ARCTIC SEAS.— PART VII. PORT KENNEDY. 
11 
Let us now proceed to express (20) and (21) in terms of u, 
2 , 35+4 , 57 cos v-\- 0’45 cos 2v (20) 
neglecting smaller terms, and v is reckoned from Perigee, which occurred at noon, on 
1st July. 
The angle u= 0 at midnight of July 12th, and nt— 0 at Perigee at noon of July 1st. 
u= 0, at July 12 d 12 h 
nt — 0 „ 10 
Diff. ll d 12 h 
This is equivalent to 152°, since the periodic time is 27 ‘3 days. 
Hence we have 
n 140 
— 152 =273 w 
280 
2 ^= 304 °+^ 
Substituting this value in (34) and (35) we obtain 
M' cos (m— s— v) = +0'41 Msin<£ 
+M (— 0 - 35 cos^+0'29 sin<£) cos 
+ M ( — 0 - 34 cos <£— 0 - 30 sin <£) sin (38) 
M/sin (m— s— i m )= — 0‘41 Mcos <j>) 
+M (-0-30 cos <f>— 0-35 sin <£) cos (^.v) 
+ M (0-30 cos <£—0‘34 sin <f>) sin (39) 
280 
As a first approximation, 2 fg u ma y ma de equal to u, and afterwards, if neces- 
sary, the expansions (36) and (37) employed. 
Equations (17) and (18) give us 
Aj=M' cos (m — S cos 2o-cos i s 
Bj= — M' sin (m — -s— iJ+S cos 2cr sin i s 
' or, since o-=22°, when u= 0, on 12th July, 1859, 
Ai=M 7 cos (m— s— i m ) + 0‘69S cos^ s 
B x = — M' sin (m—s—i m )-j-0'69S sini, 
C 2 
