24 



This, remembering (8), is the equation of the orbit. It is a 



conic whose focus is the sun, and axis is (m, m 1; m 2 ) =:>.. The 



f c 2 



eccentricity is e = .y , t the semi-parameter, p = — . Hence. 



the semi-major axis is c 1 M j ( M 2 — f -), or a by (11). The center is 



— a e (m, m„ m,) = — a e ,«. We may put the orbit, therefore, 



in the form : 



?= — a e <>~ r <>. a cos E+> b sin E. e<l. 



i s = — a e />.+/'• a cosh E-j-v b sinh E. e>l. 



This substituted in (7) and integrated gives Kepler's equation 



Q 



E — e sin E = — r (t — t, ) e<l. 



,,0, a b 



(13) 



E — e sinh E = -^- (t — t„) e>l. 



ab 



For analytical treatment see Dr. Dzisbek's Theories of Planetary 

 Motion, pp. 1-13. 



Notes concerning tests of the l'i rdue exi'ebimental rx)COMOTivE. By 

 Wm. F. M. Goss. 



The Purdue experimental Locomotive Plant was installed early in the 

 present year. It has been fully described in a paper read before the Amer- 

 ican Society of Mechanical Engineers at its San Francisco meeting, and a 

 brief reference to the plan of mounting must serve the present purpose. 



The driving wheels of the locomotive rest upon other wheels which are 

 carried by shafts running in fixed bearings. When, as in the process of 

 running, the drivers turn, their supporting wheels are driven by rolling 

 contact. The locomotive as a whole instead of moving forward, remains 

 at rest while the track, that is, the periphery of the supporting wheels, 

 moves rearward. The locomotive draw-bar is connected with a series of 

 scale-beams which constitute a traction dynamometer. Friction brakes 

 on the shafts of the supporting wheels, interpose a resistance to the turn- 

 ing of the latter and, by so doing, supply a load for the locomotive. The 

 whole arrangement is such that while the locomotive is fired in the usual 

 way, it may be run under any load an<l at any speed, the conditions being 

 similar to those of the track. 



