DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
379 
Hence 
Therefore 
•343-cc-T6I^'+T61c?w ±-002 = 0, 
•U98-x---580^'+-086p ±-002 = 0. 
= —'5S — '38d7i+'20p ±-0091 
X = -436 ±-222c?n--032^0+- 003 / 
Here dn depends on an extrapolated value from a Dg line, taken because the v.^ 
showed a diminished value corresponding to the usual satellite modification of If 
this is correct d^i is the observation error on 21858 and is 'Idjo with d\ = ±-03. This 
is certainly the most d p7'io7'i probable supposition. If on the contrary hypothesis is 
normal is 21552-65 +-14^-786-45 = 20766-20 and dii = 2-95 +-14p. This gives 
f= — 1-70 —-05p,+-20^'±-009, 
x= 1-091 +-03p — -03jo'+-003. 
Taking now the case of D,8 = 19116 we have already seen that a change of on 
the limit, or is the sequent produce the same change, so that [y^^] Hja (2y^]) is the 
same as Djg, and the D qualification test remains unchanged, although the mantissa is 
altered by 2y^-^ = 174-8y. 
Supposing this displacement to take place the mantissa of Dig is 
835908 + 124-82/-28-21^+3p±-5 = 197 {4243-188 + -6330^--143^+-015j98±-002}. 
Here again, as in the case of Djg, the question arises whether the value of the 
normal sequent be taken as that of Djg or D^g which latter is (li= 62-4 larger. 
The condition then for the exact multiple of A'g is 
1-802 +-633^--907x--143^+-015^8 (or + 62-4/197) = 0. 
The two cases give 
$ = — '58, 1-505 + -63302/—-020p5+-03p'+-015jO8 (or+-316) = O') 
^ = -170, l-063 + -6330y--03 p5±’03/+-015y)8 (or+-316) = oi 
Neither can be easily satisfied with djg, but with dgg the conditions can be satisfied 
with ^2 = —3, —2, for the two cases respectively.* 
The remainders in the two cases are —-077 for ^ = — '58 and +-113 for ^ = —r70. 
The list of F lines also give the following which can be used as tests. 
( 1 ) (6) 17747-14 = Fj ( 2 ) (lOAg), i.e.,f{2) mantissa = 195 Ag, 
(2) (5) 17594-17 = F^ (2) (7A'g), 
(3) (2) 1797278 = F, (2) (lOA'g + Ag). 
* See, however, final oi'der below. 
