596 
Similarly 
Therefore 
MOTION OP A PROJECTILE 
C = i-w 3 ; C ■=. ^co 3 snw 3 a dn <o 3 a. 
2 2 
(ax—l 
w z 
-»f£z 
dx 
= ^ x ~ log (1 —cn a) (1—cnwa) (1—cn « 3 a 
- . 1 x sn x dn x — sn a dn a ^ 
if 
%Jo 
cn x — cn a 
. 1 P % sn x dn x — sn wa dn wa , 
+ 0 w/ —--dx 
z jo cn x — cn o) a 
.1 9 p x sn x dn x — sn <o 3 a dn w 3 a , 
+ -C 0 2 / -o-dx. 
2 Jo cn x — cn w 3 a 
Now 
of which 
sn a dn a 
cn x — cn a 
dx 
sn a cn x dn a + sn a cn a dn a 
cn 2 x — cn 3 a 
dx; 
sn a cn x dn a i 
- 2 -o dx 
cn 3 x — cn 3 a 
1 j 1 — cn (a + x) 1 + cn (a — x) 
4 °° 1 + cn (a + x) 1 — cn (a — x) ’ 
as can easily be verified by differentiation ; 
n , ±i Qtr 1 - cn (a + x) 1 + cn (a —x) 
101 dn ° 1 + cn (a + x) 1— cn (a-— x) 
sn (a + x) dn (a + x) ^ sn (a + x) dn (a + x) 
1 — cn (a + x) 1 + cn (a + x) 
^ sn (a—x) dn (a—x) ^ sn (a—x) dn (a—x) 
1 + cn (a—x) 1 — cn (a—x) 
= g dn (a + x) ^ dn (a— x) 
sn (a + x) sn (a—x) 
___ dn (a + x) sn (a—x) + sn (a + x) dn (a—x) 
sn (a + x) sn (a—x) 
„ sn a cn x dn a 
= 4 - 5 — 
cn w x — cn 3 a 
