62 OF UNDISTURBED MOTION. 



but the mutual actions and relations of the ship and the 

 water will be the same, as if the water were actually at rest, 

 and the ship in motion, Laplace (§ J. P. 3.) views this 

 subject in the more popular Hght, and employs much mathe- 

 matical reasoning", to deduce from it the principles, here laid 

 down as fundamental. (§ 4. P. 14. §. 5. P. 15.) 



219. Definition. A space or surface, 



of which all the points remain spontaneously 



at equal distances from each other, is said to 



be quiescent, or at rest within itself. 



Scholium. The term " spontaneously" is introduced, 

 in order to exclude, from the definition of a quiescent 

 space, any surface, of which the points are only retained 

 at rest by means of a centripetal force, while they revolve 

 round a common centre ; for, with respect to such a re- 

 volving space or surface, the motions of any body will de- 

 viate from the laws which govern them in other cases. 



220. Definition. When a point is con- 

 sidered as in motion with respect to a quies- 

 cent space, the right line, joining any two of 

 its proximate places, is called its direction, 

 and such a point is often simply denominated 

 a moving point. 



Scholium. Supposing the point to remain continually 

 in one right line drawn in the quiescent space, that line is 

 always the line of its direction ; if it describes several right 

 lines, each line is the line of its direction as long as it 

 continues in it; but if its path becomes curved, we can no 

 longer consider it as perfectly coinciding at any time with 

 a right line, and we must recur to the letter of the defini- 



