THE GEOMETRY OF MOTION 197 



of taking a smaller and smaller element of the man, and 

 the stages we have indicated from man to button, bead 

 and geometrical point, indicate how certain elements of 

 the perceptual motion are dropped at each stage, till in 

 conception we reach as a limit an ideal motion capable of 

 being fairly easily described. 



The motion of a point along a curve is the simplest 

 ideal motion we can discuss. Obviously, however, it will 

 enable us to classify and describe with considerable exact- 

 ness a number of our perceptions with regard to the man's 

 motion. Harness the button to the point, and the man 

 to the button ; then if the point move along its path, 

 carrying button and man with it, we shall have a means 

 of describing a good deal of the real motion of the man. 

 When he starts, when he stops, when he goes fast, when 

 he goes slowly, what time he takes from one landing to 

 another will be deducible from the motion of the point. 

 Of course this point-motion does not enable us to fully 

 describe the motion of the man. For instance, it is con- 

 ceivable that he may have turned several somersaults in 

 going upstairs. About such eccentricities in the man's 

 motion the motion of the point may tell us nothing at all. 

 Even had the man been incapable of moving his arms, 

 leg.s, head, etc., — had he been a rigid body — the point- 

 motion would have been incapable of fully describing his 

 motion. As a rigid body the man might have been 

 turned round and about the point without changing its 

 motion. Did he go upstairs backwards or forwards, head 

 or feet uppermost, or partly in one, partly in another of 

 these modes ? Clearly the motion of the point can tell 

 us nothing of all this. The motion of the point can tell 

 us nothing of how the man as a rigid body might have 

 turned about the point ; we should want to know at each 

 instant of the motion which way the man was facing, what 

 was his aspect, and further how he was changing his 

 aspect or rotating about the point. The description of 

 the ideal point- motion would have to be supplemented, 

 even if the man were supposed to be a rigid body, by a 

 description of the rotating or spinning motion. The first 



