256 Proceedings of the Eoyal Society of Edinburgh. [Sess. 
‘‘the application of relativity mechanics to Palmer’s formula results in 
a definite reduction of the discrepancy between observed and computed 
values, but does not in any way obliterate the discrepancy.” In several 
cases calculated values of X seem to have no closely observed correlative, 
and many values of X observed by one physicist are not obtained by 
another. Watson makes the following comment, which is instructive : — 
“ It seems probable that as Hasselberg’s measurements in the yellow- 
green part of the spectrum were visual, and the eye has a maximum of 
sensitiveness in this place, these additional lines were too weak to be 
recorded photographically, and, indeed, indications of several lines can be 
seen which are too weak to measure.” It is surprising that such a few 
simple values of S and should give rise to such a proportionally large 
number of values of X. There is another point of interest which arises, 
and which deserves mention. In the secondary spectrum a considerable 
number of lines are found, the wave-leno^ths of which are less than 
X = 3646, which is the theoretical limit of the primary spectrum according 
to Palmer’s formula. For a given n, the limit for X = n'^/'N according 
to the Palmer formula, and from equation (10) the limit for X = '^^7NE(5^. 
Since R(5'^ can be greater than unity, as is indicated in the table for E(5^, 
it follows that equation (10) will give rise to lines of wave-length less 
than the minimum wave-length to be expected according to the Palmer 
formula. 
{Issued separately July 6 , 1922 .) 
