DR. VV. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 357 



of collaterals, formed by the addition of ouns to the limit D(oo). As such increase 

 tends to increase intensity it may account for these surviving when the typical ones 

 are either too faint or are destroyed to form the collaterals. It is useless to attempt 

 to determine these multiples, because the observation errors are so large themselves 

 as to be a large multiple of the oun, and at the same time we have no knowledge <>!' 

 what the typical VI) (m) should be. In general in the 2nd group the successive 

 denominators are formed by the successive addition of smaller and smaller multiples 

 of the oun until probably a constant value is reached. In the present case, with the 

 quantity 155(5, that limit is certainly not reached. But it may be instructive, in 

 order to illustrate the nature of the suggestion, to find what the collaterals ought to 

 be if the denominators of VD(t) remain the same for TO > 4, viz., "091707. The 

 multiples are found to be 7S, 15<S, 33d The series of the observed D,, lines may then 

 be exhibited by the following scheme, where d stands for '091707 : 



D ( oo)-VD (2+d-99A 8 -155<J), 



D(oo)-VD(4+d), 



The line D 12 (2) is interesting. PASCHEN gave it as 19859'9 with the remark 

 " Wahrscheinlich doppelt 1<)856'9, 19864'6," and he allotted 19864'6 to D 13 and 

 19856 '9 to the Principal series. But in [II., p. 56] reasons were given against the 

 latter allocation. In fact the line is very close (probably within observation errors) 

 to the collateral formed by adding one oun to D 12 . The wave-length of such would 

 be 19857'S = D,., (2) ( + S) [see Note 2 at end]. 



Sr. 



The value of S is calculated as 277 '8 9 from A, + A a =125x4, which gives 

 $ = 361'64?^. The differences as shown in the table are extremely close to multiples 

 of S. Moreover, the limits of variation for the first two are so small that the 

 variations of ROWLAND'S standards from the correct values for his scale may become 

 of importance. For D(3) the values should be 2 less, whilst for D(2), failing direct 

 observations for reduction to vacuo, recourse must be had to extrapolation on 

 KAYSER and RUNGE'S formula,* which has been done. In order to bring the 

 differences for D u (3) and D a (4) and of D u (4) and D u (4) to multiples of S within 

 error limits, it is necessary to take about '4 or D(oo) = 31027 '25. When this is 

 done the denominators can be arranged as in the table. The difference of the two 



* RANDALL appears to have done this for D n but not for DU, which also makes his value of v\ = 392 6 

 instead of 394-42, which is close to the true value. 



