490 
PHYSICS: H. S. UHLER 
strictly constant for either the a or the 5 series of the X 5165 carbon band. 
In the case of the a series the phase increases from about 0.263 to 0.268 
at least, while for the b series it decreases from 0.250 to 0.235 or less. 
The values of c used by Thiele were 0.266 and 0.2445 for the a and 5 
series respectively. 
The fact that the variations of the phase are real and not fictitious 
may be established by the following considerations. Each of the seven 
lines +36 to +42 would have to be displaced in the same direction, 
relatively to the corresponding group of lines ( — 37 to — 43), by 0.104 A 
to change the value of c from 0.2686 to 0.2629. This shift is too great 
to be admitted, for, the arithmetical sum of all the fourteen residuals 
(Xcaic. — Xobs.) divided by 14 only equals 0.007 A. In Hke manner, for 
the 5 series, the average residual is 0.016 A whereas the displacement 
SERIES 
+ BRANCH . n . 
— BRANCH 
. n'. 
c 
X INTERVAL 
+ 3,. 
•+ 9 
- 3,... 
- 9 
0.2632 
I 5164.4-5153.4 
+ 3,. 
•+ 9 
- 4, . . . 
-10 
0.2633 
+ 9,. 
. + 16 
- 9,... 
-16 
0.2626 
1 5155.7-5129.8 
+ 9,. 
. + 16 
-10,... 
-17 
0.2625 
+20,. 
.+26 
-20,... 
/-27 
0.2666 
5116.0-5075.5 
+36,. 
.+42 
-36,... 
-42 
0.2684 
1 5008.0-4944.9 
or 
+36,. 
.+42 
-37,... 
,-43 
0.2686 
5 
+ 8,. 
. + 18 
- 8,... 
,-18 
0.2499 
5156.3-5119.4 
5 
+23,. 
.+29 
-23,... 
-29 
0.2417 
5095.4-5052.8 
8 . . . 
+35,. 
..+41 
-35,... 
,-41 
0.2375 
5009.6-4951.6 
5 
+52,. 
. ,+60 
-52,... 
,-60 
0.2344 
4843.2-4746.6 
required to change c from 0.2344 to 0.2499 would be 0.355 A. By apply- 
ing the same method and tests to the two apparent series of doublets 
which start at the first head of the X3883 cyanogen band I have been 
able to show that these series cannot be combined as the positive and 
negative branches of a single Theile series with a constant phase. 
In conclusion, it may not be superfluous to remark that equation (2) 
is unsatisfactory in two respects: (a) as an interpolation formula it is 
too complicated, since modern wave-lengths require the retention of 
at least eight parameters, and {h) it predicts tails much too far away 
from the heads and in a region of the ultra-violet where no tails have 
been found experimentally. For additional details and comments 
reference must be made to the Astrophysical Journal in which the present 
paper will be presented in full. 
