. Edinburgh New Philosophical Journal . suppose onr imaginary circumference to be divided into por- tions equal to the spaces through which any point moves, in its rotation, in given times. Let us also imagine a vertical plane to touch the circle in its lowest point, and the circle, with the points marked upon it, to be orthographically pro- jected upon that plane, as in the annexed dia- gram. Again, from the points thus projected up- on the circumference of the ellipse, let perpendi- culars be drawn to a line touching the ellipse in its lowest point. These perpendiculars will be equal to the
. Edinburgh New Philosophical Journal . suppose onr imaginary circumference to be divided into por- tions equal to the spaces through which any point moves, in its rotation, in given times. Let us also imagine a vertical plane to touch the circle in its lowest point, and the circle, with the points marked upon it, to be orthographically pro- jected upon that plane, as in the annexed dia- gram. Again, from the points thus projected up- on the circumference of the ellipse, let perpendi- culars be drawn to a line touching the ellipse in its lowest point. These perpendiculars will be equal to the abscissae of the ellipse for the projected points, and set off upon the conjugate axis. Let the same distances be set off upon the tangent line which were previously set off upon the circumference of the circle: these will be the dis- tances through which any point in the circumference would move in the given times, if allowed to advance in a rectilineal direction. Through these points let vertical lines be drawn equal to the spaces through which the lowest point in the circumference would descend in the same times, if the rota- tion were stopped and the top allowed to fall, turning on its pivot. The curve connecting the lower extremities of these vertical lines will be an approximation to the parabola, and, in fact, for a small portion at the vertex, may be regarded as a parabola, the vertical lines being equal to its abscissae. Now, it is a familiar law in dynamics, that, if two forces act upon the same body in the same direction, the resulting force is the sum of the two; but if in opposite directions, the dif- ference ; and forces are measured by the motions which they produce in the same mass and in the same time. In the pre- ceding diagram, the perpendiculars on the upper side of the horizontal line show the spaces through which the lowest point in the circumference would be raised, in the given times, by the rotatory motion alone; those under the hori- zontal line show t
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