THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. 579 
find that the Rypserc-TuizLE formula satisfies the observations well within their 
mean errors, the agreement being on the whole even closer than in Professor 
THIELE'S computations. I have carried out the necessary computations for ten 
“series, viz., for the five pairs a, 8B, y+, J+, and e+, but will present here, for 
the sake of brevity, only the results of the first two pairs. Since Professor THIELE 
employed wave-lengths in his calculations, I follow his example and use the second of 
equations (6) : | 
ae) a, " a, 1 
Myr — Gm+pype te Gmapy? + Xe 
Series : log a, A de 
a+ 0:87883 516510 2241°1 
a— 0°88016 5165710 2188°5 
B+ 0°87840 5165°18 2271°6 
B- 0°87973 5165°18 2219-0 
In the following comparisons I give now the results for every fifth line of the series : 
at; (m+p) d obs. Acomp.  O.-C. a—; (m+) X obs. A comp. | O.-C. 
5:0 5161°77 81 — 04 4:5 5162°41 43 — ‘02 
10:0 5151°87 "94 = 07/ 9°5 5153:21 ‘26 — ‘05 
15:0 5135°63 66 — 03 14:5 5137:°62 65 — 03 
20:0 511317 ‘17 ‘00 19°5 5115°84 "82 +02 
25:0 508480 76 | +:04 24°5 5088°11 ‘05 +06 
30:0 5050°86 79) || —- 07 29:5 5054:73 68 +05 
35:0 5011°66 67 - 01 34:5 5016°12 “10 +02 
40:0 4967°84 87 — 03 39°5 4972°78 ‘78 -00 
45°5 491516 20 — 04 
B+; (m+p,) Xd obs. A comp. | O.-C. B-; (m+) d obs. Acomp.| O.-C. 
5:0 5161°95 88 +07 4°5 5162-60 51 +:09 
10:0 5151:97 2-01 —-04 9°5 5153-32 °32 ‘00 
15:0 5135-70 “71 =-O} 14°5 5137-72 fl +01 
20:0 5113°17 Ol — ‘04 19°5 5115°84 *86 = 02 
25:0 5084-80 ‘78 +:02 24°5 5088:11 07 | +:04 
30°0 5050-86 “81 +05 29°5 5054°73 69 | +:°04 
35°0 5011°66 69 — 03 34:5 5016:12 at, 00 
40-0 4967°84 ‘92 —-08 39:5 4972°78 “81 — 03 
We notice that all the four series possess “tails,” a result which has already been 
obtained by Professor Time. Geometrically speaking, this means that the transversal 
representing the series is not parallel to the ray Ove, but intersects this line at a certain 
point. We shall see that this is a general feature of the band-series. 
