A Theory of Natural Philosophy by Roger Joseph Boscovich

Author:Roger Joseph Boscovich [Boscovich, Roger Joseph]
Language: eng
Format: epub
Tags: Métaphysique, Philosophie
Published: 0101-01-01T00:00:00+00:00

let the vertical line BO represent gravity, draw from the point O, to meet the straight lines BH, BF, the straight lines OR, OI parallel to BF, BH ; also producing BK upwards to the same extent,.draw through K the straight line KE, KL, parallel to BF, BH to meet BH BF. Then it is clear that BE, BL will be equal opposite to BR, BI. Now, according to the usual method by means of resolution of forces, the gravity BO is supposed to be resolved into the two parts BR, BI, of which the first acts upon the plane AC the second upon DC. Also if the angle HCF is sufficiently acute, then the angle at R is also sufficiently acute ; for these angles must be equal to one another. For, each is the supplement of the angle HBF, the one in the parallelogram, the other on account of BHC BFC being right angles. This being so, it may happen that each of the sides BR, RO, or BI, will be greater than BO, to any desired extent. Thus each of the forces, which act upon the planes, may be greater than gravity alone, to any desired extent. Many will wonder that it is possible that gravity, by a mere application of this kind, surpasses itself to so great an extent, gives an effect that is so much greater.

Answer to the difficulty by the ordinary method ; in my Theory there is no occasion for any difficulty.

285. A difficulty of this land even according to the ordinary opinion is easily avoided by comparing the case of the lever, with which we will deal later ; in it the mere application of a force situated at a much greater distance gives a far greater effect. But with my Theory there is no occasion for any difficulty of the sort. For there is no actual resolution of gravity into the two parts BR, BI, each acting on one of the planes; but gravity induces an approach to the planes, to within the distance at which repulsive forces acting perpendicular to the planes upon the sphere compound into a force BK, equal opposite to the gravity BO ; this force sustains the sphere impedes further approach to the planes. To represent this, the forces BE, BL are required ; these are equal opposite to BR, BI; that is all there need be said about the matter. Now, since the forces are mutual, there are repulsions acting upon the planes, these repulsions are equal opposite to BE, BL ; thus the forces acting are represented by BR, BI, which are those into which the ordinary method resolves gravity.

Explanation in the case of a sphere suspended by inclined strings.

286. But if, in Fig. 47, a heavy sphere P is suspended by a string BP, this is held up by inclined strings AB, DB, gravity is represented by BH ; let BK be equal opposite to it, let HI, KL be parallel to the string DB, HR, KE parallel to the string AB.

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