254 Proceedings of the Eoyal Society of Edinburgh. [Sess. 
corresponding to parabolic orbits. The following table gives the values 
of R and S for assigned values of 0. 
e. 
R. 
5. 
28 
4-5568 
-19701 
29 
4-6000 
-22001 
30 
4-6515 
-25512 
31 
4-7094 
-30822 
32 
4-7605 
-32059 
33 
4-8208 
-37936 
34 
4-8900 
•39861 
35 
4-9540 
•40890 
36 
5-0275 
•43500 
37 
5-1020 
•46341 
38 
5-1820 1 
•49339 
39 
5-2674 
•52645 
40 
5 3560 
•55901 
41 
5-4570 
•58670 
42 
5-5668 
•63469 
43 
5-6655 
•68701 
44 
5-7824 
•76310 
It is obvious that, on account of the large variation possible in S which 
is represented by a rational fraction between 0 and 1, a large number of 
lines will arise. We confine ourselves to eight simple values of S obtained 
by interpolation, together with the appropriate value of R^^ and the 
proper sequence for . 
S. 
R32. 
1 
1-2998 
^1 = 1,2, 3 . . . 
1 
•53040 
= ] , 2, 3 . . . 
1 
4 
•29025 
= 1, 2, 3 . . . 
1 
•18250 
1, 2, 3 . . . 
2-5009 
?ij = 2, 4, 6, 8 . . . 
3 
4 
3-2418 
7q = 3, 6, 9, 12 . . . 
2 
5 
•78370 
7^^-2, 4, 6, 8 . . . 
3, 
5 
1-9757 
n ^ = 3 , 6, 9, 12 . . . 
A value of 1/A is obtainable from the subtraction of a value of 
NR'^'7%'^ from a value of where the values of and 
are different if the S’s are the same, and where n-^ may equal n^' or be 
different from if the S’s are different. We shall use the notation 
(n^, ^ 2 ) — (%', n^) to denote the values of n taken to obtain the wave- 
length which corresponds; e.g. (6, 12) — (4, 2) indicates that n^ = 6 is taken 
in the set for S given by 
— i ’ ^^d that the corresponding value for 
