HISTORICAL NOTE. 



Before the time of Galilei there existed no dynamical theory, and the 

 statical results that had been obtained were of a vague character. The older 

 statical researches professed to give an account of the action of force in certain 

 circumstances, but the forces so considered were at first entirely undefined. 

 The idea had however been established that a force prevents motion, which 

 would take place in the absence of the force, and this gave the notion that 

 force was directed, its direction being opposite to that in which motion would 

 take place if the force were not applied. Further the force exerted to prevent 

 any motion was supposed to be measurable by the tension of a chain pulled 

 in the direction of the force so as to produce the same effect, and the tension 

 itself was supposed to be measurable by the weight the chain would support 

 if it passed over a smooth pulley and produced the required effect. The 

 whole of the ideas thus sketched depended on gravity, there was nothing 

 cosmical about the scheme. 



Galilei discovered by experiment that the velocity of a falling body is 

 proportional to the time during which it has been falling, and was thus led to 

 the idea of acceleration. He recognised in the motion of a body on a smooth 

 horizontal plane that a body, which the existing statical theory would have 

 regarded as under no force, moves uniformly in a straight line, and he was 

 thus led to connect the presence of force rather with the production of 

 acceleration, than with the prevention of motion. 



Newton found that the idea of acceleration, thus introduced by Galilei, 

 availed for the description of the motions of the bodies of the solar system 

 equally with the motion of falling bodies near the earth's surface, and he 

 made the idea of force, as that which produces acceleration, the cardinal notion 

 in his philosophy. Newton also introduced the idea of mass, as distinct from 

 weight, and stated that the mass of a body is the quantity of matter it 

 contains. He formulated his theory in a series of definitions, in the three 

 celebrated Laws of Motion, which he described as Axiomata sive Leges Motus, 

 and in the Scholia attached thereto. We give here a translation of the three 

 Laws of Motion : 



" First Law. Every body remains in its state of rest or of uniform motion 

 " in a straight line, except in so far as it is compelled by impressed forces 

 " to change its state." 



" Second Law. Change of motion is proportional to the impressed moving 

 " force, and takes place in the direction in which that force is impressed." 



" Third Law. Eeaction is always equal and opposite to action ; or the 

 "actions of two bodies one on the other are always equal and oppositely 

 "directed." 



