Section III, 1921 [125] Trans. R.S.C. 



A Reversible Pendtdum 



By H. F. Dawes, M.A., Ph.D., Professor of Physics, McMaster 

 University, Toronto 



(Presented by John Patterson, F. R.S.C.) 



(Read May Meeting, 1921) 



1. In the accurate determination of "g" by means of a Reversible 

 Pendulum there must be taken into account the following physical 

 properties of the motion requiring corrections or compensation which 

 vary with the design of the pendulum. 



{a) Temperature. 



(b) Buoyancy of Air. This force acts through the Centre of the 

 Geometrical Figure of the pendulum so that its moments about the 

 axes of rotation will be unequal unless the external form is symmetrical 

 about a Centre of Figure and, of course, all cavities are air tight. 

 In the Kater form the pendulum is not symmetrical so that observa- 

 tions must be corrected for this effect or the error eliminated by using 

 the pendulum in a vacuum. In Repsold's pendulum the figure is 

 symmetrical. 



(c) Flow of Air. The net efïect of the flow of air past the moving 

 pendulum is to increase its equivalent mass and Moment of Inertia 

 as shown by Stokes, Du Buat, Bessel. For a symmetrical pendulum 

 this increase is the same for both axes. 



{d) Viscous Resistance of Air. For a pendulum of symmetrical 

 figure the viscosity of the air will produce equal damping for the 

 two axes. When, therefore, the actual damped periods are equal 

 the undamped periods will also be equal and it will be necessary to 

 make only a single correction for damping, viz., the equality period 

 from which "g" is to be calculated. 



{e) Determination of Equality Period. Kater's method consisted 

 in making successive trials until very exact equality of the periods 

 about the two knife edges was attained. Bessel showed that approxi- 

 mate equality only is required, the com.mon period being calculated 

 from observed periods which are nearly equal. 



Several methods may be used to vary the period of the pendulum: 

 (1) By altering the positions of the knife edges, (2) By changing the 

 moment of inertia about the axes by means of movable weights. In 

 order to determine the Equality Period one may make a series of 



