particularly as given hy French Writers. 29 



nics the elementary principles of the science are in various 

 ways simplified and established. The most distinguished 

 among the latter deduce, as will be shown, two independent 

 principles from experience ; and what I wish especially to offer 

 to the consideration of mathematicians is the question how far 

 these systems can be identified, and which is the more true 

 and logical one : — Whether with three laws we have some- 

 thing superfluous, or with two something defective. 



In stating the three laws of motion for the purpose of this 

 comparison, we must, in order to avoid confusion and false 

 reasoning, reject entirely their application to statics. If we 

 do this, (which has not always been sufficiently attended to,) 

 and express them in the simplest form as they regard the mo- 

 tion of bodies, we shall have them as follows : — 



Law 1. A body in motion, not acted upon by any force; 

 will move on in a straight line with a uniform velocity. 



Law % When any force acts upon a body in motion, the 

 change of motion which it produces is in the direction, and 

 proportional to the magnitude, of the force which acts. 



Law 3. When pressure communicates motion to a body, 

 the moving force is as the pressure. 



If we carefully look in the best French treatises for the 

 principles which they borrow from experience, we shall find 

 them to be these two : 



Firsts The law of inertia^ that a body not acted upon by 

 any force would go on for ever with a uniform velocity. 



Second^ That the velocity communicated is proportional to 

 the force. * 



The first of these principles coincides with the first law of 

 motion, which the best French, as well as English writers, 

 agree in considering as a result of experience, -f* The se- 

 cond and third laws of motion are both reduced to the second 

 principle of the foreign mechanicians ; and the point to be 

 considered is, whether the steps of this part of the reasoning 

 are allowable and satisfactory. *' ^^^^^^ ^' 



The principle that the velocity communicated is as the pres- 

 sure, leads immediately to the inference that the accelerating 

 force is as the pressure, and consequently, for the same body, 



f See Note A, p. 36. t See Note B, p. 37. 



