[BARNES] SPHERES MOVING THROUGH WATER 57 



Replacing the mass by the density we find the accelerating force 

 on a sphere moving in a fluid like water under gravity is 



dv I o — p 



dt "" \o ^ 1(0/ 

 when o = density of the sphere 



p = density of the fluid. 

 The total kinetic energy of the sphere and fluid is 



^ {M + I Ml) V 



Experimental. 



The spheres of various metals were suspended with a wire of plati- 

 noid 0-38 mm. in diameter and approximately 108 cms. long. The 

 wire was suspended from a knife edge supported on a frame clamped 

 to the experimental tank. About one-third the length of the wire 

 suspension was immersed in the water. This tank was 15 feet long 

 and 2 feet wide, and 2 feet deep. The pendulum oscillations were, 

 therefore, indep^dent of any important influence due to the sides. 

 The equivalent length of each pendulum w^as measured by removing 

 the frame to a convenient support away from the tank and finding 

 the time of vibration in air. In this way by assuming gravity at 

 Montreal the various corrections are included sufficiently well for the 

 purposes of the investigation, and the equivalent length of each 

 pendulum obtained. 



The time of vibration was taken on a B.A. chronograph of the 

 usual type. The record of each swing was made by depressing a key 

 when the sphere was seen to pass the middle point of the arc. In this 

 way the time was estimated in successive groups of 10, 25 or 50 swings 

 and the mean taken. 



Arc of Swing. 



The effect of the arc on the time of swing of a pendulum vibrat- 

 ing in water should be more carefully studied. This was pointed out 

 by Stokes in his discussion of the experiments already referred to. 



Osborne Reynolds'^ was the first to show that a flat disc moved 

 through water in a direction at right angles to its flat side or parallel 

 to its main axis developes a vortex on its rear face which follows it, 

 and reduces the resistance to motion. This factor is well recognized 

 in the operation of screw propeller blades, and is shown by the fact that 

 a propeller with a slip of from 20 to 30% is more efficient than one with 

 less. 



1 Nature 14, p. 477 (1876). 



