that Matter takes up no Room in the JEther. 849 



14. It had been my intention, in case there had been any 

 indication of positive results, to determine the corrections 

 which must be made for possible disturbing influences, 

 especially such as might be suspected of contributing diurnal 

 or semi-diurnal terms to the azimuth of the suspended plate: 

 for example, changes in the temperature of the apparatus, 

 and in the elements of the surrounding magnetic field. 

 Against such disturbances every precaution had been taken 

 at the outset ; and when the observations failed to show 

 anything periodic emerging above the accidental errors, it 

 did not seem necessary to consider them further. The 

 experiment indeed was brought to an end by the failure of a 

 suspension, the renewal of which would have involved 

 a considerable expenditure of time; the result to be achieved 

 being in all likelihood only a moderate lowering of the limit 

 given in § 21. 



Theory and Conclusions. 



15. Before the (null) results of the observations can be 

 discussed, it will be necessary to give an outline of the theory 

 of the experiment, in order to show what should have been 

 observed if F 2 p (§ 2) had been great enough to give rise 

 to measurable effects. The starting-point is an equation, 

 numbered (29) in the 1909 paper already cited, and giving 

 the force m(X, Y, Z) experienced by a material particle of 

 mass m at (#, y, z) owing to the motion of another particle 

 of mass m' at (V, y f , z'). This equation maybe written 



\r 6 r 1 )\dt) V r 1 ) dt dt 



,/6? _ 30ggW d£ _ SOfyZdy' dz' _/l _ 3|2\ dV 



V r 7 J dt dt~ r 1 dt dt \r 3 r*J~dt 2 



r 5 dt 2 r b dt 2 J 



with similar expressions for ??iY, niL (1) 



where f, 77, £ = #' — #, y' — y, z' — z ; and pis the density of the 

 aether. 



16. Suppose, now, that the particles m, m' are constituents 

 of a body moving through the aether with a velocity (U, V, W) 

 which may be considered uniform throughout the body; and 

 let the variations of U, V, W be so slow that terms involving 



