354 Mr. Woolhouse on the Deposit of Submarine Cables. 
But 
m \3 m = 
(= cos @ } se 1 —a 
SS = cos o— (2) +2, 
COS @— a 
cos 0+ 
Guyeners | 
Bl i‘ et 
SS SS dw i eas a RE 
B lt+e £08 += 
which, finally integrated and corrected so as to make Tp —a=py 
when w=0, gives 
im ow a l—@ ae la. acosw+1 
ow, ay a ieee lta. cos @—a 
2 
Ff ot «(7 -«) l—acosw+sina V1—a? 
-> ] 
B cea w gre anata 
mn 2 
m4 +1) 
i ¢ jane (6) 
(1+ a?) V1—a2 acos@+]1 
If the value of T—a by (3) be substituted, we shall obtain an 
equation of the curve exhibiting the radius of curvature at any 
point as a function of w. 
To adapt the expressions to numerical calculation, assume 
2=tan2u, cosk=tanu, cosw=tand; . . (7) 
then 
2 =2 cosec 2 4 =2 cot 2 beats 2 
5 ee COSEC Kp, a as FB; Lic Bb; 
and ceili a! Le 
Dg aN 
Therefore 
