Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics.

L1EYS WITI TRIUlANULAR APE1'RTUE. 811
(p +-qtan30o)2 bX
p - q^ tan2 30~
47req tan 30~ 27-e 27re
{] + cos -os — (p - qtan 30) - cos -(p + q tan 30)}
bx bx bX
2p + 6q'tan200 4pq tan300+4 q tan2 30 27re
ta= 300)-2O " - -J -- cos (p -qtan 30)
(p2-q2tan 30")- (p'- q tan2300)2 b,
4p q tan 300 - 4q tan2 300 2,r e
+ ( qtan 300o cs (pq tan 300).
2p2 - 2 q'2 tan2 30~ 4 eq tan 300
CQS
(pQ- q2 tan" 30)2" bX
Let p = r cos 0, q = r sin 0: which is the same as referring M
to the central point of the screen by polar co-ordinates. Then
observing that tan2 300 =, and restoring the factors
b2X2 b X2
- and 47r,
4 7r2 Îi7Tq2
this may be put in the form
3.b4X4 1
32 7r4. r4 ' sin0. sin2 (0 - 60).sin2 (0 - 120~)
3 47ryre
x { - sin (0-o60).sin (0-120~).cos -— ) sin0)
4 vbX 3)
- sin (0 - 1200).sin (0-180~).cos( b ( - sin(O- 60~)
- sin (0 -180~). sin (0 - 240o).cos ( s. sin ( - 120)).
'The maximum value it will be found is when r = 0, and is