

ATOJL 



be applied to the analyii* of problema connected with material bodies by 

 Morning tJm* t for the purpose of this analysis, to be homogeneous. All that 

 m required to make the results applicable to the real case is that the smallest 

 portion* of the substance of which we take any notice shall be sensibly of the 

 ^yp^ ijjj,^ Thua, if a railway contractor has to make a tunnel through a hill 

 of gravel, and if one cubic yard of the gravel is so like another cubic yard 

 that for the purposes of the contract they may be taken as equivalent, then, 

 in estimating the work required to remove the gravel from the tunnel, he may, 

 without fear of error, make his calculations as if the gravel were a continuous 

 But if a worm has to make his way through the gravel, it makes 



the greatest possible difference to him whether he tries to push right against 

 a piece of gravel, or directs his course through one of the intervals between 

 the pieces; to him, therefore, the gravel is by no means a homogeneous and 

 continuous substance. 



In the same way, a theory that some particular substance, say water, is 

 homogeneous and continuous may be a good working theory up to a certain 

 point, but may fail when we come to deal with quantities so minute or so 

 attenuated that their heterogeneity of structure comes into prominence. Whether 

 this heterogeneity of structure is or is not consistent with homogeneity and 

 continuity of substance is another question. 



The extreme form of the doctrine of continuity is that stated by Descartes, 

 who maintains that the whole universe is equally full of matter, and that this 

 matter is all of one kind, having no essential property besides that of extension. 

 All the properties which we perceive in matter he reduces to its parts being 

 movable among one another, and so capable of all the varieties which we can 

 perceive to follow from the motion of its parts (Principia, IL 23). Descartes's 

 own attempts to deduce the different qualities and actions of bodies in this way 

 are not of much value. More than a century was required to invent methods 

 of investigating the conditions of the motion of systems of bodies such as 

 Descartes imagined. But the hydrodynamical discovery of Helmholtz that a 

 vortex in a perfect liquid possesses certain permanent characteristics, has been 

 applied by Sir W. Thomson to form a theory of vortex atoms in a homogeneous, 

 incompressible, and frictionless liquid, to which we shall return at the proper 

 time. 



