Physical action is, therefore, impression, or transmission of force in lines, and must accordingly be explained geometrically.
This may be readily accomplished geometrically or analytically, and it will be found that the envelope is a cardioid, i.e.
It may be shown geometrically that the secondary Caustics caustic, if the second by refrac- medium be less refrac- tion.
Such a curve may be regarded geometrically as actually described, or kinematically as in the course of description by the motion of a point; in the former point of view, it is the locus of all the points which satisfy a given condition; in the latter, it is the locus of a point moving subject to a given condition.
But it can be shown, analytically or geometrically, that if the given curve has a node, the first polar passes through this node, which therefore counts as two intersections, and that if the curve has a cusp, the first polar passes through the cusp, touching the curve there, and hence the cusp counts as three intersections.
