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A treatise on statics Volume 2; with applications to physics (Inglés) Tapa blanda – 9 may 2012


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Tapa blanda, 9 may 2012
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1889 Excerpt: ...its sides BC, CA, AB intersecting in a point, P, at which the conical angle is w. Thus, then, to find the point on any given line, AP, drawn through A at which the triangle subtends to, we take two given points M, N on two of the arcs and find the point, L, on the third such that LM+LN is a given quantity. There are two solutions, since, given base and sum of sides of a spherical triangle, the locus of the vertex is a sphero-conic. 5. Show that the complete solution of equations (8), p. 246, from u, v, w will necessarily be indeterminate. dP dLP dP (To any values found for u. v, v may be added terms-r-» r--r-» x J ax dy dz where P is any function of, y, z which has a single (unambiguous) value for given values of x, y, «.) 6. For the conical angle subtended by a given plane circle at any point in space, show that the angles a, r, tr, 8 in example 1 can be exhibited by a plane construction. 317. Attraction of a Thin Uniform Straight Bar. Let the line AB (Fig. 276), represent a straight bar the area of whose transverse section is k square centimetres, this area being very small; let the mass of the bar be p grammes per cubic centimetre of substance; let /' /! S. P be the position of a mass of 1 gramme A S b supposed to be condensed into an in, finitely small volume. It is required to find the magnitude and direction of the attraction of the bar on the particle at P. Draw PO perpendicular to AB; take any point, M, on AB; let OM = s, and consider the attraction on P of the elementary length ds at M. The mass at P being 1 gramme, and the mass of ds being p. kds, if y is the constant of gravitation (Art. 315), the attraction of ds on P is, in dynes, kpds yPM-W This force acts in the line PM. Resolve it into a component along PO and a component perp...

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