THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 573 
On the other hand, from the Rypprrc-THIELE formula (3) 
ae 1A) a, (m + p.)? R 
Hence, if the transversal CD be drawn in such a manner that 
UGE 
AKOZOD SE 2’ 
we find 
Cém=Vm—Vo and ¢pD=ve -Vv,, and hence 
€)C5 = Vo — Vy 5 Colg—=Vg—Vo, - > + - = CD ve — V9 Q.L.D. 
If, now, all the series belonging to the same «-group be arranged in our diagram, 
in every case the lines could be made to fall upon the rays Oy, Or, . . . Ove , so that 
aN 
7 8 9 10..--... oO 
Fie, 2. 
to an observer stationed at O all these series would seem to coalesce into one. In 
virtue of equation (4) the same geometrical property holds good, if we consider wave- 
lengths instead of wave-frequencies. 
From the above theorem we deduce at once the following corollary : 
If we fix upon a straight line, on any arbitrary scale, the lines of a given series in 
such a way that the distances between two lines express the differences of the 
corresponding wave lengths or frequencies, and if from any point outside we draw 
‘Straight paths through these spectral lines, then the lines of any other series belonging 
to the same u-group can be represented as the points of intersection of these straight 
paths with a certain transversal line. 
An illustration of this geometrical relation is given in fig. 2 for some series 
