358 PROF. A. FOWLER AND MR. C. C. L. GREGORY ON THE ULTRA-VIOLET 
second decimal place in v and d x are entitled to but little weight, but they have been 
included for the more consistent determination of d 2 , which is given in tenths. The 
observed positions of some of the unresolved a/3 and Se pairs are replaced by estimated 
positions of the components, in order that the course of the series may be more 
completely traced. 
When due allowance is made for irregularities in the second differences, which are 
very sensitive to small errors in the wave-lengths, it is clear that the series as a whole 
cannot be satisfactorily represented by the usual approximate formula v = a + b 
(m + y) 2 . Such a formula represents a series in which the distances between 
successive lines (d x ) are in arithmetical progression, so that the second differences ( d 2 ) 
would be constant, and not one of the series approximates closely to this condition. 
The actual wave-numbers of the members of the different series could only be 
effectively plotted on a very large scale, but the peculiarities of the series can be 
shown better in some respects by curves which have d x for ordinates, and successive 
integral values of m for abscissae, the initial value of m being chosen arbitrarily. 
Such curves are shown in fig. 2, and it will be seen that they depart widely from the 
linear form implied by the above-mentioned formula. The curves also fail to show 
any symmetry in the arrangement of the groups of series on the two sides of the 
central maximum, such as might have been expected from the general appearance of 
the spectrum. 
Considering the series a, f3, y, it will be seen that they begin with coincident, or 
nearly coincident, faint lines on the red side, and that the distance from line to line at 
first diminishes slightly and then increases. In 0 and y the subsequent increase is 
continuous, so far as the series can be identified, and if the later lines have been 
correctly assigned, no other members in the immediate neighbourhood are to be 
expected. In the a series, the distance d x passes through a maximum value, as in the 
case of the main series of A 3883 cyanogen which has recently been further discussed 
by Birge. # The a curve, however, differs from the cyanogen curves in having a 
double curvature, and while the greatest value of d x occurs among the weaker lines 
near the end of the series in cyanogen, it occurs among the brighter members in 
ammonia a. The later portion of the a curve is rather steep, and the identification of 
the next member of the series, which is involved in the secondary central maximum, 
is consequently difficult; the line A 3372'19 [y 29645'97), however, fits fairly well on 
the continued curve, and if this really belongs to the series it would probably be the 
last member. 
The series S, e, £, resemble the first three in commencing with faint unresolved lines, 
which are far removed from the central maximum, but the d x —m curves show no 
change of curvature near the beginning of the series. In the ^ series the distance 
between successive lines increases continuously as the central maximum is approached, 
but in e and £ it passes through a maximum as in a. 
* ‘ Astrophys. Jour.,’ vol. 46, p. 85 (September, 1917). 
