163 
//YOX-plane. All the series with asymptotes P,S,D, then get into 
the plane z—1, those with asymptotes P,, D, ete. in the plane 
z= 2. etc. 
By means of this plate we can now easily demonstrate, how the 
whole system may be built up, when only some spectral lines are 
known. 
Let us suppose e.g. that 3 lines of the P series with S, asymptote 
S, P, or Principal series have been observed, then the curve Y= Sitter 
can be drawn in the YO X-plane and the curve Y = P, in the YOZ 
plane. The latter yields for z= 1 the asymptotes P,, P,, P,, which 
may be drawn in the YOX-plane. S, and P, being known, the S 
series with P, asymptote (P, S, or 2°¢ subordinate series) is given 
for the greater part (i.e. without the rotation). If one more line is 
known of this series, the curve Y= P, S, is perfectly determined, 
and so also the curve Y= P, S,; and Y= P,S,. If we now draw 
the curve Y =S, in the YOZplane, the former yields at once the 
asymptotes S, , S, etc. 
_ If one line is known of a Diffuse series, e.g. that with P, asymp- 
tote (P, D, or 1% subordinate series), then the curve Y= P, D, 
may be drawn in its main features (so without rotation), and it is 
perfectly determined by a second line. So all the D series are known, 
and all the D asymptotes may be found by drawing the curve 
Y =D. in the YOZplane. Now all the asymptotes of the Funda- 
mental series are known, so they may all be drawn without it being 
necessary that one knows one line of it by observation. So the whole 
system of series is known through six lines, provided only one com- 
ponent be used, as has been expressly stated. We draw attention to 
the fact, that this is possible only by the idea of unity, by which 
we are guided: | | 
For all the series the eurve by which they may be denoted in 
the indicated way, is the same. 
Besides the easy survey of the whole system of series and the 
well-arranged whole, which we owe to this way of considering 
the matter, our plate can teach us several things more. 
It shows us in what region there are still lines wanting in the 
‚spectrum, and where endeavours to find new lines have a great 
chance of success. 
Reversely, if new lines have been found from the experiments 
in a certain spectral region we can by marking their frequencies 
on the Y-axis and by drawing lines //X-axis, determine the points 
of intersection of these lines and the traced curves, and see which 
of these points of intersection then coincide with the linesz=1.2.8., 
