58 THE ROYAL SOCIETY OF CANADA 



When a sphere moves through water the viscous resistance is 

 proportional to its area. Hence a large sphere will be damped much 

 more slowly than a small one of the same material and of two equal 

 spheres of different densities the heavier will swing for a longer time 

 before being brought to rest. If a sphere is followed by a vortex, it 

 means the motion is more complicated for large arcs than for small 

 ones. The precise nature of this effect cannot be determined without 

 more extended investigation. The experiments here described indi- 

 cate that some effect is present, but were not carried on long enough to 

 arrive at a satisfactory determination. 



The arc of swing used in these experiments varied from about 

 30 cms. to a few millimeters. In the case of the lighter spheres the 

 damping was sufficient to reduce the arc from 20 cms. to a few milli- 

 meters in about 25 swings. In the case of the larger and heavier 

 spheres the damping was very much less. As the only object of these 

 experiments was to determine the approximate accuracy with which 

 the accelerating force acting on a sphere under water could be cal- 

 culated from observations on the time of swing in water, no great 

 attempt was made to secure the utmost accuracy. Indeed this would 

 have been useless at the present stage since the calculation of the 

 momentum imparted by the sphere to the water target did not war- 

 rant greater refinement. 



The Spheres. 



Two lead spheres were first used. The large one having a 

 volume of 355 cubic centimeters was specially cast in the laboratory 

 from lead scrap. Its density was found, by weighing in air and water, 

 to be 11-33 and its total mass 4 kilograms. The small sphere was 

 one we already had. Its volume was 60 c.c, and density 11-30. 

 Both these spheres were used for the calibration of the water target. 



Two spheres of iron were obtained similar to the lead and are 

 specified in the table. 



One sphere of brass was turned out of rod, as well as one of 

 magnesium. 



The spheres of zinc and aluminium were cast in a mould and then 

 turned as much as necessary to give a smooth surface. 



Density Measurements. 



The densities of the various spheres were obtained by weighing 

 in air and in tap water free from excess of dissolved air. Tap water 

 was chosen because this was the water which filled the tank in which 

 the measurement of the time of swing was made. 



