A system of mechanics, being the substance of lectures upon that branch of natural philosophy / By T. Parkinson.

  • Parkinson, Thomas, 1745-1830.
Date:
1785
Catalogue details

Licence: Public Domain Mark

Credit: A system of mechanics, being the substance of lectures upon that branch of natural philosophy / By T. Parkinson. Source: Wellcome Collection.

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    489. Cor.r. Becaufe Ax Sa -+- B x S3 + Cx Sc,he. = A+'B+C, x „„ - AxSA'+BxSB'+CxSC , Scc.x SG (410), SP= 4+B + c> te:7SG-~-SK- 490. Cor. 2. The diftancs of the center of percuffion from the r . , AxGA'+BxGB' + CxGC* center ofgravrty, or GP, is equal to Zjrg+i,te. * SG~’ -&C. (479)- 491. Cor. 3. In the fame body, or fyftem of bodies, 5, C9 &c. zf+S +77, &c. x £G x G P = A x GA% -P B x GBz-hCx GC\ &c. £G * GP is aifo a given quantity, wherever the point err r 1 1 1 i f Ax GAZ A- B x GBz or fuipenfion be placed, became -j—8cc, is given 1 Al —J— JTJ ^ OC v * and it S G be infinitely great, or the velocities of A, B, C, &c. be equal to each other, GP is evanefeent. 492* Cor. 4. If a circle be deferibed from G as a center, with a radius equal to SG, and, the plane of motion remaining as before, the points of fufpenfion be in different points of the periphery of this circle, the diftance between the centers of gravity and percuf- fion. will be invariable; for SG being given, GP is given (lad con) r 1 r . j AxSA2 BxSBZ 493. Cor.5. If particles, whole magnitudes are — >z i SPZ C x SC2 concentrated in P, the fame angular velocity will be generated, in thefe particles, by a force F a cling for a given time, and in A, B, C, &c. at their refpeftive diftances SA, SB, SC\ &c. For, let X, T, Z, &c. be refpeftively in equilibrio with A, B} C, &c. and their moments are inverfely as their perpendicular di- ftances (272), or A x SA ; X x SP :: SP : SA, and A x SAZ — X'