THE MEANING OP PERCEPTION 



169 



that is, differences in measurements of y and a; and i that may 

 be as small as we like; ^ is a measurement of space in a certain 

 (vertical) direction; x is also a measurement of space in a 

 horizontal direction perpendicular to that of ?/ ; ^ is a time 



measurement, and v is a velocity — that is, it is a ratio, -. Time, 



in scientific investigations is always a space measurement; 

 if, for instance, we use a clock, time is the position of the hands 

 relative to their zero position. Thus the equation represents 

 nothing but the ratios of measurements of space; the crest of 



longitudinal 

 motion of crest 



(at the moment t,j 

 mean le^el 



(ai We moment tg) 



Fia. 48. — Diagram of a Wave in Two Positions. 



the wave, which we may take to be an Atlantic roller travelling 

 uniformly, moves with a certain velocity, -y — that is, at a certain 

 moment, t^, the crest of the wave, which is travelling in the 

 direction ox, is at a certain position {x=^o), and the water level 

 is at a certain height {y-^. A moment later {t^ the crest is at 

 a different position, x^, and the water level, which was originally 

 at the position represented by y^, has now sunk to the posi- 

 tion 2/2- Obviously, then, our differential equation tells us liow 

 the crest of the wave is displaced along the direction ox, while 

 the water level at any position in the line ox is being displaced 

 along the up and down direction oy. It takes a moment of 



