AND ITS SELF-CONSERVATION. 159 



Since, then, the quantity of force impressed by and 

 upon each body, in the case of any gravitating pair, 

 is precisely the same whatever the relative mass, it 

 follows, necessarily, that the two bodies will each 

 acquire, through their mutual action, precisely the 

 same quantity of motion as the other. And yet, it is 

 not to be forgotten that the quantity of motion de- 

 pends directly and essentially upon the quantity of 

 matter. 



It is here, indeed, that we find time entering in a 

 definite, quantitative way, into consideration as an essen- 

 tial element of motion. We saw at an earlier stage of 

 our inquiry, that motion is a change of space-relations. 

 But change necessarily implies succession. Hence, 

 motion can take place only as a continuous modification 

 of space-relation between bodies. 



Fundamentally, however, the space-relations exist 

 between the ultimate force-centers. We have, indeed, 

 already traced the law of variation of that order of 

 space-relations directly constituted by the force of 

 gravity. It is required now, especially, to trace the 

 law of change of space-relations as relations of distance; 

 for this is conspicuously the class of space-relations whose 

 change constitutes motion. 



Note now, again, that all space-relations, whether of 

 distance or of direction, are primarily relations between 

 ultimate force-centers; whence it follows that the quan- 

 tity of change in those relations will necessarily depend 

 directly upon the number of force-centers involved in 

 the change. The greater the number of force-centers 

 that is, the greater the quantity of " matter," the space- 

 relations of which undergo ^change the greater must 



