THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 559 
A scarcely less convincing test of the superiority of the RypBrrG-THIELE equation 
is afforded by the discussion of another empirical law which we owe to Rypsere. This 
law may be expressed as follows: (see Kaysmr, H.d./S., p. 557). The wave-frequency 
of the first line of the principal series is equal to the difference of the wave-frequencies 
of the tails of the principal and subsidiary series. It must be remarked, however, that 
if we take the first components [7.e. those of greater wave-lengths] of the subsidiary 
series, the law refers to the second components [shorter wave-lengths] of the principal 
series. Here are the figures corresponding to the two formule : 
KR. k _— Comp. 
Ry-Th. Ones Obs. — Comp 
Ist Line of 
BS, SS, Wittens | es: Sree) erence! _ KR. Ry-Th 
Li: 43584 28627 14957 | 43498 28589 14909 14907 Sa eo 
Na: 41542 24521 17021 | 41468 24486 16982 16977 eee 
K: 35086 22006 13080 | 35030 21994 13036 13045 Bae hao8 
Rb: 33762 20919 12843 | 33755 20965 12790 12811 -~32 421 
Gs: 31509 19743 11766 | 31496 19748 11748 11726 24g S28 
From the last two columns we see that Rypperre’s law is represented in a distinctly 
better manner if the Rypperc-THIELEe formula is used. More important advantages 
of the latter will, however, appear in a subsequent part of the investigation upon 
which we can enter only after having examined the line-series of the other elements. 
Of the remaining elements of the first vertical column in MENDELEJEF’s series we 
can investigate here only Silver, of which four lines of the 1st subsidiary series are 
known. This being the minimum number of lines necessary for computing the 
constants of our equation, we must omit those series in which less than four lines 
have been observed. Doubtless in some of these cases three lines would be sutfticient, 
because we have seen already that in a considerable number of series « =0 or (m+ } 
an integer, so that our equation contains only three unknowns. But to decide whethex 
the series belongs to this special group we still require at least four data. 
6. Silver. 
lst Susstprary Serius (1st Component). 
log a, =4'96094 — 10 
« = 30646°4 
log b, = 4'15268, — 10 
(m+) v obs. vy comp. | Obs. — Comp. 
30 18275°8 18275°8 0-0 
4:0 23741:1 | 23741:1 0:0 
5:0 26242°6 26242°6 0-0 
60 27593-7 27594-0 —0°3 
TRANS. ROY. SOC. EDIN., VOL. XLI. PART III. (NO. 24) 84 
