THE GEOMETRY OF MOTION 209 



but the staircase is rushing perhaps 1000 miles an hour 

 round the axis of the earth, while the earth itself may be 

 bowling 66,000 miles an hour round the sun. The sun 

 itself is moving towards the constellation of Lyra at some 

 20,000 miles an hour, while Lyra itself is doubtless in 

 rapid motion with regard to other stars, which, so far 

 from being " fixed," may be travelling thousands of miles 

 an hour relatively to each other. Clearly it is not only 

 impossible to tell how many thousand miles an hour we 

 are each one of us to be conceived as speeding through 

 space, but the expression itself is meaningless. We can 

 only say how fast one thing is moving relatively to another, 

 since all things whatsoever are in motion, and no one can 

 be taken as the standard thing, which is definitely " at rest." 

 Is it correct to say that the earth actually goes round 

 the sun, or that the sun goes round the earth ? Either 

 or neither ; both are conceptions which describe phases 

 of our perception. Relatively to the earth the sun 

 describes approximately an ellipse round the earth in a 

 focus, relatively to the sun the earth describes approxi- 

 mately an ellipse about the sun in a focus. Relatively to 

 Jupiter neither statement is correct. Why, then, do we 

 say that it is more scientific to suppose the earth to go 

 round the sun ? Simply for this reason : the sun as 

 centre of the planetary system enables us to describe in 

 conception the routine of our perceptions far more 

 clearly and briefly than the earth as centre. Neither of 

 these systems is the description of an absolute motion 

 actually occurring in the world of phenomena. Once 

 realise the relativity of motion and the symmetry of the 

 planetary system is seen to depend largely on the stand- 

 point from which we perceive it : the theory of planetary 

 ellipses can thus be easily recognised as a mode of 

 description peculiar to an inhabitant of a solar system. 



§ 8. — Position. The Map of the Path 



Relatively to O and its frame, then, our point P 

 describes a continuous curve or path, and its position at 



14 



