H. A. Bumstead — Lor entz-Fitz Gerald Hypothesis. 505 



We must also observe that the " apparent " acceleration 

 (fi •> «/"/) d^ers from the " true '' acceleration not only on 

 account of the different scale of length in the x direction, but 

 also because of the larger unit of time given by a moving 

 clock. Thus 



/' = l f- 



(8) 



J i ' -i nY J i 



In equations (6) put — — for cos 0, and — for sin ; put for E 



its value from (1) and for r its value from (7) ; substituting in 

 (8) the values thus obtained f or f x and/,., we obtain. 



/,' = V" ^ * 



/.' = V" ^ y 



The resultant " apparent " acceleration will thus be 



r 



When r/ is an " apparent " unit vector in the direction r' . 



When there is relative motion of the planet with respect to 

 the sun, however, the compensation is not perfect. In fact, 

 deviations from the Newtonian law may be introduced which 

 would not exist if the longitudinal and transverse masses were 

 equal. This may be most easily seen when the attracting 

 body is at rest in the ether with a planet moving about it ; in 

 this case the force given by electrical theory is the ordinary elec- 

 trostatic force ; it will be in the direction of the radius vector 

 and will vary according to the inverse square of the distance. 

 But the resultant acceleration will not be along the radius 

 vector if the longitudinal and transverse masses are different. 

 Let <£>be the angle between the radius vector and the tangent 

 to the path ; and let the forces and accelerations, tangential 

 and normal to the path, be respectively F t , F n ,y tJ( / n . Then 



F t = V 2 -^cos4>; F n = V 2 ^sm<A 



/.-.8=«fti-So-^*i 



