r 
a Problem in physical Astronomy . 
551 
ay 
+ -^r + 
+ ~ 
47 
2J 4 
_L _2__ 
2 y * 2y 
1 
1 3 « I 
47 1 
3 tty 
477 
4. JL- 
1 i6vy 
3 
477 
-rb.r 
3 - 5 - 7-3 yyy 
4.6.84 
_L __ 3-5-7-9-5iy 
' 4.6.8.10.6 
, _3-5-7-9-ii-7i/ 
* 4.6.8.10.12.8 ,wc * 
And this equation, more concisely expressed and divided by y, 
gives 
2J 7 
~5 
+ 
4 r 
3 
3 
47 3 
5 
') Q. ~ 
5 
3«7 
47 3 
— 3 - 5 - 7-377 
2y ay I6y i 6 y j y 4.6,84 T 4 ;6,8,io .6 ■ 4.6.8 .10.12.8 
+ 
3 - 5 - 7 - 9 - 577 3 | 3 ^- 7 - 9 .n. 7 vr 
+ 
Now the fluent of the series on the second side of this equation 
is found, by the methods which have been long known, to be 
J- 5 - 7-3 77 1 3 - 5 - 7 - 9-5 7 4 . 3.57.9.1 i . yy 6 . . 
&c. and the fluent of 
',&c. 
. 4. 3 - 5 - 7 - 9 - 57 4 , 
4.6.84.2 » 4.6.8.10.6.4 * 4.6.8.10.12.8.6 
the terms on the first side will be very easily obtained, by the 
following assumption, and attention to what was shewn in Art. 
2. of this paper. 
For the fluent of the terms on the first side of this equation, 
assume 
+ sU.h.y; then will the fluxion of this 
a 
+ 
x 
,,4 
. 4. 
+ 
7 ° ' 7 
p 
y “« y 
expression be 
~-6fl 4 b 2 c 
f “y~“““y 
5 * , 3 b 
y 5 ' y 
+ .X 
* y 
g 
y 
r 
~ 
+ 
‘ + 
+ 
c 
y 
X 
7 
1 
>• 
y 
Q. 
-f- u 
JL 
yy_ 
2 fuy 
+g-)j 
j 
