DYNAMICS. 27 



termining A or B, &c. ; each of these coefficients 

 is therefore either indeterminate, or it is equal to 

 nothing ; but no one of them can be indeterminate, 

 or can admit of innumerable values, otherwise V 

 itself would be indeterminate, and might have more 

 values than one at the same instant, which is im- 

 possible. A and B, &c. must therefore be each 

 equal to 0, so that V = C ; in other words, the 

 velocity remains uniform. 



D\ALEMBERT has given a different demonstration of 

 this, Dy?iamique 9 chap. !. See also another by 

 EULER, Mechanica, torn. 1. 63. 



This proposition is the first law of motion, and, toge- 

 ther with the proposition 21. constitutes what is 

 termed the INERTIA or INACTIVITY of matter. 



d. The inertia has been considered by some philoso- 

 phers as merely the expression of a law of human 

 thought, by which we are detennined, when we 

 see a change, to infer the action of a cause. This 

 seems to be inaccurate. That a change never hap- 

 pens in the motion of any body, without an equal 

 and opposite change in the motion of some other 

 body, is as much a fact, independent of the mind 

 that perceives it, as impenetrability, cohesion, or any 

 other phenomenon of the material world. 



e. If a body move in a curve, the continued action of 

 an external force must be inferred: if that action 

 were to cease at any point, the body would continue 

 its motion in a straight line touching its curvilineal 

 path in that point. 



61. The cause of motion is denominated Force, 

 and a force is always measured by the effect, that 



is, 



