370 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
all but the last gave sets, but only by admitting values of links so abnormal that they 
were not counted in the general list. Also in the AuY linkage the sets beginning at 
17788, 28152 were found to exist. They are reproduced here :— 
1. 26236 17260-76 43497 
3830-99 30067 46Q1'44 34669 5636-00 40305 3192'35 
2. 25387 17256-97 42644 
5640-57 31028 4808-31 35634 3821'55 39456 3188'54 
3. 20776 17262-04 38038 
3189-54 23966 3817-32 27783 5647'31 33431 4607-51 
4. 23805 17258-49 41064 
3195-78 27001 3822-33 30823 5618-55 36442 462P83 
3810-21 27615 4804-05 32219 3194-83 35414 5640-40 
5. 24592 17263-13 41855 
3191-06 27783 5647-81 33431 4607'51 38038 3816-78 
6. 27783 17260-17 45043 
5647-81 33431 4607-51 38038 3816'78 41855 3188-07 
7. 30109 17252-89 47361 
3194-84 33303 582P20 38924 4598'98 43523 3838 
8. 17788 17256-26 35045 
3813- 90 21601 4608-08 26209 5839-11 31848 3196'09 
9(a). 28152 17260-49 45412 
3815-65 31967 4810-61 36578 5637-59 42216 3196’67 
9 (b). 28155 17257-32 45412 
3814- 60 31970 4608-46 36578 5637'59 42216 3196'67 
An examination of the above shows that, with the exception of Nos. 8 and 9 from 
AuY, all contain very abnormal links. It is noticeable also that in all except 3 and 4 
the links occur in cyclic order backwards or forwards of a, b, c, d, viz.: (l) b, c, d> a ; 
(2) d , c, b, a; (5) a, d, c, b ; (6) d, c, b, a ; (7) a, d, c, b ; (8) b, c,d,a ; (9) b;c, d, a ; 
whilst in (3) the order is a, b, d, c, and in (4) a, b, d, c, or b, c, a, d. In (l) 30067 
has no link in the general list. In (2) 39456 has not been attached to any linkage 
and the other two belong to the X and Y linkages. In (3) all are included in the 
S(3). No. (4) shows two possible sets both contravening the cyclic rule. If the 
links shown are real displaced links the two sets form a complete cycle like that in 
fig. e of Plate 6. But 36442 belongs to the Y linkage, whilst in the second the three 
intermediate lines belong to other linkages. It is probable, therefore, that both sets in 
No. 4 are spurious. Nos. 3, 5 and 6 have portions in common. In (7) the last two 
intermediate belong to the X and Y linkages. The set is therefore probably spurious. 
Nos. 8 and 9 show all good links whilst 9 shows that two clinks are possible but 31970 
