412 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. * 
for these groups until the whole system of D and F series is placed on a secure and 
comprehensive foundation. The above notation, therefore, is only to be regarded as 
one which in this communication serves to identify certain of those groups here more 
specially discussed. 
The material was treated by the same method as in Kr, and search made for the 
above separations in the region where F ( 2 ) lines should be expected. From the lines 
thus obtained the actual F lines were sought for, bearing in mind the large sequence 
displacements so common in the low orders. In only three cases—those for F 2 , 3 , g— 
were suitable undisplaced lines found for m = 2 , and of these only Fg, Fg gave 
observed lines for m = S. 
They were- 
—separations from Fg— 
m. Fg. 
F 3 . 
Fo. 
2. ( 8 ) 18812-55 
432-46 
( 8 ) 18380-09 619-82 
(1) 18192-73 
3. (1) 24253-30 
432-49 
(<1) 23820-81 
5. (2) 28108-52 
432-00 
(1) 127676-52 
For m = 4, Fg showed no undisplaced line, but in good position for m = 5 there were 
lines for Fg, Fg. From the three lines for Fg the following formula was found 
J, 
30740T7+ ^-N/|m +-986181-622^^- 
•014730-1003^ 1^ 
m J 
We can at once apply two tests to this as to fulfilling the conditions for F series. 
The limit 30740 must be a d-sequent, i.e., must differ by oun multiple displacement 
from some other known d-sequent, and the first ^-sequent must depend directly on a 
multiple of A^. We already have a very accurate d-sequent found as the limit of the 
1864 series, viz., 30725'30 + f'. On this a displacement produces a change of 4-97 
so that — 3^1 produces 30725-30 + ^' + 3 x 4-97 = 30740-21+ and this condition is 
accurately satisfied by fi = f^+'04 where belongs to the present case. For the 
second test the mantissa of ^{ 2 ) is 
978816-I2Ifi = 89 (10997-93-l-36fi) = 89 (A2--27--36fi-.'r) 
which again is seen to satisfy the test exactly. The satisfaction of these two conditions 
must give full confidence as to the correctness of the allocation of the Fg lines. 
From this formula lines were calciilated from w = 4 to 27 and the other sets 
allocated by their corresponding separations. They are not reproduced here, however, 
beyond m = 15, partly because they are only of importance in a systematic 
arrangement of the X spectrum, and partly because the lines to be identified are 
so close that it becomes a matter of extreme difficulty to allocate them correctly. For 
instance, the calculated values of Fg (14) and Fj (15) are 30064-38 and 64-16; of 
F 4 (l 2 )and Fg(l6) are 30360-47 and 60-29 with many other examples. With the 
high orders successive lines become close, and with the large number of separate 
series involved the observed spectrum should he expected to be crowded, as indeed 
in this region it is. 
