ba 
ey 
_/ 
434 Mr. Bowditch on the motion of a pendulum : 
large number; but it is unnecessary to enlarge on the subject, since . 
the method of finding these curves is very easy from what is here 
taught, and there appears to be such an endless variety, that it would” 
be useless to attempt to note them. ee, 
21. The equations (B) are exactly similar to those for finding the ; 
apparent motion of the earth viewed from the moon, in the sapiee.. 
mentioned in Mr. Dean’s paper on this subject. or let the inelina. 
tion of the lunar orbit and equator be 6° 39’=4, the greatest equation’ 
of the moon’s centre 6° 18'=d', at and a’t’ the mean motions. of the. 
moon from her node and perigee in the time ¢; ¢+90° and 0490 the : 
mean distance of the moon from these points when ¢=0, ¢ onsequently , 
the distance at the time ¢ will be respectively at-+e+90°, at+e490% 
The sines of these angles multiplied respectively by 6 and will give 
nearly the earth’s declination x, and the equation of the moon’s centre. 
. ¥% which may therefore be put under the form x=é cosine (att) and 
fan ctaine ae isis we — pregecy like the equine Bat ; 
2 x will apply. to the motion of the earth received from tel moonand re- 
a * 
e 
* =. es : is 
: 4 2 # eS & He” ee 
Oe * ad — * ‘ i, a 
. ferred to the concave surface of the visible hemisphere, and the form’ 
of the curves described will depend on the ratio or the terms a, 4 OF © 
: on the’ mean motions of the moon counted from the perigee and node 
a. 
' feck i p18) are @=1°004021, a'=0-991548, and as a’ is nearly equal 
, =805 neatly, con ; 
na ® 
-¥ asin ay Stieeycle of motions of the earth ast from the moon, 
C01 n ipleted i in about 80} revolutions counted from the node, as 
‘ - | has observed in his paper. The values r,s corres: ar 
ng Ipound pendulum which completes its motions | int ‘the Be 
> oo of revolutions may-be found ae making (asi in bie eM; 
= 
z “<8 The values of a, a’, given in La Place’s lunar theory (Mee. Cele sf 
~ 
Fl 
al 
=. : 
ee 
| 
ie 
