x Room for Voluntary Determination. 181 



Every line, whether straight or curved, may be 

 described as produced by the motion of a point P 

 this is actually the case when it is drawn by 

 a pencil and consequently the equation which 

 describes the direction of a curve at any place 

 may also be read as describing the direction of the 

 motion of P at that place. Equations usually speak 

 a perfectly unambiguous language, but in singular 

 solutions an exception arises ; the equation which 

 describes the direction of motion at that point of any 

 C where it touches S will be equally satisfied by P 

 either continuing to move along its C, or at that 

 point leaving the C and moving along S. So that the 

 equation which describes the direction of the motion 

 of P at any point of S does not absolutely determine 

 its path, but leaves undetermined which of two paths 

 it is to take, those paths being along curves of unlike 

 kinds. 



Where there is thus mechanical indetermination, 

 there is, or may be, room for voluntary determination 

 to enter. An agency like the Will, which is not 

 properly a force, inasmuch as it cannot exert energy, 

 may nevertheless determine the motion of a point 

 along one of these two curves rather than the other. 

 It is no objection to this that the indetermination 

 shown in a singular solution cannot be realised under 

 experimental conditions. It is impossible to do this, 

 just as it is impossible to make a cone stand on its apex. 

 But it does not seem by any means impossible that it 

 may be realised among molecular or atomic actions. 



