594 
MOTION OF A PROJECTILE 
Therefore 
2c 2 
X — A 
X*-A* 
sn a dn a 
_ c 2 (&' + k) 3 (1 “Cn x) snx dn x — (1 — cn x) 3 (1—cn a) 2 ' 
c 3 + A' 3 (cn x cn a) (cn x — cn wa) (cn x — cn <o 2 a) 8 
A 
This fraction has a quotient 
2 ( k 1 + k) 3 sn a dn a 
c 3 + k 3 (1 — cn a) 2 
__ _ 1 3c 2 dc 
2 c 3 + k 3 da 
--lx** <■*+*> 
= \ Ta log C 1 Cn ( 1—cn wa ) (1 ~cn <o 2 a) 
since 
and therefore 
Also 
and 
1 — cna 
k' -\-Jc 
1 — cn <oa = 
% 
1 — cn co 2 a — 
c+k* 
k' + k 
toe + k? 
k'+k 
<o 2 c + k 3 
(1 — cn a) (1 — cn coa) (1 — cn <o 2 a) = (~~~ 
c 6 + k 6 
dc ( k 1 + k) sn a dn a # 
da (1 — cn a) 2 * 
sn a dn a sn coa dn coa __ sn co 2 a dn to 2 a 
(1—cn a) 2 (1 — cn coa) 2 (1—cn co 2 a) 2 
- -%/&■£> 
the value of 
when 
ye 
— b 3 \ . sn x dn x 
or 
,12 dp 3 / ~ (1—cnx) s 
s 3 —1, or g = 1 or w or <o 2 , 
x = a or <oa or <o 2 a„ 
and therefore when 
