348 Mr. Woolhouse on the Deposit of Submarine Cables. 
we have 
24008 0 _ 1 4 (cos 0) —bn sin? w+ )(m—n eos.) £08 0, 
; a 5 =9£(Tsina) —g' + bnsinwcosw + b'(m—ncose@)sine; 
or, after transposing and dividing by 9’, 
! 
0= Be (T—a) cos w} —e sin? w+ (2 cos ») cos w 
ds b\n 
d b! fm (1) 
0= ai (t—4) sin@} —1+esin wcose +Fe (—cosm ) sino 
Multiply these respectively by cos, sinw, and add; and next 
multiply them by sin @, cos, and subtract ; then 
ge f & ) 
7, = Sinw— 7 el — — cos w 
ds b (2) 
dw : 
(T—a) Js = 8 Oe SIN @ 
The latter of these equations gives 
T—a=p(cosw—esinw); .... + (3) 
and at the lowest point where a=0, T)>—a=py. 
From the equations (2) we also obtain 
sin @— F e(™ — cose ) 
a eds Pant wen 
T—a_ cos @—e sin w 
To integrate this equation, put e=cotd; then 2 is evidently the 
limiting angle or maximum value of @, and 
sin (A—@) 
sna 
sin w= sin A. cos (\—@) — cos \ sin (A—@), 
cos w= cosdcos (A—o) + sin Asin (A—@). 
Substituting these values in (4) and integrating, remembering 
that T—a=p, when w=0, we get 
shar. sin? A log ——_—_——- BU AL 6) So iis aint aL 
Po sin (A—@) 
b! sin X 
+544 
cos a—esinwo= " 
log 
“cg za 9, mM. __tangr } 
cosAsin Nlog SANE o) +qsin?r a Alog taniQ. —a 
b! ) sin X b! m tan 1X 
=! 2 _ 2 xr ee —__2 _. 
(sin A+ | cos log Aa ea Pee cos A log inl al 
‘ 1 
—wcosr sind 1-5). dew nog 2a oll ote hotel qteng, GUS Mana 
