i 5 6

]*he Resolution of some General Problems

+

MP aM

2 ? 6

XCOs./>-a.Z-f --77 X

N

4 f p-\-a 2?

. MP , a M

T TIT T —r~ XCos.p-fa.Z

**f P~ a

&C.

So that, from the general method of operation before laiddown, it appears that the proper correction for the value of

I — w, arising from the terms, ^xcof. azand L xcos. uz, be-

fore neglected in the respective values of i— w\ 3 and i— w)

p

will be expressed by e into -77 x

—4.

N

ML J

y " p-a 2?

cos. p-a. 2- X —— -f-z I

■ p~»\

ixJi.

e*f p—a

o_ ~~

4. ME JL “ M _ X' 2P ' 6

N

«y x +

aM cos, q-6 1 — a-

JL

4. _L JJ x cos - ?+«■ g

r a —r-n* 1 00c.

In respect to which it may be observed, that no regard hasbeen had to such quantities as would arise from the multiplica-tion of the new terms in £, by the series 1—/ 3(3 . B cos ( 3 z4- 1 —» C cos. y z 4 &c. ( as ought, in strictness, to have beendone); because these terms being very small, they will, aftermultiplication into the small quantities 1 — ( 3(3 xB, 1 — yyxC &cc.be so far reduced, as to become quite inconsiderable. And itmay be observed farther, that even the whole product arisingfrom the multiplication o f the value of £ into the said series,except the terms — eh 4i—/ 3 / 3 .{/Bcos.jGz 4 1— yy. efC cos y z&c. might be also rejected, without producing an error ofmore than a few seconds, in finding the place of the moon inher orbit.

Having shewn what alteration will be caused in the value of1 —w (the reciprocal of the distance of the body from the cen-ter of force) from the taking in of any small, assigned termsin the values of 1 —to' - 3 and 1—w 1 ” 4 , it may be a pro-per place here to shew (as it is of great importance to beknown) what change will arise in the said value of 1 — wfrom the addition of any small, new terms, A sin. nz,

and