Revolving about Fixed Axes. 275 



the direction of the side Am, which indicates that velocity, con- 

 sequently no other direction nor amount can he assigned to it, 

 when projected, than the diagonal Av of the parallelogram Amvk. 

 If the velocity of the ball be doubled, the centdfiigal velocity 

 increasing as the square of the increased velocity in the circle, it 

 would be = 39.44x4=157.76feet per second, and the initial pro- 

 jectile velocity would be = v'25.14^ + 158- =160 feet per second ; 

 and the two first would be represented by the ^des Ah and An, 

 respectively, of the parallelogram Anyh, and the diagonal Ay 

 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 ivhich 

 it may be discharged. But with such low velocities a pound ball 

 would not indicate those directions by its path, for the reasons 

 given above. 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, as 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 

 circle in which leaden balls were revolved, it was found that with 

 very high velocities they were forced through the tube with diffi- 

 culty, and a 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 through the tube 

 without any apparent friction. 



In performing the first experiment, 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, supposed to be thus deflected, they would fall 

 to the centre of attraction. Now as this is the fact, the tangent 

 B:r 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 xv representing 



