THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 577 
The remaining computations are now simple. We have 
1 1 _ as ae 
v—v, 1809174 (4195)? — (21952? 
1 a 1 fs a, Li 
y, Vv, 21590°61 (6-195)? — (2195)? 
and hence 
log a, = 6'26686 — 10 
log b, = 561075 — 10. 
But from (5) and (2) we find 
b= 5 A, 
1 bg” 1 Ay 
(04) — A = 
Vo — Vz A,” Vy —Vz (2°195)? 
+ bs. 
And finally from these relations : 
log a, = 4°95464 — 10; log 6, =4°41367, -10; ve=41464'9. 
These constants differ slightly from those previously computed under the assump- 
tion that x + =2°200, but they represent the observations almost equally well. 
It may be remarked that the relation (e) can also be derived from a well-known 
geometrical theorem. If, in fig. 1, we take any four points a,, #,, 4, and a, on the 
line AB and the four corresponding points ¢,, ¢,, ¢, and ¢, on the transversal CD , so 
that w, and c, lie on the same ray Ov,, a, and c, on the ray Ov,, etc., then we know 
from geometry that 
Cilig Cy Cl 
Qa, Wy CC, CyCy 
But we remember that a,a,=(y+m)’—(x+ m)? and c,c,=v,—v, etc., so that 
Vamavz io as = (y+ bm)? — (x ar p)? ‘ (w ats p)? (z ae p.)? 
Vs—Ve Vovy (2th) —(etp)? (wtp)?—-ytp)? 
(2 - x)(w -y) : (Vy — Vz) (Vy — Vz) = (2+ yt 2pu)(z2+ wt Qu) 
(y ea x)(w 7" 2) (v, = Vz) (Vi) — vy) (x te ts 2u)(y aT 2m) ; 
which is identical with (e). 
or 
B. Banp-SpPEcTRA. 
The fact that the Rypperc-THIELE equation represents both line- and band-series is 
perhaps most strikingly demonstrated by the following computations where the wave- 
lengths of the lines of the Cyanogen-band (see Kaysur, Handbuch, vol. ii. p. 479) 
are used for determining the wave-lengths of the first triplet series of Oxygen given 
on p. 564. If in equation (8) 
yeu ei 
we take for / successively the wave-lengths of the 40th, 50th, etc., line of the Cyanogen- 
band, /, being the wave-length for the 100th line for instance, and if we further make 
log a, = 960800 — 10 
log B, = 7°63969, — 10, 
