520 Astronomy and Electrical Theory of Matter. 



given in the usual textbooks, the following proof, by my brother 

 Alfred Lodge, may be worth citing : — 



>} 



vp =7i 

 pp'=V 



but jp' or T'H is vectorially equal to T'C+CH, which are of mag- 

 nitudes a and ae respectively. So the equivalent velocities are :— 

 ha 

 £F perpendicular to T'C or PS, the radius vector ; 



and 



hae 



-tt~ perpendicular to CH, the major axis 



Also 



2ira 



b 2 h ° TV(l-e 2 ) 



So the constant velocity perpendicular to radius vector is fi/h, 

 while the constant velocity parallel to minor axis is fie/h. 



Assuming the result, the proof becomes obvious ; for then, 

 geometrically, the resultant velocity perpendicular to radius 

 vector is 



dQ 

 dt 



£± 



-^COS 



which, with r 2 dd/dt=h, gives 

 orbit referred to either focus 

 1 



:he ordi 



equation to an elliptic 



(1+6 cos 6). 



Note 2. Prof. Eddington points out, at the top of page 323, that 

 the complication of the difference between longitudinal and 

 transverse inertia can be evaded by always working in terms of 

 momentum ; and this working exhibits the behaviour of the 

 inertia-factor (taking the velocity of light as unity, for brevity in 

 writing) thus : — 



By electrical theory, 



m=ra (l — v 2 )'*, 

 a function of speed, not of direction. 



