406 



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



The mean of the two first separations is 1777'90 or exact i/, and we have an exact 

 parallel inequality. The inequality is due to two successive \%S displacements, and 

 37159 is exactly 2%& extra on the calculated 37174, or 76^ from the first satellite. 



The first two orders of the two groups are represented in the following scheme in 

 which the satellite separations are given as sequent displacements from d u : 



The 79A 2 group. The 70A 2 group. 



m = 1. 



[19623-05] (2)21400-95 (2)22210-48 [16013-45] (1)17791-35 



195fS 



(8) 18607 



485 



47f8 

 (1)19989-72 (6/021769-99 



29f8 

 (1) 20581-64 



(1)38120-37 (1)39907-58 (1) 40717'94 



[17725-39] (3) 19503-29 



122^8 

 148 (1)20305-60 



= 2. 



(1) 38199-58 



44J8 



(1)38217-68 (3}28548-26.e.M 



288 288 



(10) 38366-36 



463 



(1) 37159-39 

 199|8 



(In) 37166-43 

 1978 



38940-81 



198^8 



39754-48 

 198J8 



(2)37606-15 (1)39386-98 

 123J8 122|8 



14<5 (1)38285-86 



Without dealing with the whole of the material at disposal we will illustrate its 

 application by considering in more detail the portion of the spectrum given on p. 382 

 in which the majority of the lines undoubtedly belong to D (l) systems. It is to be 

 noticed that the effectiveness of the method in the present case depends on the facts, 

 (l) that the observation errors do not exceed d\ = '05, and (2) that with m = 1 it is 

 consequently possible to determine the values of the mantissse to within 6 units in 

 the sixth significant figures, whilst a displacement of one oun in the sequent produces 

 a change in X of the order 1'2, or twenty-four times the maximum observation error. 

 The limit 51025 being supposed displaced by y^ becomes 51025'29 10'62?/ + The 

 mantissse of the sequences are then calculated with this limit, and expressed in terms 

 of A 2 , $ t , x and p where A 2 = 10998'2 + x, and p is the ratio of the observation error 

 to the maximum (d\ = '05). The series more fully discussed above is definitely taken 

 as depending on the limit y 0. In other words the mantissa of 19989 is exactly 80A 2 

 which condition requires, writing q for its p, 



3'2 + 30'29-6g + 80a; = 0, 



and gives a relation between and x. The term in x in each mantissa is then 

 eliminated by means of it. There can be little doubt about the allocation of 19889, 



