434 
DR. W. M. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
These differences may be written 
72G24 = 40f (l782-I8-050t^+-3Idj^i) 32076 = 18 (1782-00-’047^-•047dri+TSdi/,) 
= 40^(1793-18... „ ) = 171(1807-1... „ ) 
The first consequence to be drawn from these numbers is that as S is to be of the 
same order of magnitude as calcidated from and As it can only take place in the 
first arrangement since the co-efficients of f (the only variable capable of large values) 
are practically eq^ial. In other words A^— 40f^, A 2 = 18^, the same multiples as in X. 
This is one quite definite conclusion of importance. 
But further we know that d must be one of the following sets 1783-5, 84-4, 85-3, 
86-1, 87-0, of which the first two thongli perhaps possible are improbable and the last 
three ecjnally probable. We will state the results for the first, third, and fifth, the 
others being intermediate. The values of c/i'j, dp 2 being uncertain to about unity, the 
values of ^ can only be estimated to the same order. Taking Aj, in order to produce 
the required values of ^ must have the respective values of —27, —64, —100 within 
a few units, and the nmnbers inside the brackets for A^, Ao, become 
l783-53--050^+-31di/i 1783-27-047^--047d;/i + -65d)/2 
1785-38-... „ 1785-00 ... 
1787-18-... „ 1786-7... 
where now ^cannot exceed a few units. The respective limits become 50473, 50436, 
50400. One of these is close to a S limit. There is another corresponding to the — 
displacement about 31 ahead and giving — 5375 about. We already have an 
accurate value of one d sequence, viz., the F (co) = 29964-20. Combined with the 
limit this should give a D line = S ( oo) —29964-20, i.e., near 20509, 20472, or 20435, or 
the 31 higher values. We only find the following possible lines, viz. (2) 20515 and 
(4) 20438-8 (W.), (O) 20446-38 (B.lt.), 20473, the fii’st and fourth being C.li.’s copper 
electrode lines. The first is one of a chain of 2680 separations, or stretching 
l)ack to 15136 and by 2689 to the strong line (lO) 23204-6 (R.) or 7-57 (W). It has 
none of the signs of a D line. The line 20438 is one of the strongest in this neighliour- 
hood has no separation link, hut 5625-8 back to 14813 + 2 (W) to which also 20446 
has the (di) 5649 link, viz.,5633. Again the 14813 shows a D modified set, viz., 
(0) 14813 (W) 5382-71 (4) 20195-71 (W) 2672-41 (5) 22868-12 (W), 
5385-91 (0) 20198-91 (R) 2669-16 (l) ‘07 (R). 
Hence here we have all the signs of a Dji line in 20438 with the above as a satellite 
set, at the F separation (56...) behind. Now it is a very striking fact that the 
measures of W. and of R.R. for these lines not only differ by amounts larger than 
can he attributed to observation errors, hut also that their intensities are not 
