M. Poinsot on the Percussion of Bodies. 433 
the following three equations :— 
( By? 4222+ 6?y2)X — BxyY —yazL= —B?X,.—y*zM, +6? yNo 
—a2xyX + (02x? +9722? + 0%) ¥ —y*yz LZ — ay? Yy—a*2Nyt ¥? zl, \ . (4) 
—oazX — B2yzY + (022? + By? + 226?) Z= — 2°? Z,—B?yL, +07x Mo, 
: from which the components X, Y, Z of the foree —Q may be 
found. By changing the signs of these components, we shall, of 
course, obtain those of the required percussion Q. 
RESOLUTION OF THE PRECEDING EqQuaTIons. 
11. The three equations (4) being of the first degree in 
X, Y, Z, may at once be solved by known formule. Thus if 
X, Y, Z be represented by the three fractions 
EGE S'5 = N. 
eh a ie 
we shall have for the common denominator the value 
{= 
D 
sags (Ot +A Pa? + Bey + P29) + 2B + oP) a* 
LPL PPLE LE) A +BY, 
and for the numerators the values 
N., 2 9 
aR — [x2 (2a? + By? + 222) +17 (a2a? + By?) + B?(a2a2 +22”) + 028797] Xo 
— wy (a2? + By? + 922? + 0282) Y9—we(a2a? + By? +222 + ay?) Lo 
4 aye B29) — (0a? + oy? + oP? + 2%y?)My 
+ y (aa? + B?y? + B?2? + a7B?)No, 
ane I + y+ oz? + a°B?)Xo 
— [y2(a2a? + By? + 922”) + a2( B22 +9222) +-9?(a2a? + By?) + a2 By? ] 
Ayelet + By? +22 + Ba My 
+ 2(y2a? + By? + 922? + By?) Ly t+ vyz(y?—2) My 
—x(a*x* + By? 36 are t+ a?B?)No, 
— wy (02a? + BPy?+ 22? +027") Xo 
—y2(a2a? + By? +92? + By)V, 
—[2%(a2a® + B2y* +222) +.02(B?y? + 922) + B%(a2a® + 922%) + a28%y"] Z, 
(Bn? + By? +422? + By?) Ly 
+ a(a2a? + y? + 22? + 2°97?) + wyz(a?—B*)N 9. 
12. If, then, in the expression 
i 
ae By? a 
Q= VX VFR = VNENSIN: 
