350 Mr. Woolhouse on the Deposit of Submarine Cables. 
The first of these and (10) give 
(T—a)(1+ cos o@)=2p94+-y Ep) 
(T—a)(1—cos o) =y—2e(s—z) 
And from (9), (11) we deduce 
T—a sn(A—o) T—a ; 
z= —__ -__+_—_ = ——_ (cos w—e SIN @) 
Po sin » Po 
=i-e= +e is 
Po Po 
The coordinates and length of the curve, as compared with po, 
the radius of eurvature at the lowest point, are hence determined 
by the simple formule 
tan } (Xo) = tan $2. 244, ] 
T—a_ sind i 
Po  sin(A—@)"”” 
ori fa 
“oa Bs (1 + cos w) 2; ws lale uae (13) 
a 53a ore. 
Po = Po 4 
Saab eed = sin @: 
Po Po Po 
The Tables given by the Astronomer Royal can be constructed 
with the greatest possible facility from these formule; and if 
the first of them be replaced by equation (8), the calculations 
may be performed for given values of w. 
For any integral value of e, up to 10, the constants may be 
taken from the following Table :— 
e. r. cos X. secd. |logtan}d.| logsina. 
° i 
1] 45 0-0 | 0-70711 | 1:41420 | 9-61722 | 9°84949 
2) 26 33:9 0°89444 1-11802 937303 9:65052 
3 | 18 26:1 0:94868 105410 9:21026 9:50000 
4 | 14°22 0:97015 1:03077 9-09027 9:38478 
5 | 11 186 0:98057 101981 8:99572 9°-29251 
6 9 27:7 0:98639 1:01379 891783 921590 
7 8 78 0-98994 1:01016 8°85167 9°15051 
“2 te Ay A} 0:99227 1:00779 8-79419 9-09354 
9 6 20°4 099389 1:00614 874340 9°04309 
10 5 426 | 099504 | 1-:00499 | 869789 | 8-99784 
At any time during the actual operation of laying the cable; 
it is evident that the ship’s velocity, the depth of the sea, and 
the tension and inclination of the cable at the ship, can be ascer- 
tained by observation. With deep water the inclination will 
