518 Sir Oliver Lodge on Astronomical 



In my August paper (p. 81) I dealt only with transverse 

 inertia, since I was considering a central force in a nearly 

 circular orbit — in other words, I dealt with the variation o£ 

 m but not with the corresponding variation of v required to 

 keep the moment of momentum constant. But, since the 

 absolute motion with respect to the aether was what was 

 under consideration, I ought to have treated it more gene- 

 rally, and not been satisfied with the ordinary equation o£ 

 particle dynamics; for the force along the radius vector is by 

 no means perpendicular to the absolute motion through the 

 aether, when the centre itself is in motion. 



So taking v as the planet's orbital velocity, and V the Sun's 

 true proper motion, both vectors, the whole momentum is 

 m(u + V), and rhe force acting on it has therefore four 

 terms, 



dv dm .ydm dV 



dt dt dt dt 



The first term is what I took into account in August. The 

 second term Prof. Eddington introduced in October, and 

 showed that it overpowers and just reverses the effect of the 

 first term, putting the variable factor into the numerator 

 instead of into the denominator ; though, as he says, this 

 merelv changes the sign of the direction of solar motion 

 needed to account for a given effect. The third term he also 

 considers, and estimates its influence, showing that it only 

 produces periodic effects which do not accumulate. 



The fourth term he treats a's zero. 



But if it should happen that the Sun is part of a rapidly 

 moving spiral nebula, this term also may possibly turn out 

 to have some finite magnitude. Indeed, there seems already 

 some dawning suspicion that what Mr. Jeans calls our " local 

 universe " is demonstrably subject to acceleration of some 

 kind (see a reference to new tentative work by Prof. Kapteyn, 

 on page 421 of the November number of ' The Observatory '). 

 If such cosmic acceleration exists, it would have curious 

 residual (though minute) effects, especially on the outer 

 planets; for resultant force would not then act along the 

 radius vector of an orbit, except on the average. 



Without further reference to the fourth term thus intro- 

 duced, let us summarise the position: — 



Admittedly a certain drift allotted to the solar system will 

 explain the behaviour of Mercury and Mars, but it gives 

 results also for Earth and Yenus which are too big. And 

 though I contrived to evade this, on page 91, by choosing a 



