The purely mathematical part of the phoronomic propositions coming thus into consideration forms what Professor Aronhold has called "Kinematic Geometry." It is, however, really a part of Phoronomy, and there does not appear any reason why it should not receive that name. If along with this the masses of the moving point-systems be also taken into consideration, we have "Phoronomic Mechanics." This is unquestionably what the later French writers (see p. 16) mean by "pure Kinematics." I shall be glad if my view of the matter be generally accepted, so that some sort of common understanding may be reached as to the general directions of these studies. It is greatly to be wished that some end could be brought to this multitude of new names.
Until recently only the lower and simpler part of Phoronomy, that namely which relates to the motion of a point, has been sys- tematically taught in our German Polytechnic Schools; and this has been so frequently treated in text-books as to be familiar to all practical mechanicians who take any interest in the theory of their subject. Problems connected with point-systems have been only occasionally treated -- in the text-books familiar to practical men they appear but seldom, and then rather as interest- ing corollaries than as important problems. These problems, however, are of the highest importance in Kinematics, and it is only to them that we need turn our attention here. I must therefore suppose that the following propositions, here taking their place in our investigations, will be in great part new to my Engineer readers. One of the most important characteristics of the method of treatment we shall employ is that it enables us to make the progressive changes of position visible in form to the imagination; I have tried, wherever it has appeared possible, to develope this conception still more fully than has hitherto been done.
5. Relative Motion in a Plane.
We are unable to grasp with our senses the absolute motion of a point; we observe only the relation of its successive positions to other points or bodies in our neighbourhood. This relation,
