OF UNDISTURBED MOTION. 69 



combination or separation of relations that is considered ; 

 in the same manner as by combining the relation of son to 

 father, and brother to brother, we obtain the relation of 

 nephew to uncle, so by combining the motion of a man 

 walking in a ship, with the motion of the ship, we deter- 

 mine the relative velocity of the man with respect to the 

 earth's surface. 



Scholium 2. When an arm is made to slide upon a 

 bar, and a thread, fixed to the bar, is made to pass, over a 

 pulley at the end of the arm next the bar, to a slider 

 which is moveable along the arm, the slider moves on the 

 arm with the same velocity as the arm on the bar; but if 

 the thread, instead of being fixed to the slider, be passed 

 again over a pulley attached to it, and then brought back 

 to be fixed to the arm, the motion of the slider will be only 

 half that of the arm; and this will be true in whatever po- 

 sition the arm be fixed. Here we have two motions in the 

 slider, one in common with the arm, and the other pecu- 

 liar to itself, which may be either equal or unequal to the 

 first ; and by tracing a fine on a fixed plane, with a point 

 attached to" the slider, we may easily examine the joint 

 result of both the motions. 



Scholium 3. The line described by the tracing point 

 of this apparatus will be precisely the same, whether it is 

 simply drawn along by the hand in the given direction, or 

 made to move on the arm with a velocity equal to that of 

 the arm, or when the arm is in a diff*erent position, with 

 only half that velocity. The line AB, for example, may 



be either simply drawn in the y D ji 



direction AB, or it may be 



traced by the equal motions 



AC and AD of the arm and its ^ q e 



slider, or by the unequal motions AE and AF. 



