STATEMENT OF LEIBNIZ S PHILOSOPHY 93 



same quantity of force is conserved. And in fact action 

 is nothing but the exercise of force, and amounts to the 

 product of the force into the time 1 .' Accordingly this 

 motive force or vis viva, the amount of which is constant, 

 includes direction, as well as quantity, of motion. For 

 the measure of it is height, or position relatively to the 

 surface of the earth. Descartes's l quantity of motion ' 

 (mv) is the effect of a given force regarded merely as acting 

 during a given time. Leibniz's vis viva (mv 2 ) is the effect 

 of a given force regarded also as acting through a given 

 distance. And Descartes did not take account of the 

 direction of motion, because he did not take into con- 

 sideration the distance through which the force acts. 



Leibniz's Theory of Matter. 



(i) Materia prima. 



This doctrine of the conservation of force, as Leibniz 

 conceives it, involves the rejection of the theory that 

 material substance is nothing but extension 2 . Extension 



for motion requires time, but it none the less involves force.' Lettre 

 a Des Maizeaux (1711) (E. 676 a ; G. vii. 534). 



1 Lettre a Bayle (undated) (E. 192 a ; G. iii. 60), cf. G. Math, 

 vi. 117. Of course, from one point of view, Leibniz's statement is 

 not quite accurate, since there are many forms .of energy of which 

 it takes no account. It is, however, on right lines. And indeed 

 (as Du Bois-Keymond and Stallo have pointed out) Leibniz in one 

 passage anticipates the modern theory of the transformation of 

 energy (the apparent loss of molar motion being represented by 

 increase of molecular motion), although the idea was not worked 

 out until a much more recent time. ' I had maintained,' says 

 Leibniz, ' that active forces are conserved in the world. It is objected 

 that two soft, or non-elastic bodies, when they collide, lose some 

 of their force. I answer, No. It is true that the "wholes" lose 

 force in respect of their total motion ; but the parts received it, 

 being agitated within the whole by the force of the collision. Thus 

 it is only apparently that the loss occurs. The forces are not 

 destroyed, but dissipated among the particles. That is not losing 

 them but doing as is done by those who turn large money into 

 small change.' Cinquieme Lettre a Clarke, 99 (E. 775 a; G. vii. 414). 



2 Projet d'une Lettre a Arnauld (1686) (G. ii. 72) : 'Extension is an 

 attribute which cannot constitute a concrete [accompli'} being. We 

 cannot draw from it any activity or change. It expresses only 

 a present state, and not at all the future and the past, which the 

 notion of a substance ought to express. When two triangles are 



