OUTLINES OF NATURAL PHILOSOPHY. 



This parabola has its axis perpendicular to the hori- 

 zon, and touches all the parabolas described by the 

 projectile, when thrown in the same vertical plane, 

 and with the same velocity, but at different eleva- 

 tions. 



SECT. VI. 



0? MOTION ACCELERATED OR RETARDED BY A 

 VARIABLE FORCE. 



99. JL HE changes of motion, whether in velocity 

 or direction, are always made gradually, and ne- 

 ver, as it is expressed, per saltuin. Though they 

 may not, like those treated of in the last section, be 

 exactly proportional to the time, they are always 

 proportional to a function of the force and the 

 time jointly, which function vanishes when either 

 the time or the force is equal to nothing. This 

 follows from the fundamental equation of Dyna- 

 mics, F = - or v = F r . 



a. The above is called the LAW OF CONTINUITY, which, 

 in what respects free motions, is never violated. 



This 



