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 «, 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.2A+cos.* B+-cos.2C =1, cos.2. A’+cos.? B’/+cos.?C/=1, 
cos.2 A” -+-cos.2B” + 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 pomts, as was formerly remarked. , Again, 
the preceding results are easily applied to any solid, by usmg dm for 
any indefinite element of the solid x, 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 , 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 ordinary sign 
of the integration of differentials. 
Put F cos. a=P, F cos. b=Q, F cos. c=R, change m into dm, . 
and use s instead of S$; then (h) and (i) become sPdm=0, sQdm 
=0, sRdm=0, (A); s(Py—Qz)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. 
— 
Arr. VIII.—On Shooting Stars —Communicated for this Journal, 
by Mr. Exsas 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 
