THE LAWS OF MOTION 295 



appreciating the statements that we may legitimately make 

 with regard to the dance not only of two but of any 

 number of corpuscles. In general we may assert that 

 whether we are dealing with the continuous ether or with 

 discontinuous atoms and molecules, then if we fix our 

 attention on a geometrical point which symbolises an ele- 

 ment of ether, atom, or molecule, the acceleration {not the 

 velocity) of this point will depend on the position of this 

 point or element relative to other points or elements (and 

 possibly in certain cases on its velocities relative to those 

 points or elements). For particles of gross " matter," on the 

 other hand, we find it as a general (if not invariable) rule suffi- 

 cient to assert that the mode in which their velocity is 

 being spurted and shunted depends solely on their position 

 relative to other particles. In particular, if two particles be 

 alone in the field, their mutual accelerations will depend 

 on their relative position and may be conceived as taking 

 place in the line joining them, but in opposite senses. 



^ 6. — Velocity as an Epitome of Past History. Mechanism 



and Materialism 



There are one or two points in these statements which 

 deserve special notice. If we avoid the metaphysical idea 

 of force, and consider causation as pure antecedence in 

 phenomena (pp. 1 28-1 3 1), then the cause of change of 

 motion or acceleration must in our conceptual model of 

 the phenomenal world be associated with relative position. 

 The given velocities of a system at any time may be 

 looked upon as the sum of the past changes of motion ; 

 or the causes of a given motion can only be conceived as 

 lying in the totality of all past relative positions of the 

 system. Thus force, as the conceptual idea of moving 

 cause, could only be defined as the history of the relative 

 positions of a system. This history determines the actual 

 velocities of the parts of the system, while actual position 

 determines how the velocities are instantaneously changing. 

 The " actual position," however, is the conceptual .equivalent 

 of the mode in which we perceptually distinguish coexisting 



