ARCTIC SEAS.— PART YII. PORT KENNEDY. 
cos (m — c) =cos ( v — n) X 
sin (to' — c) = 0‘886 sin ( v — n ) X 
1 + 0U08 sin 2 (y—n) 
+ 0'017 sin 4 (y—n) 
+&c. 
1 + 0'108 sin 2 (y — n) 
+ 0'017 sin 4 (y—n) 
+&c 
From these equations we have, remembering that 
71=247° 
cos (to' — c) = — 0'42 cost; — 0 - 99 sinT;+&c. 
sin (to' — c) = ~h 0‘85 cost; — 0 '36 sinT;+&c. 
We now have — 
COS ( TO — s — i m ) = cos (s' — to' — i m ) 
=cos{(— to'+c) + (— c-}-.s'— i n4 )} 
=cos (— to'+c+</>) 
where <£= — 
Expanding and substituting from (29) we find 
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[ 28 ) 
cos (to — s — i m ) 
{— 0'42 cos 0’85 sin <f)}eosv 
+ { — 0‘99 cos <£— 0’.36 sin </>} sin v 
In like manner we have 
sm ( ?n—s—i m ) = 
{ — 0‘85 cos (f>— 0'42 sin </>} cos v 
+ { +0'36 cos <f>— 0’99 sin <^»} sin v 
(30) 
(31) 
Substituting in (30) and (31), for v, its value v=nt-\-2e sin nt (25), 
we obtain, writing 
A= — 0‘42 cos 0'85 sin <£' 
B= — 0'99 cos <£— 0‘36 sin <f>, 
cos ( m—s—i r ) — 
— Ae+Acos nt-\-Ae cos 2nt-\-kc. 
+ B sin nt + Be sin 2nt + &c. 
where 
MDCCCLXXVIII. 
sin (to — s—i m ) — 
-A'e+A' cos nt-\- Ae cos 2nt-{-kc. 
+B' sin nt-\-B'e sin 2nt-\-kc. 
A'= — 0 85 cos </>— 0*42 sin <f> 
B'= +0-36 cos <£— 0-99 sin <f> 
(32) 
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