The mathematical principles of mechanical philosophy, and their application to elementary mechanics and architecture, but chiefly to the theory of universal gravitation / [John Henry Pratt].
- Pratt, John H. (John Henry), 1809-1871.
- Date:
- 1842
Licence: Public Domain Mark
Credit: The mathematical principles of mechanical philosophy, and their application to elementary mechanics and architecture, but chiefly to the theory of universal gravitation / [John Henry Pratt]. Source: Wellcome Collection.
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![inextensible string passing round their wheels alternately, one end of the string being attached to a fixed point M any where in the plane of the first wheel of bx over which it passes; and the other end being carried (as represented in the figure) to another system of blocks corresponding to the force P2, each block having n2 wheels; and so on : and lastly, let the string be passed over a simple wheel at C and be stretched by a weight W hanging by it. The string is imagined to be perfectly flexible, and the wheels perfectly smooth: consequently the string will be stretched uniformly throughout, with a tension equal to the weight W. It is very evident, then, that since the wheels of and bx are all equal, the portions of string connecting them are parallel, and (they being 2nx in number) the tension of Axax equals the weight 2nx W; in the same manner the tension of A2 a2 is 2n2W; and soon. Consequently by this imaginary contrivance the weight W produces forces at the points AXA2 ..in the directions A1a1, A2a2.and in the proportion of n1n2.; that is, in the proportion of PXP2. But Px P2. are in equilibrium: and since the unit of force may be any force, a system of forces in the same propor¬ tion as Px P2. acting at the same points and in the same directions as Px P2 ..will be in equilibrium. Hence if we remove the forces Px P2 and replace them in the manner described above, W will be at rest: and this will be the case of whatever magnitude W be, since by increasing or diminishing W, the forces Px P2.are altered so as to retain their proportion unchanged. Wherefore, however much we alter W, we cannot thereby cause the moveable block (oq) of any of the systems (as ax bx) to move. This shews that the relation of the magnitudes of the forces Px P2 their directions, and points of application is such, that if we forcibly make the block cq, or any other block, to approach or recede from the other block b] of the system by an indefinitely small space, then the other moveable blocks will 4](https://iiif.wellcomecollection.org/image/b29286700_0089.jp2/full/800%2C/0/default.jpg)
