. The London, Edinburgh and Dublin philosophical magazine and journal of science. Dynamical Lord Kelvin*. THE method of drawing meridianal curves of capillarysurfaces of revolution, described in Popular Lecturesand Addresses, vol. i., 2nd edition, pp. 31-42, and illustratedby woodcuts made from large scale curves, worked out ac-cording to it with great care and success by Professor Perrywhen a student in the Natural Philosophy Class of Glasgow * Communicated by the Author. 444 Lord Kelvin on Graphic Solution University, suggests a corresponding method for the solutionof dynamical p
. The London, Edinburgh and Dublin philosophical magazine and journal of science. Dynamical Lord Kelvin*. THE method of drawing meridianal curves of capillarysurfaces of revolution, described in Popular Lecturesand Addresses, vol. i., 2nd edition, pp. 31-42, and illustratedby woodcuts made from large scale curves, worked out ac-cording to it with great care and success by Professor Perrywhen a student in the Natural Philosophy Class of Glasgow * Communicated by the Author. 444 Lord Kelvin on Graphic Solution University, suggests a corresponding method for the solutionof dynamical problems. In dynamical problems regarding the motion of a singleparticle in a plane, it gives the following plan for drawingany possible path under the influence of a force of which thepotential is given for every point of the plane. Suppose,for example, it is required to find the path of a particleprojected, with any given velocity, in any given directionthrough any given point P0 (fig. 1). Calculate the normalcomponent force at this point; and divide the square of the Fig. velocity by this value, to find the radius of curvatureof the path at that point. Taking this radius on the com-passes, find the centre of curvature, C0, in the line, PUK,perpendicular to the given direction through P0, and describea small arc, P0PiQi, making P^ equal to about half theleno-th intended for the second arc. Calculate the alteredvelocity for the position Ql5 according to the potential law ;and, as before for P0, calculate a fresh radius of curvaturefor Q! by finding the normal component force for the altereddirection of normal and for the velocity corresponding to theposition of Qi- With this radius, find the position of thecentre of curvature, Ci, in PiC0L, the line of the radiusthrough Px- With this centre of curvature, and the freshradius of curvature, describe an arc PjP2Q2 making P2Q2 equalto about half the length intended for the third arc ; calculateradius of curvature for position Q2
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
