ARCTIC SEAS.— PART VII. PORT KENNEDY. 
7 
but, by Seth Ward’s hypothesis,'"' we have, also 
a (1— -e 2 ) 
2 a—r=z — j—x 
1 — e cos ( nt ) 
where (nt) is the mean anomaly, measured from perigee. From this we find, 
P a 1— ecos (nt) / 9jft v 
p m r 1 — 2ecos (nt)-\-e 2 ' ' 
hence we find 
(j£) = (l — |f) — e cos (nt ) + 1 cos (2nt ) + &c (21) 
Substituting for e in this equation, its value we obtain 
(£■)’= 0-999— 0'05 cos (/if) + 0 '00 12 cos (2 nt) 
( 22 ) 
2°. We have, also, 
sin 2 /a = 2 sin /a cos /a 
= 2 sin I sin (v — n) ^/l — sin 2 I sin 2 (v — n) 
where v is reckoned from perigee, and n is the interval from perigee to the 
ascending node of the moon’s orbit with the equinoctial, and 1 = 27° 40', is the 
inclination of the moon’s orbit to the equinoctial. 
Hence we find, since sin I = 0'464 
sin 2/x =2 sin I sin (v—n) |~1 sin 2 1 sin 2 (v—n) 
L — §■ sin 4 I sin 4 (v— n)-\-&c. . . (23) 
Sin 2 /a= 0'89 sin (v— w) + 0’012 sin 3(v—n)-\-&c (24) 
The perigee occurred July, l d 0 h , and the ascending node, 19 d 17 h ; hence 
n— 18 d 17 h =247°. 
Substituting this value of n, we find 
sin 2 /a=— 0‘35 sin 'y+0 , 82 cos 'r+0'01 sin 3v 
— 0'004 cos Sv+cfec (24) 
By the well known expansion of the true anomaly in terms of the mean anomaly, 
we have 
* This hypothesis, according to which the angular motion of the revolving body about the focus in 
which the central body is not, is uniform, is mentioned by Bishop Bkinkley (‘Astronomy,’ p. 155 of 
1st edition) under the title of the Simple Elliptic Hypothesis, and was much in use between the times 
of Kepler and Newtoil 
