Mr, Woolhouse on the Deposit of Submarine Cables. 855 
l—« acosw+1 tanwtan@+1__ tan?3r 
= tan?12r 
l+a coso—a tan@—tany tan (9—y)’ 
l—acosa+sneaV1—a? __1—cos(A+o) 
cos @— a ~ COS @— cosr 
2 sin? (+e) _ sn 3(A+@) 
~ 2 sind (A+o) sin} (A—o@) ~ sind(A—o)' 
Again, if sin p= sino V1 =a? then cosy= ——~ Bre ed 
acosw+] acos@ +1’ 
Bis cosy (l—a)(l—cos@) _ 21ytan?1 
tan Weapon = (Pad tenay™ 3A tan* 3. 
Hence 
T— tan? x B! = ( m, 3 
log Pa ses ett OS a (@—z) B tan X a) 
sing(A+o@) sin? sau es >> 26, y \. 
tani. 
login) =a) aa tan—! (tan 3A tand@) 
Or, if 
l—« l—« 21 ] f O° 
C= Ty gem 008 2m, “=, tm 2X, ¢s= loge x arcof 1°, 
(i-«) 
av,——oe Q 2 —_——— 
n cos* f/m 7a l—a 
—_—_- = aie > = 4/1=* tan, 
¢,= ———___— 
*(1+a2) /I—a2 tandr\n 
(144) 
An) one), 
Me= 23 1 a2) VY1—a2  *sindr RS 
then 
T—a C sin 4 (A+@) 
log rae ie log dC (Cae BF cao +c log ee es 
—eqtan=? (¢;tan 3) b (is bates mila eects oan 
in which @ is expressed in degrees, and the logarithms are now 
adapted to the system of Briggs as commonly used. 
The logarithmic values of the constants, including the angle 
py and the limiting angle 2, are given in the following Table for 
integral values of e, and supposing that m=n*, 
* When the ship is stationary, or e=0, the curve is the common cate- 
T~ 
nary, and A=90°, a=0; .*. by (6) ae 
»l—a 
= secw, and by (3 cosa; 
