44 
Proceedings of Eoyal Society of Edinburgh. [jan. 7, 
The interpretation of this is eased by putting it into the form 
<£ = 
V 9 
where 
/t> 
OJ 2 \ /w 2 
cos | — x - cot — ej - ix cos [ — x + 1 d-j 
9 
9 
)}. (31). 
Q = { \jay (if £ _ o,y?) + caff £)J 
faff S" Vf) + *° ,, (Vf)J}’ (32); 
e = tan 
.“KVfc-ys-KV:-) 
4 
“*(%/: i - Vi) + “K'V; J) 
E = J ffft + Vy) - eay W f)l 
+ [ sa ff r, +M f }) - sa ff ff } ’ 
(33); 
(34); 
and 
/= tan 
cay{t f + w ff)~ sa v(o \f) 
(35). 
my (* fh + “ f 'f) ~ Cay ( m f 
Now, remembering that cay (oo ) = say (so ) = \ / g , we see that if 
^ \/ X - is large, and tsj ^ w f * s ^ ar o e positive, we have 
9 
and therefore 
R= 0 , Q= fn, e =0 . . 
/ 2 tt /a fix \ 
(b^sj — cos I <ot J . . , 
v * V 9 V 9 J 
whence, and by (25) with b = 0, 
. 1 • [w 2 x \ 1 / g . 
; ‘ 9 V 9 L \ 9 / «> V 2wa J 
or, since o> J (x/g) is very large, 
f . io /' 2 tt . /m^x \ 
^-yv7 3,n (v w V • • • 
(36) ; 
(37) 
(38) ; 
(39). 
