56 THE ROYAL SOCIETY OF CANADA 



fluid is carried by the sphere and adds to its inertia without adding to 

 its weight. In a pendulum as the velocity increases in the first half 

 of the swing, energy is transferred to the fluid in setting it in motion, 

 and this energy is returned again to the body as its velocity slows 

 down during the second half of the swing. A spherical bubble of air 

 rising through water possesses considerable inertia almost entirely 

 due to the mass of water carried by the air. 



A small sphere allowed to fall freely in a fluid is accelerated 

 until the viscous resistance balances the downward force, and a con- 

 stant velocity results. When a pendulum is swung in water the 

 spherical ball must be large enough and heavy enough to prevent any 

 approach to a terminal velocity being reached over its arc of swing. 

 The viscous resistance produces a considerable damping effect which 

 is serious when working with small light spheres. Having selected 

 the kind of spheres most suitable to use it was necessary to test them 

 by measuring their time of swing in water and comparing the value 

 of the accelerating force so obtained with that calculated from Stokes' 

 law. As the present paper deals entirely with the effective use of 

 the law, the method of calibrating the water target will be described 

 in another place. 



Calculation of the Accelerating Force. 



The correction to be applied to the value of gravity for spheres 

 of various densities may be easily calculated from the simple law of 

 the pendulum. 



If M is the mass of the pendulum sphere and Mi the mass of an 

 equivalent sphere of water then the simple energy equation of the 

 pendulum for small arcs becomes 



{M - Ml) g _ In'' {M +\ Ml) 

 21 ~ ^ T^ 



The left hand term takes into account the buoyancy and the right, the 

 addition of the quantity of water demanded by Stokesi law. 



From the above we have 



^ 



I 



{M - Ml) 

 (ikf + fMi) ^ 



for the time of swing of a pendulum in water. 



