Section III, 1917 [55] Trans. R.S.C. 



On Stokes Law for Spheres Moving through Water. 



By H. T. Barnes, D.Sc, F.R.S.C. 



McGill University, Montreal. 

 (Read May Meeting, 1917.) 



During the progress of some experiments on the production and 

 measurement of high pressure vortex rings in water, it was found 

 necessary to construct a form of ballistic pendulum, or water target, 

 with which to obtain the momentum and energy carried by the rings. 



Naturally a good deal of time was devoted to a study of this 

 underwater dynamometer, and the best method to use it. To make 

 a direct calculation of the momentum from the target itself, and its 

 movement under water, could not be done with any approach to 

 accuracy. It became necessary, therefore, to resort to some method for 

 calibrating the instrument which would involve the movement of 

 bodies whose laws were already known. Various methods suggested 

 themselves for this purpose, but the simplest appeared to be the use 

 of a pendulum consisting of a heavy sphere attached to a long and very 

 fine wire. When such a sphere is deflected to one side and allowed 

 to swing freely against the target a quantity of momentum is im- 

 parted which can be calculated. The impulsive force can in this way 

 be changed, and the scale of the target calibrated. The scale was 

 obtained on a smoked chronograph sheet by a pointer attached to the 

 moving arm of the target. Two spheres of lead which were cast of 

 difïerent sizes, and hung so as to be of approximately the same 

 length were used in the calibration. 



The law governing the movement of a spherical body in a fluid 

 medium was worked out by Stokes in 1850 (G. G. Stokes, Collected 

 Works, Vol. 3 1901). The well known method of correcting pendu- 

 lum observations in air makes use of this law, but when applied to a 

 fluid like water it was not altogether clear with what accuracy, it 

 could be used. Stokes gives some pendulum observations in water 

 from the measurements of Du Buat (1786), Bessel (1828), and Baily 

 (1832), but it was thought better to make some experiments with the 

 special spheres used in this work. 



The law states that .the efïective inertia of a sphere moving 

 through a fluid comes from the addition to its own mass of half the 

 mass of the fluid that would fill the space occupied by the sphere. This- 



