region. For 

 m = 4 ... 7 they are respectively in wave-numbers 



47079-52, 48500-56, 49349'39, 49896'60, 



The detailed discussion immediately following will show the evidence for their 

 existence by sounding. The existence of a parallel set at a distance -(e + v) is 

 brought to light which show for the above calculated lines values of O C = '09, '00, 



14, -'01. 



The agreement is remarkably close and would seem to show that the value of 

 D ( oo ) used is very close to its true value, about one or two units in excess. The 

 results of the discussion are exhibited as a whole in Plate 3, fig. 4. 



As in the previous cases, the linkings with the observed lines ;, = 1,2, .'! are given, in order to show 

 that the method is justified where it can be tested. 



1. 2. 3. 



(6) 2097G (5) 38560 (3) 44426 



e (4) 24158 '17 * (1)41743 "04 -v (10) 42483 '01 



0(1)22914 -86 -r(l) 36619 "27 -2e(4) 37061 '13 



r(- Si) 229 14 -00 

 -c-i>(3) 15856 



4. 5. 6. 



[47079-52] [48500-56] [49349-39] 



-e(7)43894 -OS -e [45317] -e [46166] 



-e-v(l) 41951 -09 - c -v(l) 43374 '00 - e -t>(2) 44220 "13 



-u (2) 45 196 -00 



[49896-60] 

 -446713] 



--*>(!) 44771 --01 

 -2c- i- (3) 41588 '05 



In m = 1 negative links lead to lines in the red where observation is defective. LIVEING and DEWAR 

 give a line to the nearest unit which may possibly be a -e-v link. The line 22914 is too far out to be 

 an exact r, but its difference is 4-47, which corresponds to an exact - 8 l displacement on the limit. In 

 other words, it belongs to the limit as calculated from the S series. 



In m = 4... 7 the -e-v sounders all show lines in evidence. The -e sounder for m = 5, 6 would 

 show lines just within the boundary of observation, and the absence of corresponding observed lines is 

 therefore explicable. In m = 4 the line 41951 is part of an apparent triplet. 



(1)41951-59 786-19 (1)42737-78 308-51 (2)43045-93. 



The diminished values of vj, i> 2 indicate that the second and third lines correspond to DM and D 3S lines. 

 The vajue of /j is however sufficiently close to make the difference due to observation error, in which case 



