68 Prof. R. A. Sampson on the 



sphere. Let the arc AB as it exists at any moment be 

 determined as a fraction of this unit. Let it be determined 

 again in the same way at a later moment. If the two do not 

 agree, we can say that a relative rotation of the two spheres 

 must have occurred, through a definite angle, about an axis 

 perpendicular to the plane of the great circle AB. Whether 

 any relative rotation about an axis in the plane AB has taken 

 place, or whether both spheres have executed in common 

 any other rotation about any axis whatever, the observers at 

 A and B will be unable to say. We may express this position 

 by saying that A and B are under circumstances of complete 

 geometrical relativity. 



The whole description is, however, an abstraction. It is- 

 the abstraction which lies at the basis of geometry; it 

 eliminates time from consideration and supposes figures to 

 exist with definite distances between the points. But in 

 reality any distance assigned requires time for its deter- 

 mination, and the standard case would be this : A and B 

 each have hold of a graduated measure, allowing it to slip 

 through their hands, and as they watch its successive readings 

 they signal them to one another ; each will then only be- 

 aware of the other's reading, that is to say, of the other's- 

 distance at any moment, as complicated by the time of 

 transmission of the signals. This aberrational allowance is 

 an inevitable attendant upon actual physical measures. It 

 is inseparable from motion. It would not be surprising 

 if the ideas of motion required a complete surrender of the 

 scheme of abstract geometrical relativity defined above. 



How much the physical theory of motion affects our notions- 

 of absolute and relative is very well known. Let the sphere 

 A be the Earth and the sphere B a complete opaque sheet of 

 cloud rotating with it. A Foueault pendulum set up at the 

 north pole would of itself change its plane of oscillation with 

 respect to the meridians, pointing out an absolute direction 

 in space, and an absolute rate of rotation, of which the ob- 

 server would be unaware without this, or other similar, appeal 

 to dynamics; A similar pendulum set up at the equator 

 would show no change of azimuth at all. By no conceivable 

 explanation can this familiar experiment be made consistent 

 with complete geometrical relativity of the system, geome- 

 trically self-contained, within the bounds of which it occurs*. 

 Other cases could easily be mentioned. But my purpose at 

 the moment is to pursue a little further the aberrational con- 

 siderations introduced above. 



In 1893 and 1897 Sir Oliver Lodge, considering the- 

 Michelson-Morley experiment, then not infrequently taken 



