60 LECTURE VII. 



to consist, striking an obstacle in a constant succession, may be counteracted 

 by a certain pressure, without producing any finite motion. 



Nothing however forbids us to compare two pressures, by considering the 

 initial motions which they would produce, if the opposition were removed ; 

 nor is there any dilficulty in extending the laws of the composition of motioa 

 to the composition of pressure. For since we measure forces by the motions, 

 which they produce, it is obvious that the composition of forces is included 

 in the doctrine of the composition of motions; and Avhen we combine three 

 fprces according to the laws of motion, there can be no question but that the 

 resulting motion is truly determined in a:Il cases, whatever may be its magni- 

 tude; nor can any reason be given* why it should be otherwise, when this mo- 

 tion is evanescent, and the force becomes a pres^re. The case is similar to 

 that of a fraction, which may still retain a real valud, when both its numerator 

 and denominator become less than any assignable quantity. Some authors 

 on mechanics, and indeed the most eminent, Bernoulli, Dalembert, and La- 

 place, have deduced the laws of pressure, more immediately, from the principle 

 of the equality of the eifects of equal causes ; and the demonstration may be 

 found, in an improved form, in the article Dynamics of the Supplement of the 

 Encyclopaedia Britannica ; but its steps are still tedious and intricate. 



We are therefore to consider the momentum, or quantity of motion, which 

 would be produced by any force in action, as the measure of the pressure 

 occasioned by it, when opposed; and to understand by e()ual or proportion- 

 ate pressures, such as are produced by forces which would generate equal or 

 proportionate momenta in a given time. And it may be inferred, that two con- 

 trary pressures will balance each other, when the momenta, which the forces 

 would separately produce, in contrary directions, are equal ; and that any 

 one pressure will counterbalance two otl>ers, when it would produce a mo- 

 mentum, ccjual and contrary to the momentum which would be derived from 

 the joint result of the other forces. For, supposing each of two forces op- 

 posed to each other to act for an instant, and to remain inactive for the next 

 equal instant, while the other force is exerted, it is obvious that these effects 

 will neutralise each other, so that the body, on which they are supposed to 

 operate, will retain its situation ; but such an action is precisely half of the con- 

 tinuedactionof each force ; consequently, since the halves completely counteract 



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