47 Prof. T. H. Havelock. 
all values of 4; hence, under these conditions, we have on the surface ap = a, 
gue 2 = 14 Asetibg Agetib + Age 4... (27) 
where 
A; = te *—@,, 
As = je" "—4 Bie~*"—(8,— 8’), 
As = 346 —§ Bie *—1 (B2— Bi”) e- 2" — (B3—28, 82+ Bi), 
P00 Se CODDS O00 OD O0o000000000n0000000000000000000 00000000000 00N00000D0N00000 
slo memnaseseleielele\eie)s[e\e\ee{e\e]s[ele/ele(e(n\a\o10/0]e/ele/e)s1e\ele\elaleie\o.e|e[elelele|sfalelojelolele(clerelsieteleleleine aeice 
Now Stokes’ method gives z, and dz/dw, in the form of a series like (27) ; 
write this as 
cz = 1+ Cre”? + Coeto + Cyehio4 .... (28) 
From Stokes’ equations, Co, Cs, ..., are obtained as power series in C,; 
these have been carried up to the tenth order by Wilton,* whose results 
we quote now—in so far as they are needed here— 
—C, = 8, 
Co = 0+ 0-504 + 2:41708 + 1559708 + 64-0851 
—Czg = 1-508 + 158305 + 8:21507+4 55-0109, 
Cy = 2667044 434708 + 24-0108 + 166-251, 
—Cs = 520805 + 11-5374 67-4029, 
2 
~ = 147435044 19-0808 + 154°7584 1997510, (29) 
With the units adopted here, the last expression corresponds to 1/9. 
Further, in Stokes’ investigations the wave-length was taken as 27, while 
in the above work we have used 7; the result is that in comparing the two 
methods by means of (27) and (29), Cy, Co, Cs, Cy, ..., correspond respectively 
to A, $ As, 3A3, 4Ag, ejeiss 
For the numerical calculations in the case e~2¢ = #, we use the values of 
Ai, 82, and B3 given in (25); then from (27) we obtain 
A; = 0:24727 ; 4 Az = 0:06385 ; zAz3 = 0:0249; 
ZA, = 0:0115; 4A;5 = 0:0058; ...... (30) 
On the other hand, if we take 3 equal to Ai, we get from this series 
in (29) 
—C, = 0:24727; Cz = 0:06382 ; —C3 = 0:0248; 
Cz, = 00114; —C; = 00058; ...... (31) 
* J. R. Wilton, ‘Phil. Mag.,’ Ser. 6, vol. 27, p. 385 (1914), 
141 
