DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
447 
The Value of the Oun. —The preceding results for the D and F series afford material 
for the more exact determination of the onn. The D„ line 23899 must have a 
mantissa which is a multiple of the oun, though not necessarily of A^. The mantissa 
of the F(l)=—7404 should be a multiple of Ao. Paschen’s estimate for the 
maximum error of the F(l) is lA, and Kayser’s for the D(l) is '02A. These 
mantissse are, introducing the actual errors as d\ — p^, '02 p 2 
985098 + 4-06p2-35-66^ 
764245+ 137i>i-25-03^^ = 723 {1057'047 + •0i90pi--0346^}. 
In the case of F (l), given that its mantissa is a multiple of A^, the multiple must be 
723 for 724 or 725 would alter Ag by 1‘5, whereas we already have its value as close 
to 1057'0. The mantissa of is so large that by itself it is not possible to determine 
the oun multiple. But the difference of the mantissse of andy is much smaller and 
also an oun multiple. It is 
220853-137^1+ 4-06po-10-66^^ 
= 209 {1057-047+ -0190^1--0346^}-5(ii +2-I77i9i + 4-0G^r>-3•67t< 
Even this is too large to settle the multiple on account of the observation errors and 
uncertainty in It may be an oun more or less. The following consideration, 
however, will give some indication on this point. The mantissa of the satellite 23782 
as found above was 4 A 2 —6(ii above that of D^. Consequently its complete mantissa is 
209 A 2 —5^i±(5]— ( 4 A 2 —G(ii) = 205A2 + ^i±(ii above that of y(l) or = 928A^ or or 
+ 2(ii. Now this is so close to the Aa multiple as to point to the fact that thia satellite 
is the fundamental one, in which the rule is a multiple of Ag for the mantissa when 
there is no relative displacement with the second or third of the triplet satellite set. 
But here the observed z/j is 179'92 = 179‘50 + '42 and '41 is tbe change produced by an 
oun displacement. In other words the mantissse of the D 22 lines are either 
M (Aa), M(A 2 ) + (^i, or M (Ao) —(ii, M (Aa). But it cannot be M (A 2 ) —(ij. Hence if 
the multiple law holds here it must be in the Hia satellite, the — must be 
taken above, or the difference is 209 A 2 —Gti^ and 16‘4 —I77pi + 4‘06jOa —3‘69^ = 0. 
This is easily satisfied by moderate values of the ps and Further, the mantissa of 
23782 is 928 A 2 .* 
This makes the mantissa of Du = 932 Aa— 6 ^ 1 , whence 
932 A 2 = 985098 + 6(^1 + ... = 985184-9 + 4j32-35-6G^ 
A2 = 1057-064 +-004^2-‘0382^. 
* It may be noted in passing that the satellite separation is 116'57, but is reproduced in the F series 
as 115'65 (P.) for /a = 1, 116’12 (R.) for m = 2. The latter, more reliable, is ’45 less than the corre¬ 
sponding satellite separation. This general effect is therefore completely explained by the F limit for the 
second series being (^2 ia place of 6 ^ 12 . 
3 P 
VOL. CCXX.—'A. 
