ON LAGRANGE’S BALLISTIC PROBLEM. 
201 
Tlie terms with coefficients a u a 2 , a 3 are 
-20, £ 
_cr VRj + ^i/ [ \R 1 + 5j/ + 
+ io l '£±Iii)%i 5 / s + R J -Yl 
2^(R 1+S ,)li|J 
1 ( 8 - 8 , 
R, + 8 4 
1+2 
/ s + R, 
+3 (S+s 1 y +4 |'|_fE L y +6 ('s±R,'‘ 
3 ' \R, + 8 4 
1 / 8~8, 
(J 
R, + Si 
u ii+sir \ih+sj + \i h+si 
s + Hi \ . /U + RA 2 /s + R, 
1 + 
R 1 +V + VR 1 +. i y ^\Ri+sJ ^Xlli+sJ L 
+ 
+ 
s + R, 
The terms with coefficients a 4 , a 5 , ..., are 
4~ 11 AY J(£— 
and so on. 
The term with coefficient K, is 
(T 
++)■{+«■ 
!K, 
1 3 V (»• + »,)» 1 
cr dcrf { a J 
The term with coefficient L, is 
2 T A 0 \ 4 f (r-Ri ) 4 (58i-4R,-?-)(r + 6 - 1 ) 5 l 
15 Ao-aJl cr j 
The terms with coefficients A U5 A l5 A 2 , A ;i are 
l(. r -Z. K A 4 ji + 4 ( A +10 YI±£l\ , 
Lo-Ua + .s-Y l UR + 8,/ UR + 8,/ ' VRj+Sj 
+ 20(£ ±£l V'+ 35 / r 
+«i VI 
R, + s, 
• 2 A, (Rj + 81 ) 
i__a_ 
cr 8cr 
1 (r —Ri 
cr UR + 81 
1+3 
r + 81 \ 
+ 6 
r + 8 . 
Ri + S,/ \Ri+ 8 i 
+ 101 aU) +15 (b i + +s.) } 
2!Aj( B, +5 i) 1 1^‘[^L(^)*{ 1+2 (£^) + 3(|^)+4(^)V 5 (|±^)*}; 
cr 8cr 
- 2 »A S (R I +«.)’( — 
1 /r—Ri 
cr VRj + 81 
1 + 
/ 'T + 8] 
VR1 + 81/ VRj + Si/ ^VR]+8i/ VR x + 8iV /_ 
+ + Y + ( r + s 1 y + ^ r + 8 , Y| 
The terms with coefficients A 4 , A-, ..., are 
-.asm «4*jrm 
and so on. 
2 f 2 
