220 SCIENCE AND METHOD. 



longer with a yard-measure, but by the time light 

 takes to traverse it, and this is exactly what 

 Michelson has done. 



A body that is spherical when in repose will thus 

 assume the form of a flattened ellipsoid of revolution 

 when it is in motion. But the observer will always 

 believe it to be spherical, because he has himself under- 

 gone an analogous deformation, as well as all the 

 objects that serve him as points of reference. On the 

 contrary, the surfaces of the waves of light, which have 

 remained exactly spherical, will appear to him as 

 elongated ellipsoids. 



What will happen then? Imagine an observer and 

 a source involved together in the transposition. The 

 wave surfaces emanating from the source will be 

 spheres, having as centre the successive positions of 

 the source. The distance of this centre from the actual 

 position of the source will be proportional to the time 

 elapsed since the emission — that is to say, to the radius 

 of the sphere. All these spheres are accordingly 

 homothetic one to the other, in relation to the actual 

 position S of the source. But for our observer, on 

 account of the contraction, all these spheres will 

 appear as elongated ellipsoids, and all these ellip- 

 soids will still be homothetic in relation to the point 

 S ; the excentricity of all the ellipsoids is the 

 same, and depends solely upon the Earth's velocity. 

 Wg shall select our law of contraction in such a way 

 tJiiU S 7 a ill be t lie focus of the meridian section of tJie 

 ellipsoid. 



This time the compensation is exact, and this is 

 explained by Michelson's experiments. 



I said above that, according to the ordinary theories, 



