Revolving about Fixed Aves. — Q75 
the direction of the side Am, which indicates that velocity, con- 
sequently no other direction nor amount can be assigned to it, 
when projected, than the diagonal Av of the parallelogram Amvk. 
If the velocity of the ball be doubled, the centrifugal velocity 
increasing as the square of the increased velocity in the circle, it 
» would be=39.44 x 4= 157.76 feet per second, and the initial pro- 
jectile velocity would be=~“25.14? + 158? = 160 feet per second ; 
and the two first would be represented by the sides Ah and in; 
respectively, of the parallelogram Anyh, and the diagonal A; y 
would indicate the direction and relative proportion of the initial 
projectile velocity. ‘With four revolutions in a second, the initial 
projectile velocity would be 635 feet per second, in the direction 
of the line Az. At least such would be the directions for those“ 
three velocities at the instant the ball leaves the point from which 
it may be discharged. But with such low velocities a pound ball 
would not indicate those directions: by its path, for the reasons 
givenabove. With very high increasing velocities, however, the. 
experimenter will find that a small leaden ball will move in direc- 
tions approaching that of the radius, a8 shown in the diagram. 
In repeated experiments made with a machine revolving vertical- 
ly, and having a tube placed in the direction of a tangent to the 
cirele in which leaden balls were revolved, it was found that with 
very high velocities they were forced through the tube with diffi- 
culty, anda portion of each was removed by the friction, and the 
upper part of the tube, on the inside, was worn smooth. But 
with much lower velocities the balls passed Hiradghs the tube 
Without any apparent friction.- 
In performing the first experimieht, the bar, (A, Fig. 1,) mov- 
ing with uniform velocity in every part of the circle BD, has the 
same centrifugal force at v that it would have after revolving for 
a minute or more; for the amount of that force depends upon 
the curvature and the circular velocity, and consequently was ex- 
cited to the amount of thirty-nine pounds instantaneously, and if 
it had been discharged at three inches from B it would have been 
projected with that force. If this were not the case with bodies 
moving in space, stipposed to be thus deflected, they would fall 
to the centre of attraction. Now as this is the fact, the tangent 
Bz in the diagram only serves, as every mathematician knows, 
to show geometrically the amount of deflection in a unit of time, 
measured at right’ angles to that line, the space zv representing 
