ON LAGRANGE’S BALLISTIC PROBLEM. 
197 
The equation for A 7 is 
105 
{ -9B j + 45 (B, + 1)*} A. + 2 {B a —9B, (B 1 + 1)} AA + |! B, 1 AA 
-105 
+ 45 
-10 
2 ! 
{ — 8B 2 + 36 (B, + 1 )“} AA + 2 {B„—8B, (B,+ 1)} AA + £ B, 2 4! A - 
V 6 
S,’ 2! 
-7B 2 +28(B l + l) 2 }++ + 2{B 3 -7B I (B 1 + l)}+A + ^B, 1 +A 
s' 
4! A., 
■<i 
{-6B 2 +21(B 1 + l) ! }i^ + 2{B 2 -6B 1 (B,4 1)}AA + £b,» 6! A “ 
S' 8 
“*1 
+ 
S, 5 2! 
{-5B 2 + 15 (B, + l) s } Ar +2 {Bj—5B, (B 1 + 1)} AA + f-B,*AA 
S' 4 
-^1 -1 
The equation for A 8 is 
105 
-1o5(A{B,-^(B 1 + 1)(B 1 -1)}. 
CO \ 1 / 
{- 963 + 90 .( 6 ,+ 1 )B 2 -165 (B 1 + l) 3 }|i + 2{B 3 -9(2B 1 +l)B 2 + 45B 1 (B 1 +l) 2 }^^ 
^1 
S' 8 
-105 
+1 {2B 1 B 2 -9B 1 2 (B, + l)} ^A +1 B.’AA 
{-8B 3 + 72(B, + l)B 2 -120(B 1 + l)“}+A 
+ 2{B 3 -8(2B 1 + 1)B j + 36B 1 (B 1 + 1) , } 8! A ” 
S' 7 
^1 
+ 45 
+ £ {2B 1 B 2 -8B I ’(B,+ 1)} ±iA + |b, s AA 
{-7B j + 56(B 1 + 1)B 2 -84(B,+ l) s } +A 
+ 2 {B 3 -7 (2B 1 + 1)B 2 + 28B 1 (B 1 +1) 
21 4! A 4 
S' « 
+ | {2B.B.-7B,* (B, + 1)}NA + | B,* 6! A ' 
S' 4 
-10 
- 6 B 3 + 42 (B, + 1 ) B 2 —56 (B, +1 ) 3 } 
4! A 4 
S' 8 
+ 2 {B 3 - 6 ( 2 B 1 + 1 )B 2 + 21 B 1 (B 1 + 1 ) 
,21 5 ! A, 
J S' 5 
92 ! A 9 3 7 ! A 
+ |j { 2 B,B 2 - 6 B , 2 (B 1 + 1 )} AA + h B. 3 +A 
*1 -I 
+ 
{-5B 3 + 30 (B J+ 1 ) B a —35 (B, + l) 3 } ++ 
+ 2 {B 3 —5(2B, + 1)B 2 +15B 1 (B 1 +1) 2 } 
6 ! A , 3 
S' 4 
= -10-(f- n )"{B J -Y(3B 1 + l)B 2 + 22 (B l + l)’(B 1 -l)}. 
CO \^i, 
+ % {2B,Ba—5B,’ (B,+1)} At 3 + |i B,» A^ 
\ 10 
