2 S3 



DYNAMICS. 



evidence cannot surely be impaired by inquiry. First 

 impressions often need to lie corrected by subsequent 

 reflection. Even ome of the common axioms of geo- 

 metry have l>een contested. Much more must tin- fir-t 

 principles of physical science be open to discussion. It 

 was held as a first principle* by Ari-totle, that the c.irtli 

 is at -rest merely because it appears to be so, and it re- 

 quired nearly two thousand years to shew that this prin- 

 ciple is 



Second Lair, or Law of Several Forces. 



The effect is always proportional to the force impres- 

 of motion. gw j > mi \ jukes place in the direction in which the force 

 arts ; or, more precisely, provided the force exerted is 

 the same, the effect of its momentary action is the same, 

 whether the body was previously at rest or in motion, 

 and whether it is acted on by that force alone, or sub- 

 jected at the same time to the action of several other 

 forces ; so that the effect of the joint action of several 

 forces is an exact compound of their separate effects, or 

 the same as if each had acted successively. Thus the 

 effect of two forces at once on a body in the same di- 

 rection, is equal to the sum of their single or separate 

 effects, &c. 



This is a proposition which cannot be deduced either 

 from the general definition of matter, or from the first 

 law. We can infer, indeed, that when the body is act- 

 ed on by several forces, the motion that ensues must be 

 uniform and rectilineal ; for, though urged in several 

 directions, it can set out only in one direction, and in 

 whatever direction it sets out, it must continue to move 

 uniformly by the first law. 



This seems to be the amount of what can be proved 

 by reasoning from the general principles. The parti- 

 cular direction in which the body shall set out, depends 

 in many cases on the effect of each force ; and that this 

 effect would be the same as when the force acted alone, 

 could be gathered only from experience. To say that 

 this law is a mere affair of definition, and that in all cases 

 we measure a force by the effect which it is found to 

 have produced, -whether alone or in combination, seems 

 to be very unphilosophical. We measure a force by 

 the effect which we find it has produced in a given 

 case; (the more nearly the body was at rest, and the 

 less under the influence of other forces the better,) but 

 experience alone could inform us, that the measure de- 

 duced in this case would exactly agree wkh the effect 

 of the same force in all other cases. If, indeed, the 

 influencing circumstances in all other cases were the 

 same ; we would be justified in concluding that the ef- 

 fect would be the same. But how could we know un- 

 less from experience, that the circumstance of other 

 forces acting in combination would not be an iiifluencing 

 circumstance ? 



Analogical experience could by no means have led 

 us to the conclusion. We find that a very slight diffe- 

 rence of circumstances is sufficient to change the me- 

 chanical action of bodies. We find that at sensible 

 distances bodies attract, while at insensible distances 

 they repel one another, so that a mere difference of dis- 

 tance, less than the millionth part of an inch, is suffi- 

 cient to change the action from attraction to repulsion, 

 that i<, from one direction to another directly opposite. 

 We find in chemistry, that two bodies, which separately 

 burn animal matter, yet in a state of combination exert 

 no such action. How could we know unless from ex- 

 perience, that in the case offerees also, the qualities of 



the ingredient are not in great measure lost in those 

 nf the compound ? In Mtbnating the effect on the body, 

 we have a difficulty in abstaining from the notion that 

 the body has been immediately under the influence of 

 all the forces ; but we should consider that an event has 

 intervened, that a new single action has arisen from all 

 the separate actions, that it is only a knowledge of this 

 action which can enable us to calculate the effect, and 

 that this action can be learned only by experience. 

 Many attempts have been made to demonstrate the law, 

 but the view given above is sufficient to shew that such 

 attempts must be fruitless. The same conclusion i> 

 suggested, when we carefully analyse the most cele- 

 brated of these pretended demonstrations. The gene- 

 ral definition of matter, and the first law, are found to 

 be totally inadequate to conduct to the second. The 

 mathematician, labouring under the burden of his task, 

 finds himself, at every step, obliged to make assump- 

 tions of the same nature as the proposition to be proved. 

 Thus lately, Dr Olynthus Gregory, in his valuable 

 work on mechanics, (p. 16.) first assumes, that when 

 forces act in the same direction, the result is obviously 

 equal to the sum of the separate effects, and when in 

 opposite directions, equal to their difference. He, in- 

 deed, wishes to give this principle the air of demonstra- 

 tion, by referring to the definition of force, and the 

 third law of motion. But it has appeared already that 

 the mere definition is quite insufficient, and, as to the 

 third law, it is perhaps even less obvious than the se- 

 cond. Having made this assumption, he advances with 

 its aid to the case of two forces acting at an angle. 

 But he has not gone far, when he is obliged to make 

 another assumption, viz. that " if to a material point 

 already kept in equilibrium by a system of forces, ano- 

 ther system is applied also in equilibrium, this will not 

 destroy the pre-existing equilibrium." This is by no 

 means manifest, from the general definitions of force 

 and of body. It is a second assumption of the very 

 same nature as the proposition to be proved. It as- 

 sumes that the action of forces will not be altered by 

 their composition with other forces. It is in fact a case 

 of the law in question ; nor is it a case either more ob- 

 vious to reason, or more easily confirmed by experience, 

 than many other cases. Other assumptions of exactly 

 the same nature are drawn in as he advances, and yet 

 he professes to tread in the path of the celebrated D'A- 

 lembert, and even to improve upon his demonstration, 

 after it had been already improved by Francseur. 



There is an illusion on this point, arising from our 

 mathematical habits. In pure geometry, the length of 

 the reasoning that conducts us to the conclusion, does 

 not in the least impair the certainty of that conclusion, 

 or our conviction of its truth. Each previous step 

 being certain, the last must be certain also. \\"e are 

 apt to have the same opinion of physical science ; but in 

 doing so we shall often be egregiously mistaken. If 

 the principle from which we set out is doubtful, the 

 conclusion must be at least as doubtful, however pure 

 our subsequent reasoning, and however free it may nave 

 been from other assumptions. But if, at a number of 

 stages in the reasoning, we assume other doubtful prin- 

 ciples, the conclusion must depend on the chance that 

 all these principles are true, and is therefore probably 

 much more doubtful than any of them ; just as in throw- 

 ing a die there is much less chance for an ace in each of 

 ten successive throws, than in one throw. If we la- 

 bour so much to shew that this law is indemonstrable, 

 it is not because we undervalue the force and advan- 



Motion. 



