DR. W. M. HICKS: A CRITICAL STUDY OP 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 oun. The D n line 23899 must have a 

 mantissa which is a multiple of the oun, though not necessarily of A 2 . The mantissa 

 of the F(l)= 7404 should he a multiple of A 2 . PASCHEN'S estimate for the 

 maximum error of the F(l) is lA, and KAYSER'S for the D(l) is '02 A. These 

 mantissas are, introducing the actual errors as d\ = p^ '02 p 2 



985098 + 4'06> 2 -35-66 

 764245 + I37p 1 -25'03 = 723 



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 A 2 by 1'5, whereas we already have its value as close 

 to 1057'0. The mantissa of d n is so large that by itself it is not possible to determine 

 the oun multiple. But the difference of the mantissse of d n and/ is much smaller and 

 also an oun multiple. It is 



220853- 137p 1 + 



= 209 { 1057'047 + -0190>,--0346} -5,^ + 2-1 77^, + 4'OG^,-3'G7 



Even this is too large to settle the multiple on account of the observation errors and 

 uncertainty in f 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 4A 2 G^ above that of D u . Consequently its complete mantissa is 

 209A 2 -5^ 1 (5 1 - (4A 2 -G(5 I ) = 205A, + ^ 1 <5 1 above that of /(l) or == 928A, or + <$, or 

 + 2<^. Now this is so close to the A a multiple, as to point to the fact that this satellite 

 is the fundamental one, in which the rule is a multiple of A, for the mantissa when 

 there is no relative displacement with the second or third of the triplet satellite set. 

 But here the observed i/ t is 179'92 = 179'50+'42 and '41 is the change produced by an 

 oun displacement. In other words the mantissse of the D 12 , D,o lines are either 

 M(A 2 ), M(A 2 ) + a,, or M(A,)- ( 5,, M(A 2 ). But it cannot be M(A,)-,5,. Hence if 

 the multiple law holds here it must be in the D ia satellite, the -S { must be 

 taken above, or the difference is 209A.,-6(5 1 and W4-17'7p l + 4'0<Sp,-8'69t**0. 

 This is easily satisfied by moderate values of the jo's and f Further, the mantissa of 

 23782 is 928A 2 .* 



This makes the mantissa of D n = 932A 2 -6<$,, whence 



932A 2 = 985098 



A 2 = 1057-064 + '004p 8 - '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 m = 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 d^ in place of d^. 



VOL. CCXX. - A. 3 P 



