DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 411 



The second set is near the end of the observed region, and the fainter D, line is 

 extrapolated by the normal i>,, this will introduce a small possible error. The third set 

 is wholly outside the observed region and was obtained by sounding. The data are 

 as follows, the lines used being regarded as linked by e to the first triplet 36487, .... 



[43801-13] d\ [45578-87] dX [46397-05] 



(l)36487-03.e -00 (Ira) 38264 -77.e -00 (1) 39082 '95.e -00 



(1) 29175-18e.e(S,) -00 (1) 30949 -88.2e -08 (< 1) 31768-93.2e --01 



(l)39372-71.t; --02 (1) 41155- 14 v(28,) -03 (< 1) 34659 -40.e.; (28]) - -07 



(l)39666-49.w -09 (1) 33841 -74.e.t; (28,)* -12 



(3)32351-67.e.w(-8,) -10 (1) 34126-78.e.w ( - 28,)*- 12 



(<1) 24749-35.e.e(8 1 ).v(S 1 ) --04 (1) 26814- 18.2e.w (28,) -03 



The formula obtained from these is 



51045'37-N/lm + -898460- ' 22504 r 

 I \ m } 



This was tested to m = 13, with good agreement with the exception of m = 4. 

 All are in the ultra-violet and require sounding. As the evidence of the efficacy of 

 sounding already adduced may be regarded as convincing, there is no advantage in 

 giving further details of the results, especially as no additional conclusions are based 

 on this formula. 



XF. We are to look for parallel F sets with the same separations as those of the 

 D satellites. Starting with the triplet 19880 as an undoubted D satellite triplet it 

 was then attempted to determine the others, by picking out those lines of larger 

 wave-length whose mantissse differed from that of 19880 by oun multiples. The data 

 are contained implicitly in the list on p. 407, independently of the form into which the 

 mantissse are there thrown. It is clear that the above condition is satisfied by all 

 those which show unsatisfied remainders of the same magnitude as that of 19880 i.e., 

 66 within error limits of, say, 6. The selected lines were 19880, 20021, 20041, 

 20312, 20500, 20559. We have shown above that the second, third, fifth and sixth 

 of these satisfy the capability test for 3(5, displacements on the limits, and have also 

 found some evidence that 20312 also belongs to this set, although perhaps with a 

 somewhat excessive observation error. It has also .appeared that 19880 cannot 

 belong to this set, but it has so happened that the satellite separations from it reproduce 

 themselves in the F series sufficiently well as to serve for identification. We shall, 

 therefore, use this allocation. The selected lines give separations from 19880 

 respectively of 140'94, 161'01, 43T98, 619'41, 679'36. In these 19880 was treated as 

 if it were a fifth satellite to 20559 and the notation adopted of F 6 , ... F, series. Such 

 series were found, and in what follows I shall chiefly confine consideration to them 

 leaving aside for the present purpose, with one or two exceptions, the very numerous 

 other groups which exist. It would not be advisable to suggest a definite notation 



* Parallel inequality. 



