ON CONFINED MOTION. 49 



Among all the curves that a body can describe, in moving from one point to 

 another, it always selects that, in which, if its velocity be supposed to be every 

 where multiplied by the distance that it describes, the sum of the infinitely 

 small products will be a minimum, that is, less than in any other path that the 

 body could take. For example, if a body move freely, and therefore with a 

 uniform velocitj^, in any regular curved surface, it will pass from one part of 

 the surface to another by the shortest possible path. This has been called the 

 principle of the least possible action ; it is however merely a mathematical in- 

 ference from the simpler laws of motion, and if those laws were even dilFerent 

 from what they are, the principle would be true in another form, and in ano- 

 ther sense of the word action. 



VOL. I. H 



