256 DEVELOPMENT AND PURPOSE CHAP. 



as it rests on knowledge of causal interconnection, and to 

 know the causes of things is to know their real nature so 

 far as it is relevant. If science contains any adequately 

 grounded generalisations, science is something more than 

 a knowledge of phenomena. But the descriptive or 

 phenomenalist view when pushed through tends to whittle 

 down its laws to abstract equations applicable only to an 

 ideal world, and concerned with the order of perception 

 only if certain elements in that order happen to correspond 

 to the concepts. Indeed, as thus treated they are in danger 

 of being reduced to tautologies. Consider, for instance, 

 the famous equation which lies at the centre of modern 



This means that the force P applied to a body to change 

 the direction or velocity of its motion, multiplied by the 

 space 5, through which its point of application moves, is 

 equal to one half of the mass to which it is applied multiplied 

 by the square of the velocity. Now as a generalisation hold- 

 ing of forces and masses conceived as realities this is a law 

 of the most far-reaching consequences. But its terms are 

 capable of being defined in a manner which brings it 

 perilously near to a tautology. Thus a force, we are told, 

 if by the name we are merely to describe what we can see, 

 is nothing but an expression for a rate of change of motion, 

 i.e. an acceleration. Acceleration is measured by the square 

 of the final velocity divided by twice the space covered in 

 the time during which the acceleration continues. Calling 

 the acceleration /, this gives the equation 



But the rate of acceleration of different bodies differs, and 

 the measure of this difference is their respective mass, m. 

 Bringing this concept into both sides of the equation, we 



have mfs = $mv*, 



and writing P for mf, we have 



Ps = \mi)\ 

 which now means that the achieved acceleration of a body 



