598 
MOTION OF A PROJECTILE, &C. 
and, finally, 
I x -f A log (1 — cn a) (1 —cn wa) (1 —cn <o%) 
Z del 
“j- Z a + co Z coa -f“ co 3 Zw 2 at 
lo „ ®iKa + x) ©40 + x ) 
D ©ija 
® 3 i a 
, ©! I (coa + x) © £ (coa + x) 
- <■> log -J , - - 1 
©, 5 coa 
1^ 
© 3 i<oa 
n 2 i n «.®ii (<° 3a + x ) © 3 J (co 2 a + x) 
55 03|co 3 a • ’ 
the equation of the trajectory 
Since 
therefore 
and 
Za = — log ©a , 
co Zoo a = — log ©wa 
dc\ 
co 2 Zco 2 a = -y- log ©co 2 a; 
da 
and therefore the coefficient of x, on the right hand side of the equation 
of the trajectory, may be written,™ 
- log (1—-cn a) (1—cn coa) (1 —cn co 2 a) ©a ©coa ©co 2 a 
Z Ctci 
— -^log©iJa ©3ja + log ©Jam © 3 |coa + log ©^aAi © 3 |co 2 a j- 
Therefore the equation of the trajectory is 
i^-y) 
== x «£log ®iJ a ® 3 S a + log ©j^coa © 3 |coa + log ©^ 00 %© 3 |co 2 a^j- 
lo 
(T 0 lS ( a + X ) 0 3g (» + *) 
— CO lot 
> 3 lot 
©lJ a 
©j| (coa + x) 
©35 ( wa "h x) 
©i 5 coa 
© 3 | coa 
©is (to 2 a + x j 
© 3 J(co 2 a + x) 
©i|co 2 a 
© 3 |co 2 a 
(To he continued .) 
