DYNAMICS. 



287 



Laws of of mechanical philosophy : they form the guide, which, 

 dusted by the tore.: D!' geometry, conducted the great 

 Newton through all the I -ibyrintlis of nature. 



Their simplicity, and the smaliness of iheir nnmber, 

 give to mechanical science a generality and beauty 

 which no other can bo 



Since they act so important a part through the whole 

 of natural philosophy, it must b<- of the greatest con- 

 sequence to establish their truth. 



The first law describes what will happ'.-n to a body 

 if left to itself, and unfolds a property of matter com- 

 monly known by the n;:me of inertia. This law may 

 therefore be called the Law of I t ri'ti. 



The second law describes what will liappen when the 

 body, impelled by any force, is at the same time acted 

 on by several other forces, or has ueen previously put 

 in motion, and therefore may be called the Law of Se- 

 veral Forces. 



The third law maintains that when one body acts on 

 another, the other reacts in a particular manner on the 

 first, and may therefore be called the Law of Reaction. 



Firtt Law, or Late of Inertia. 



A body does not change its state either of rest or of 

 motion, unless in consequence of some external cause. 



The most general principle in philosophical reason- 

 ing, indeed the foundation of all philosophy, is, that in 

 the same circumstances the same event always happens ; 

 that, in like circumstances, a like event happens ; and 

 that the liker the circumstances, the liker is the event. 



This principle is agreeable to the constitution of our 

 minds, and confirmed by universal experience. In or- 

 der, therefore, to shew, that in two given cases the 

 effects shall be alike, we have only to shew that the 

 circumstances, at least the influencing circumstances, are 

 alike. Probably all the circumstances are never alike, 

 and what are the inftm-ncina circumstances can only be 

 known from previous experience on the subject in 

 question. Again, in geometry, that property of a figure 

 which we assume for its definition, involves all the 

 other properties, so that they are deducible from it by 

 a process of reasoning. This arises from the simpli- 

 city of the subject, ami from the circumstance that all 

 the properties are of one kind. The case is different 

 with an object existing in nature. We employ for its 

 definition .such a property, or assemblage of properties, 

 as is sufficient to distinguish it from other objects. But 

 the object may possess many properties which are in- 

 dependent of this, and cannot be deduced from it bv 

 reasoning. Having premised these remarks, we pro- 

 ceed to die proofs of the law. 



Probably no body wliatsoever is absolutely at rest, 

 and every motion which we see commence, is perhaps 

 only a change on some motion that previously existed. 

 But every change evidently depends on mind, or on 

 some other body. With regard to mind, it moves the 

 body which it animates; but since it does not animate 

 every body, it is not necessarily inherent in matter, 

 and therefore its operation is to be considered as that 

 of something external. With regard to other bodies, 

 the direction of the change always depends on the di- 

 rection of xoine other body, and the m.ignitude of the 

 change oiAt~ distance ; and hence we conclude, that if 

 the action of mind and of other bodies were withheld, 

 no change could ensue ; that if the body were absolute- 

 ly at rest, it would continue at rest ; and if in motion, 

 it would continue to move uniformly in a straight line. 

 In abort, we know from experience, that the circum- 



stances on which its state of motion or rest depends, 

 are not within itself, but wholly external. So long, then, 

 as the external circumstances continue the same, . so 

 long, for instance, as there is no external action, its 

 previous state of motion or rest must continue unalter- 

 ed. This is a proof from reason. 



We find accordingly, that, in proportion as we take 

 care to diminish the effect of external action, the mo- 

 tion becomes more nearly rectilineal and uniform. A 

 ball observes this law more nearly when rolled along 

 the horizontal ground which supports its weight, than 

 when projected through the air, where gravity causes a 

 perpetual deflection, and more nearly on the ice which 

 is smooth, than on the pavement where the friction is 

 considerable. We conclude, that if the resistance of the 

 air and of friction, and the action of gravity, were com- 

 pletely removed, the law would obtain with perfect ac- 

 curacy. This is a proof more immediately from experi- 

 ence. 



Farther, by assuming this law and reasoning from it, 

 we arrive at conclusions which agree still more nearly 

 with observation, because they refer to cases in which 

 the causes of deviation have less influence. This holds 

 remarkably with regard to the motions performed in 

 vessels emptied of air, and likewise the celestial mo- 

 tions which seem to be performed in free space. 



Thus the first law is proved partly by reason, part- 

 ly by experience, and partly by its success, when as- 

 sumed as a principle of philosophy. 



It is worthy of remark, that even the first and last 

 of the three proofs are founded also on experience, 

 though more remotely than the second. Thus in the 

 first proof we rea-oa from the nature of matter, but that 

 nature we had learned only from experience. In the 

 last proof we assume the law, and apply it to the phe- 

 nomena of nature, but the success of this assumption is 

 ascertained only by experience. Indeed, it is evident, 

 that all our knowledge of external nature must be from 

 this source, either directly or indirectly through a pro- 

 cess of reasoning. To say that this law enters into our 

 very idea of matter, that it is a law of human thought, 

 and that to suppose the contrary, would be to deny 

 that matter is matter, does not alter, in the smallest de- 

 gree, the foundation of the evidence; for granting that 

 such were our idea of matter, whence did we derive it 

 unless from experience ? If philosophers chuse to set 

 out with defining matter as a substance that possesses 

 the property mentioned in this law, it is well ; but still 

 no application could br made of the law till we had 

 learned from experience that such a substance existed. 

 Besides, it is evident, that though the resistance which 

 matter offers to motion, or the effect it produces on any 

 of our senses, might be sufficient to give us a general 

 idea of matter, or to constitute its definition, yet, not- 

 withstanding this idea, we could conceive matter to 

 have obeyed a law very different from that under dis- 

 cussion. The circumstance that this law was unknown 

 to the ancients, and is a discovery of very modern date, 

 is a striking proof of what we hav,e advanced. The 

 first part of the law indeed which relates to rest, is abun- 

 dantly obvious, because instances of apparent rest, at 

 least, are continually presenting themselves. That part 

 which relates to motion is rather contrary to first ap- 

 pearances, because, in consequence of retarding and de- 

 flecting causes, we never meet with an instance of mo- 

 tion perfectly uniform and rectilineal. But though the 

 whole were a matter of vulgar observation, it would be 



? roper to direct upon it a cautious and philosophical eye. 

 f the facts on which it rests are so very obvious, their 



