Astronomy and High-speed Inertia. 87 



The sign shows that for progress the sun's effective motion 

 must be in opposite sense to that of the planet at perihelion. 



Now cos 6 cos \ is the cosine of the angle between the 

 sun's and the planet's motion, so cos a cos X is the cosine of 

 the angle between the lines of the sun's motion and of the 

 planet's motion at an apse ; or say between the sun's way 

 and the minor axis of the orbit ; call this (p. 



So the apsidal progression during n revolutions is 



7 irnviv cos d> _ N 



ec? v J 



and via cos <£ is a scalar, as it ought to be to compare 

 with c 2 . 



But the change in cc during a century (i. e. the known 

 progress of the perihelion not accounted for . by orthodox 

 gravitational perturbations) amounts to 40 or 43 seconds of 

 arc in the case of Mercury; so this gives us, for the unknown 

 motion of the sun, 



_ ec 2 doc _ ec x 43 



w cos <f>_ — x-5 x 10-4 x 400 x 180 x 3600 



43<?c ec 



6 x 180 x 36 904* 



The excentricity of Mercury is given in Gralbraith & 

 Haughton's ' Astronomy' as 20*56 per cent.; 



so -2056 



™cos</)=-y-^ U c=2-27xlO-4 C , • • • (8) 



or two and a quarter times the orbital speed of the earth. 

 I hardly think that astronomers will regard that large velocity 

 as quite unreasonable. 



From (7) it appears that a nearly circular orbit can be made 

 to revolve very easily, though the revolution would be un- 

 important, while an excentric orbit would be stiff. Another 

 curious result would seem to be that if the major axis of 

 the ellipse points along the projected component of the sun's 

 way, this extra apsidal progession disappears; whereas if the 

 minor axis lies along the sun's true way, the kind of apsidal 

 motion now under consideration reaches a maximum. Can 

 this be true ? 



In its favour we can say that the perturbation under con- 

 sideration, though depending on velocity, is equivalent to a 

 radial force varying sinuously with position, directed away 

 from the sun during that half of the orbit where the motions 



