H. A. Bumstead — Lor entz-Fitz Gerald Hypothesis. 501 



The Gravitational Pendulum. 



As a further example, consider a simple pendulum at a 

 point on the earth's surface 90° from the pole of its motion, so 

 that the string is perpendicular to the direction of motion. 

 When it vibrates in a plane at right angles to the motion the 

 path of the bob is a circular arc and the period is 



T = 2tt 4/3E 



where G is the force with which the earth attracts the bob. 

 When it vibrates in the plane of motion its path is the arc of 

 an ellipse whose axes are L and L V 1 — ft' 2 ; for the same ver- 

 tical height (that is for the same potential energy), the infini- 

 tesimal arc described will be in this case less than in the other 

 in the ratio of V 1 — (3 2 to unity. So that the period is 



v G 



giving the same ratio of masses as before. 



Comparing, say, the tirst of these with the period which the 

 pendulum would have if the earth were at rest, we have 



V±-(? v 



G r - G, 



and since 



V1-/? 2 



G=Vl-£ 2 G 



Thus the gravitational force between two bodies moving at 

 right angles to the line joining them is the same function of 

 the velocity as the electric force between two moving charges 

 in a corresponding position.* 



If we imagine the pendulum suspended at the place on the 

 earth which is foremost or rearmost in its motion, the length 

 of the string will be L ^l—ft and the period 



T = 2./j^ 7T ZZ 

 r G' 



whence 



G, = (1-/3')G„ 



which again corresponds to the electrical case when the line 

 joining the charges is parallel to the motion.f 



* See p. 503. \ See below p. 503. 



Am. Jour. Sci. — Fourth Series, Vol. XXVI, No. 155.— November, 1908. 

 35 



