DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 379 



Hence 



343-z-'161'+'161dn '002 = 0, 



'098-r-'580' + '086p '002 = 0. 

 Therefore 



' = -58-'38dn+'20p '009-1 



f A. 

 '222dn-'032p'003J 



x = 



Here dn depends on an extrapolated value from a D 3 line, taken because the v 2 

 showed a diminished value corresponding to the usual satellite modification of v,. If 

 this is correct dn is the observation error on 21858 and is '14p with d\ = '03. This 

 is certainly the most a priori probable supposition. If on the contrary hypothesis i>, is 

 normal D n is 21552'65 + '14p-786'45 = 20766'20 and dn = 2'95 + '14p. This gives 



= _170 -'05p+'20jp''009, 

 x= r091 + "03p *03p'"003. 



Taking now the case of D 18 = 19116 we have already seen that a change of y$i on 

 the limit, or 2y^ is the sequent produce the same change, so that (yS^ D 18 (2yS t ) is the 

 same as D 18 , and the D qualification test remains unchanged, although the mantissa is 

 altered by 2y^ = 174%. 



Supposing this displacement to take place the mantissa of D 18 is 



835908 + 124%-28'21+3p '5 = 197 {4243'188 + '6330^-'143 + '015p 8 '002}. 



Here again, as in the case of D 15 , the question arises whether the value of the 

 normal sequent be taken as that of D 18 or D L , 8 which latter is S t = 62 '4 larger. 

 The condition then for the exact multiple of A' 2 is 



= 0. 

 The two cases give 



= -58, I'505 + '63302/-'020p 5 +"03p'+'015p 8 (or+ '316) = Ol 

 '6330?/-'03 jo 5 + -03p'+'0l5j> 8 (or + '316) = ol 



Neither can be easily satisfied with d 16 , but with d K the conditions can be satisfied 

 with y 2 = 3, 2, for the two cases respectively.* 



The remainders in the two cases are '077 for = '58 and +'113 for = 170. 

 The list of F lines also give the following which can be used as tests. 



(1) (6) 17747'14 = F! (2) (10A,), i.e.,/(2) mantissa = 195 A a , 



(2) (5)17594'17 = F! (2) (7 A' 2 ), 



(3) (2) 1797278 = F, (2) (16A' 2 + A 2 ). 



* See, however, final order below. 



