20 LECTURE II. 



the sun and the whole solar system, he would be slowly movmg among the 

 starry worlds which surround them. Now with respect to any ettects within 

 the ship, all the subsequent relations are of no consequence, and the change 

 of his rectilinear distance from the various parts of the ship, is all that needs 

 to be considered in determining those effects. In the same manner, if the ship 

 appear, by comparison with the water only, to be moving through it with the 

 velocity of three miles an hour, ami the water be moving at the same time in 

 a contrary direction at the same rate, in consequence of a tide or current, the 

 ship will be at rest with respect to the shore, but the mutual actions of the ship 

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

 ship in motion. 



It is not sTifficient to observe the increase or decrease of distance of a mov- 

 ing point from another single point only: we must compare its successive si- 

 tuations with many other points surrounding it; and for this purpose these 

 points must be at rest among themselves, in order to be considered as belong- 

 ing to a quiescent space or surface ; which may be defined as a space or sur- 

 face, of which all the points remain always at equal distances from each other, 

 without any external influence. In this sense we must call the deck of the 

 ship a quiescent surface, whether the ship be at anchor or under sail : but we 

 must not consider a surface revolving round a centre as a quiescent surface ; 

 for it will appear hereafter that no such motion can exist without the influ- 

 ence of a centripetal force, which"renders it improper for determining the af- 

 fections of a moving body. 



When a point is in motion with respect to a quiescent space, it is often 

 simply denominated a moving point, and the right line joining any two of its 

 places, immediately contiguous to each other, is called its direction. If it re- 

 mains 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 definition, by supposing a 

 right line to be drawn through two successive points in which it is found, and 

 then if these points be conceived to approach each other without limit, we 

 shall have the line of its direction. Now such a line is called in geometry a 



