OF UNDISTURBED MOTION. 69 



instance. Wo observe, that, in general, heavy bodies fall to 

 the ground unless they are supported ; it was therefore con- ^ 

 eluded that all heavy bodies tend downwards: and since 

 flame was most frequently seen to rise upwards, it was in- 

 ferred that flamo was naturally and absolutely light. Had 

 sufficient precaution been employed in observing the effects 

 of fluids on falling and on floating bodies, in examining the 

 relations of flame to the circumambient atmosphere, and 

 in ascertaining the specific gravity of the air at dificrent 

 temperatures, it would readily have been discovered, that 

 the greater weight of the colder air was the cause of the 

 ascent of the flame ; flame being less heavy than common 

 air, but yet having no spontaneous tendency to ascend. 

 And accordingly the Epicureans, whose arguments, as 

 far as they related to matter and motion, were often more 

 accurate than those of their contemporaries, had corrected 

 this error ; for we find in the second book of Lucretius a 

 very just explanation of this phenomenon. 



" See with what force yon river's crystal stream 

 Resists the weight of many a massy beam ; 

 To sink the wood the more we vainly toil, 

 The higher it rebounds with swift recoil. ^ 



Yet fliat the beam would of itself ascend 

 Will no man rashly venture to contend. 

 Thus too the flame possesses weight, though rare, 

 Nor mounts but when compelled by heavier air.*' 



218. Definition. Motion is the change 



of rectilinear distance between two points. 



Scholium 1. Allowing the accuracy of this definition, 

 it appears that two points at least are necessary to consti- 

 tute motion ; that in all cases, when we are inquiring whe- 

 ther or no any body or point is in motion, we must recur 

 to some other point with which we can compare it, and that 



