196 
ME. AETHUE SCHUSTEE ON THE 
Values of /x/. (Velocity Potential = i p 2 2 -) 
n = 
i 
3 
5 
cr = 1 
1 3 
105 7 
29 ,. a 
12 x360 / 
1 3 
— V 
630 ' 
The determination of S is only of interest as a stepping stone to the evaluation 
of R. We must therefore return to the first of equations (14), and by its means 
determine dH/dX as a series of harmonics in the normal form. 
If we write the velocity potential xfj m T sin (rX —a), we find by means of the formulae 
of transformation previously introduced 
p cos 6 ft = (y-T+C^. + Ot + r)^,-. ( ) 
r dx V ’ 
+ -j (m— t+ 1) 
+ (m-j-r) 
(m — T + 2) \fj T m+2 + (ni + T + 1 ) ip m T 
(2m + 1) (2m + 3) 
(m-r) \jj m T + (m + t— 1) xp T m _ i 
(2m— 1) (2m+l) 
y'r cos (rX — a) 
+ 
(m—r+ 1) 
(*W +1 -lAW 1 ) 
2 (2m +1) (2m + 3) 
+ (m + T) ^ -.1 yr cos {(r+ l)X—a} 
v 7 2. (2m-l)(2m+l)j Y 1V 7 J 
I \(m T , 1 \ (^ + r )( w + T+l)^„;~ 1 -(m-T + 2)(m-r + 3)i// m+2 T ~ 1 
IP ' 2 (2m +1) (2m+ 3) 
■ , _ (m + r-1) (m + T-2)t// m _ 2 T “ 1 -(m-T)(m^T+l)t// n r 1 ] 
+ ( + ' 2.(2m-l)(2m+l) J 
yr cos {(r—1) X —a} . . (37 6fs). 
As, omitting constant factors, xp/ is equal to Q/, the tesseral function of type a and 
degree n, we may now write 
P cos 0 ^ = tfnQn t 
and tabulate those values of f n a which are not equal to zero. The following table is 
constructed in this way. 
