46 LECTURE VII. 



time. Hence the smallest possible momentum is said to be more than 

 equivalent to the greatest possible pressure : a very light weight, falling 

 from a very minute distance, will force back a very strong spring, although 

 often through an imperceptible space only. But the impulse of a -stream of 

 infinitely small particles, like those of which a fluid is supposed 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 difficulty in extending the laws of the composi- 

 tion of motion to the composition of pressure. For since we measure 

 forces by the motions which they produce, it is obvious that the composi- 

 tion of forces is included in the doctrine of the composition of motions ; 

 and when we combine three forces according to the laws of motion, there 

 can be no question but that the resulting motion is truly determined in all 

 cases, whatever may be its magnitude ; nor can any reason be given why 

 it should be otherwise, when this motion is evanescent, and the force 

 becomes a pressure. The case is similar to that of a fraction, which may 

 still retain a real value, when both its numerator and denominator become 

 less than any assignable quantity. Some authors on mechanics, and 

 indeed the most eminent, Bernoulli,* Dalembert,1* and Laplace,^ have 

 deduced the laws of pressure more immediately from the principle of the 

 equality of the effects 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 intri- 

 cate. 



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 equal or pro- 

 portionate 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 contrary 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 others, when it 

 would produce a momentum equal and contrary to the momentum which 

 would be derived from the joint result of the other forces. For, supposing 

 each [either] of two forces opposed 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 continued action of each force ; conse- 

 quently, since the halves completely counteract each other, the wholes will 

 do the same. And a similar mode of reasoning may be extended to any 

 number of forces opposed to each other. 



* Com. Petrop. I. 126. 



f On the Principles of Mechanics, Hist, et Mem. de 1'Acad. 1769, p. 278, and 

 Opuscula, I. and VI. 



t Mecanique Celeste. See also Celestial Mechanics of Laplace (by Young), 

 p. 87. 



