184 Transactions of the Boyal Society of South Africa. 
The values of the P*^ required are as follows : — 
+ 384 P4.0 = [ 9681 + 3736D + 5570^ + + DJ by,, 
- 96 r3,i ^ [10452 + 4067 +602 +40 + ] &6,i 
+ 64 P^.^ =: [11175 + 4408 +649 +42 + ] 65,1 
- 96 P^.^ = [11768 + 4751 +698 +44 + ] h^,, 
+ 384 P°.4 = [12085 + 5088 + 749 +46 + ] h^,. 
The values of D^,b,. , have been calculated with iva = 9-7547600-10, and 
the formulae given in the Monthly Notices of the Boyal Astronomical 
Society, vols. Ixix., No. 8, and Ixx., No. 2, and are as follows : — 
r. 
0 
2-1998233 
0-4997520 
1-528063 
6-214157 
34-36292 
1 
0-6558006 
0-8790111 
1-808692 
6-433653 
34-83472 
2 
0-2842813 
0-6768853 
1-919493 
7-176498 
37-23956 
3 
0-1358364 
0-4622008 
1-728920 
7-528608 
40-49590 
4 
0-0679279 
0-2999804 
1-405845 
7-228600 
42-54063 
5 
0-0348807 
0-1892447 
1-069453 
6-426559 
42-23997 
6 
0-0182250 
0-1172292 
0-776788 
5-374925 
39-58104 
7 
0-0096402 
0 0710994 
0-545466 
4-284580 
35-20792 
A general checking equation will be found in M.N.E.A.S., vol. Ixx., 
No. 2, p. 195, line 4 from foot. If therein we put m = 3, n ^ 1, and i 7 
we easily obtain — 
D3(D + 7)5,,, «(D + 1)3(D + 7)5,, ; 
or — 
(D, + 703)5,, = «(D, + IOD3 + 24D, + 22D, + 7Do)56,x, 
whence — 
65-19998 = 65-19991. 
Again, in the same general equation, put i =- — 6 ; then after expansion — 
(D, - 6D,)b,^, = «(D, - 3D3 - 15D, - 17D, - 6Do)5,„ 
whence — 
7-33149 = 7-33157. 
These two checks are more than sufficiently correct for our present 
purpose. 
In calculating the above quantities, some of the numbers involved 
were found to be as follows : — 
L I'r =9-6790830-10 
L =9-9801637-10 
L p, =9-9686574-10 
L 5,,, =^0-3423874 
L 5,,', = 7-9840858-10 
1 See M N, 
Vol. Ixix., No. 8. 
