AND THE NATURE OF FORCE. 501 



A tangential motion between two surfaces is impossible, if tbe 

 surfaces are in contact, since the matter would be continuous in 

 passing from one side of tbe surface to the other, and continuous 

 matter is rigid by our assumption. Tangential motion can only take 

 place between two surfaces when they are really divided, that is, 

 when there is a vacuum space, no matter how thin, between them. 



Suppose a smooth rigid particle falling down a smooth curved tube 

 under the action of gravity, what is the nature of the reaction of 

 the tube, which is supposed to consist of continuous matter, and 

 consequently to be rigid 1 



The motion conferred by gravity on the particle may be resolved 

 into a component at right angles to the tube, and one tangential to 

 it. The reaction is due to the rapid impacts which arise from the 

 former motion, and the velocity is due to the latter motion. The 

 particle never remains in contact with the tube. Its contacts are 

 instantaneous, that is to say, occupy no time. It is always in the 

 air, so to speak. 



Thus no forces can be exerted between the parts of a rigid body, 

 simply because no motion can take place between them. It will be 

 observed that our definition of force is based upon rectilinear 

 motion ; but there is another kind of motion which gives rise to 

 actions between the parts of bodies. This is angular motion. If a 

 body be set spinning about an axis, we know that a strain takes 

 place in it, and if the angular motion is very great, the body may 

 fly to pieces. 



Is there no strain between the parts of a rigid body when thus set 

 spinning 1 We answer, No. We can explain all strains in ordinary 

 bodies by our definition of force, but the idea of rigidity is utterly 

 incompatible with the idea of forces acting between the parts of the 

 rigid body. We are thus relieved from the necessity of attempting 

 to pursue the idea of force through a nevei--ending division of matter, 

 to which those are subjected who hold the idea that the conservation 

 of relative motion depends upon resilience. 



Rigidity is an elementary idea, which can be defined but is incapable 

 <.)f being analyzed or accounted for. 



It will be observed that we do not assert that a body neceosarily 

 moves when forces act on it. Thus a rigid body, struck by equal, 

 blows on opposite sides at the same instant, will not move. The' 

 whole motion in this case will be confined to the striking bodies. 



