14 LECTURE II. 



investigation of many particular problems of importance, to obtain, in the 

 first place, a clear conception of the properties and affections of motions of 

 all kinds. 



One of the ancient philosophers, on being asked for a definition of motion, 

 is said to have walked across the room, and to have answered, you see it, 



j but what it is I cannot tell you. It does not, however, appear absolutely 

 ^necessary to appeal to the senses for the idea of motion ; for a definition is 

 the resolution of a complex idea into the more simple elements which com- 

 pose it ; and, in the present instance, these elements are, the existence of 

 two points at a certain distance, and, after a certain interval of time, 

 the existence of the same points at a different distance ; the difference of the 

 distances being supposed to be ascertained according to that postulate of 

 geometry (which has in general been tacitly understood, but which I 

 have expressly inserted in the geometrical part of my syllabus), requiring 

 that the length of a line be capable of being identified, whether by the effect 

 of any object on the senses, or merely in imagination. 



Motion, therefore, is the change of rectilinear distance between two points.* 

 Allowing the accuracy of this definition, it appears that two points are 

 necessary to constitute motion ; that in all cases when we are inquiring 

 whether or no any body or point is in motion, we must recur to some 



, 'other point which we can compare with it, and that if a single atom existed 

 alone in the universe, it could neither be said to be in motion nor at rest. 

 This may seem in some measure paradoxical, but it is the necessary con- 

 sequence of our definition, and the paradox is only owing to the difficulty 

 of imagining the existence of a single atom, unsurrounded by innumerable 

 points of a space which we represent to ourselves as immoveable. 



It has been for want of a precise definition of the term motion, that 

 many authors have fallen into confusion with respect to absolute and rela- 

 tive motion. For the definition of motion, as the change of rectilinear 

 distance between two points, appears to be the definition of what is com- 

 monly called relative motion ; but, on a strict examination, we shall find, 

 that what we usually call absolute motion is merely relative to some space 



, which we imagine to be without motion, but which is so in imagination 

 only. The space which -we call quiescent is in general the earth's surface ; 

 yet we well know, from astronomical considerations, that every point of 

 the earth's surface is perpetually in motion, and that in very various 

 directions : nor are any material objects accessible to our senses which we 

 can consider as absolutely motionless, or even as motionless with regard to 

 each other ; since the continual variation of temperature to which all bodies 

 are liable, and the minute agitations arising from the motions of other 

 bodies with which they are connected, will always tend to produce some 

 imperceptible change of their distances. 



When, therefore, we assert that a body is absolutely at rest, we only 

 mean to compare it with some large space in which it is contained : for 

 that there exists a body absolutely at rest, in as strict a sense as an abso- 

 lutely straight line may be conceived to exist, we cannot positively affirm ; 

 and if such a quiescent body did exist, we have no criterion by which it 

 * See Descartes Princip. Philos. Part ii. 25. 



