262 
DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
hitherto, which could determine precisely an upper limit sufficiently low for the 
possible separation of Hp, would be decisive between these two alternatives, if the 
Michelson value were correct for H a , but if Houstoun’s value were correct, such an 
experiment for Hp would be much more difficult to perform. It is necessary, therefore, 
as an essential preliminary to an attack on this problem, to repeat the measurement 
of the separation in H a in order to determine the possible magnitudes in the case 
of Hp. 
Other possible interpretations of the Balmer series have been proposed, and these 
consist mainly in regarding it as a set of two or more practically coincident series. 
This has been suggested, for example, by Fowler,* but it appears to involve a more 
complicated structure than doublets for the individual lines of the series. At the 
same time, it does not at present violate any definite experimental knowledge. 
Exact superposition of series cannot, however, be expected even in the case of 
Hydrogen. Hypotheses of this type are virtually a combination of the two 
alternatives already suggested, and an experiment which could decide between these 
two alternatives could, of necessity, also give a verdict for or against the present one. 
For it would apparently be necessary in this case that H a should be a triplet. 
From the point of view of series relations, another alternative, which has 
apparently not been noticed hitherto, may be put forward at this juncture. The 
Balmer series may primarily be a series of single lines, and the other components may 
be combination lines nearly coincident with these. If the normal series is given by 
Curtis’s formula 
n = N { ----rrl 
1(2 +p) 2 (m + n) 2 ) 
where N = 109679‘2, p is negligible, and /u = 0‘000007, then the Principal series may 
be that of Lyman in the Schumann region, following the law 
n = N j—^_ - _1. 
1(1 +p) 2 (m + ju) 2 j 
Combinations of an Arc series with itself are now well established if it is a Principal 
series, and on the present view we should expect a combination series of the form 
n — N J_1_1_ 
1(2 +0“ (m + M) 8 
with a constant difference of wave number from that of Curtis, of amount 
N (2+y>) -2 —N (2 +m)~ 2 = 0'192 on calculation. The corresponding separations of PI a 
o 
and Pip then become 0‘081, 0'048 A.U. respectively, the first being nearer to 
Houstoun’s estimate. There should also be a series 
^{(2 + m) 2 (m+p) 2 } 
* ‘ Bakerian Lecture,’ 1914. 
