222 THE GRAMMAR OF SCIENCE 



hodograph of the velocity-diagram, treated as if it were 

 itself the map of an independent motion. Acceleration 

 therefore stands in just the same relation to velocity as 

 velocity stands to the position-step. As change of position 

 is represented by the steps drawn as rays of the velocity- 

 diagram or first hodograph, so change of velocity is 

 represented by the steps drawn as rays of the acceleration- 

 diagram or second hodograph.^ Whatever may be 

 demonstrated of the position-step and velocity will still 

 hold good if the words position-step and velocity be 

 replaced by the words velocity and acceleration respectively. 



§ I 3. — Acceleration as a Spurt and a Shunt 



We must now investigate somewhat more closely this 

 notion of acceleration as a proper measure of the change 

 in velocity. In a certain interval of time the speed of 

 the point P (Fig. 9, p. 210) changes from a number of 

 miles per minute represented by the number of linear 

 units in IV^ to the number of miles per minute represented 

 by the linear units in IV^, the speed has in this case (see 

 Fig. 13) quickened, or there has been what we may term 

 a spurt in the speed. Further, the bearing of the motion 

 has changed ; instead of the point P moving in the direction 

 IV^, it now moves in the direction IV^, that is to say, the 

 direction of the motion has received a shunt. Thus the 

 total change in the velocity of P as it moves from P to 

 Pg consists of a spurt and a shunt. When a train quickens 

 its speed from 40 to 60 miles an hour, and instead of 

 running due north runs north-east, we may describe its 

 motion as spurted and shunted ; technically, we say that 

 its velocity has been accelerated. Acceleration has thus 

 two fundamental factors — the spurt and the shunt.^ If 

 we consider the perceptual world around us, it is clear 



1 We might proceed in the same manner to measure the change in accelera- 

 tion by drawing a third hodograph. Fortunately this third hodograph is 

 rarely, if ever, wanted. The concepts which practically suffice to describe 

 our perceptual experiences of change are position, velocity, and acceleration. 



2 Spurt in scientific language includes a retardation or slackening of speed 

 as a negative spurt. 



