Volume 1
A course of lectures on natural philosophy and the mechanical arts / by Thomas Young.
- Thomas Young
- Date:
- 1845
Licence: Public Domain Mark
Credit: A course of lectures on natural philosophy and the mechanical arts / by Thomas Young. Source: Wellcome Collection.
Provider: This material has been provided by King’s College London. The original may be consulted at King’s College London.
80/670 page 46
![1 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, mil 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 tlie 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 measiu’e 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 tlu-ee 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,t and Laplace,J have deduced the laws of pressure more immediately from the principle of the equality of the elfects 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 pressui'e 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 i i which the forces would separately produce in contrary dii'ections, are ^ | equal; and that any one pressure will counterbalance two others, when it j j would produce a momentum equal and contrary to the momentum which j t 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 j 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 J an action is precisely half of the continued action of each force ; conse- t quently, since the halves completely counteract each other, the wholes will I [. do the same. And a similar mode of reasoning may be extended to any \ i number of forces opposed to each other. * Com. Petrop. I. 12G. t On the Principles of Mechanics, Hist, et Mem. de PAcad. 1769, p. 278, and * Opuscula, I. and VI. t Mecanique Celeste. See also Celestial Mechanics of Laplace (by Young), . ( P-87. . ,](https://iiif.wellcomecollection.org/image/b21301840_0001_0080.jp2/full/800%2C/0/default.jpg)
