Mr. Woolhouse on the Deposit of Submarine Cables. 349 
Again, substituting the value of T—a given by (3), we get 
log = = {2- (- = cos? } log = 
© sin(\A—@) 
- = +r 
— = cos d log al -(a- Py wcos sind, . (6) 
which is an equation of Ee cable curve, determining the propor- 
tionate radius of curvature in terms of the angle . 
Also since 
c= ? da, 2= , te COS @, v= (Paw sin w, 
these are functions of alone; and the constant p,, on which 
the absolute eae depend, may be found by comparing a 
calculated value of with the known depth of the sea. 
0 
By integrating the first of equations (2) we have likewise the 
following relation, 
b! (m 
T—a=pyty—5e(“s—2). te a a | 
The foregoing equations, which are general, become much 
simplified if we assume, as Mr, Airy has done, that b’/=d and 
m=n. Thus if we put 
tantXr —cosr 
14 eats) at 5 eee tL () 
the values of which are evidently comprised between 0 and 1, 
equation (5) gives 
T—a sin X 
fieae 5 ~ sin (A—a)’ apenas Big ar antaslly @ oad ae (9) 
and equation (7) becomes 
T—a=pot+y—e(s—z). . . »- » « (10) 
Equations (1) also become 
= £ ((t—a) cos @} —e(1— cosa), 
0= oe (T—a) sino} —1+esino, 
and, by immediate integration, give 
(T—a) cosw=p,+ e(s—2) 
(T—a) sin o=s—ey he Ph MF? (11) 
