On Shooting Stars. 95 
If there are three fixed points in the system to which it is in- 
variably attached, supposing that they are not in the same straight 
line ; then denoting two of them by m and n as before, and suppos- 
ing p denotes the third point, R” its reaction, A’, B’”, C” the angles 
which its direction makes with those of x, y, z supposing the origin of 
the coordinates to be at m, and using the same notation as before ; 
we shall have R” cos. A”, R” cos. B”, R” cos. C” to be severally 
added to the first members of (s), and R’(Y’ cos. A” — X” cos. B”) 
R”(Z’ cos. A” — X’ cos. C”), R”(Y¥’ cos. C’—Z’ cos. B”) re- 
spectively to be added to the first members of (t) ; (where X’, Y’, Z’ 
denote the coordinates of p ;) and we shall have six equations, which 
with cos.? A +-cos.* B+-cos.?C =1, cos.2 A’+cos.?B’+cos.?C’/=1, 
cos.2 A” +cos.?B”+cos.2C”=1, will be sufficient to determine the 
reactions and their directions ; the system being fixed in position in 
this case by the three points, as was formerly remarked. Again, 
the preceding results are easily applied to any solid, by using dm for 
any indefinite element of the solid «, y, z for its rectangular coordi- 
nates, and F for the force which is applied to dm, and a, b,c for the 
angles, which its direction makes with the axes of x, y, z, then using 
S for the sign of integration relative to the mass of the solid ; or to 
conform to usage, we may change S into s, which is the ——- sign 
of the integration of differentials. 
Put F cos. a=P, F cos. b=Q, F cos. e=R, change in ttc the} 
and use s instead of S; then (h) and (i) become sPdm=0, sQdm 
=0, sRdm=0, (A); s(Py—Qzr)dm=0, s(Pz—Rz)dm=0, s 
(Ry—Qz)dm=0, (B); which are the formule that are to be used 
when the system becomes a solid, the integral sign s referring to the 
element dm ; and the integrals are to be taken relative to the whole 
mass of the solid; 
Art. VIII.—On Shooting Stars—Communicated for this Journal, 
by Mr. Extas Loomis, Tutor in Yale College. 
Every person of a reflecting mind must have often asked himself 
the question, what are shooting stars. ‘The suddenness of their ap- 
pearance, the rapidity of their motions, their brilliancy, the trains 
which they frequently leave behind them are well calculated to awa- 
ken Curiosity ; ; and-in the absence of definite knowledge respecting 
them, it is not perhaps strange that we have been favored with an 
