TRANSACTIONS OF THE SECTIONS. 
13 
I regard as vcrv difficult any development of the disturbing function, either literal 
vMml. when the eccentricity of the disturbed body is considerable and the 
potions are large, as in the case of Encke's comet disturbed by Jupiter; and 
hock were possible, the replacement of the numerous symbols by numbers at the 
Mclusion, would be an operation of almost insurmountable difficulty. Un tne 
jllakand, io performing an arUhMiiccil development according to the ru es w ic 
lawe inreDted. not only no quantity is introduced -which has a numerical value 
kscathanvaven limit (say beneath unitv io a given decimal place), u i is equa y 
upcBsible/escept by a numerical mistake, that any quantity which is above that 
■item be omitted. , ^ ^ 
Iff, y. » are rectangular co-ordinates of a comet or planet m, and / tn 
Bonulr, 
cos/-l-ff sin/ 
y-r{:) eosZ+ffsin/}, 
z= {rj cos/4-jf sin/1, 
*Y>S, 0 >(I> 1 ,d ar® constants-which depend only on the elliptic constants of the 
phaeta, and such that 
y- cosir-}-28m^8m (w—v)8in v, 
—sinw-|-28in*-^co8(fl‘—v)8inv, 
0 — aia w—2 sin^sin (?r—v) cos v, 
= cos IT—28iti*-5-cos(ff—v) cos V, 
6 , 
3 = Bin{rr--i/)sini, 
C0B(»r—v)8mi. 
M pr'l r'a ^ ^ ) I a' 1 
I |3-^cos/-aa^sm/}~cos/+ [(C-^cosZ+iS-'Bin/ j 
^^rF'-\-00'~i-33% -n=SF'-\~ao'+33'. 
c=Fff'+off'W. m=aa'+aa'+Jd'' _ a « c 
Farley has calculated for me a table of the values of these ' 
all the planets, and also for the comets -whose period has been as 
I'fte quantities^cos/'^'sin/'^co3/,^sin/,5,fl &c. the elementary 
because they are the elements -which, by means of various combinaf 
» disturbing function R, &c. Mr. Farley has calculated the coefficients 
* quantities when they are developed in terms of sh^ the con - 
also other tables for eccentricity. ‘I. -2. • • • - *7’X^Syed when 
to be so slight, that such raiyle of development can on y mecha- 
These tables have all been construe y. gg their co- 
a^raturw. These tables are not wanted for the ‘^'^"'^'^O’Sdcntly con- 
•s cannot be developed in terms of their mean anomalies m sutncicn y 
to use so many alphabets in the in order 
^iweththat I have had recoune io this artifice of reversing the letters 
be same symbol in two different significations. 
a 
