60 OF UNDISTURBED MOTION. 



if a single atom existed alone in the universe, it could nei- 

 ther be said to be in motion nor at rest. This may seem 

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

 sequence of admitting the definition, and the paradox is 

 only owing to the diflSculty of imagining the existence of a 

 single atom, unsurrounded by innumerable points of space 

 which we represent to ourselves as immoveable. 



Scholium 2. It has been for want of a precise defini- 

 tion of the term motion, that many authors have fallen into 

 confusion with respect to absolute and relative motion. 

 For the definition of motion, as the change of rectilinear 

 distance between two points, appears to be the definition 

 of what is commonly called relative motion ; but, on a strict 

 examination, we shall find, that what we usually call abso- 

 lute motion is merely relative to some space, which we 

 imagine to be vnthout motion, but which may very often be 

 so in imagination only. The space, which we call quiescent, 

 is in general that which is in the neighbourhood of the 

 earth's surface: yet we well know, from astronomical con- 

 siderations, that every point of the earth's surface is per- 

 petually in motion, and that the direction of its motion is 

 even continually varying : nor are there any material objects 

 accessible to our senses, which we can consider as abso- 

 lutely motionless, or even as completely motionless with 

 regard to each other, since the continual variation of tem- 

 perature, to which all bodies are liable, and the minute agi- 

 tations, arising from the motions of other bodies with which 

 they are connected, will always tend to produce some 

 imperceptible change of their distances. 



Sgholium 3. These minute changes are neglected in 

 the elementary operations of practical geometry : it must 

 not, however, be forgotten that they exist, and it is right 

 to make it one of the postulates, which are the basis af 



