In an article in our last issue, on " Vis Viva and Inertia/3 we alluded to an able paper upon the subject of " Motion and Resistance," by Prof. Henry Morton, and made a brief quotation from it. The paper referred to contains, also, the following paragraph: " It may be objected that the time of action is not the true measure of a force, but rather the distance which it causes a body to move in a given time. But that this is not so, will be seen when we consider that any velocity once implanted in a body, needs no force to maintain it, so that all the motion afterwards executed by reason of that element, is a clear gain having no equivalent of expended force as its representative." This paragraph coataias the very partial enunciation of an important and fundamental law, and as it is evident, from the connection, that the author, when speaking of force as a positive, also considers with i its negative, resistance, his position is unassailable. Distance is not a measure of motion. But the real meanings of the correlatives, force and resistance, are but dimly comprehended by many even who essay their discussion. Force is regarded by many as a hidden property, distinct from the ordinary and easily discernible properties of matter as seen in its aggregated state. Others seem to regard it as an exterior and occult influence, which compels matter, but does not reside in it. Others, more rationally, we think, consider it as being simply motion of matter. But the latter is true, if true at all, only in a limited "sense. In this limited sense force implies resistance; cannot exist without resistance. This is evident from the illustration contained in the above extract from Prof. Morton's paper, that is, a body moving forever without resistance, from a previously applied force. It is, then, only while motion is imparted from masses to masses, from molecules to molecules, from atoms to atoms or molecules, from molecules to molecules or atoms, from atoms or molecules t*o masses, or from masses to atoms or molecules, that motion becomes a force. If motion is recognized, in this limited sense, as force, the true idea of resistance is expressed by saying that a body, by impact, loses motion or imparts it to masses, molecules, or atoms. In this view of the subject the relations of force and resistance exist together, and time is a measure of both, or either. Momentum, amount of motion, expressed in the works on physics, by M V, which is the weight of a body multiplied by its velocity, is not an absolute expression, unless we establish a unit of velocity. The mathematical expression of a unit of velocity is found by dividing the entire number of units of distance by the number of units in the time required for a body to move through that distance. It is (D-j-T), in which D represents the distance, and T the time. It is at once seen that neither time (T) nor distance (D) is a measure of momentum (M V), when considered separately ; and the momentum of a body, or its amount of motion, is a constant one for all times when velocity (V=D-i-T) is constant, and M is also constant. So far as motion is concerned, considered simply as motion and not as force, time is no measure of it. As soon as a body begins to impart its motion, or, as is the common method of expression, " to overcome resistance," time alone may be a measure of the motion received (force), and the motion imparted (resistance), the equality of which has long been recognized by physicists in the expression, "action and reaction are equal." For if the entire amount of motion imparted and received be uniform during a period of time, the motion imparted during a unit of that time wi]l be an exact measure of the whole motion imparted; and the motion imparted for a unit of time is only found by dividing the entire amount of motion imparted by the time. The author of the article on " Vis Viva," in the CJiemical News, from which we made an extract in our article on " Vis Viva and Inertia," in our last issue, seems to have reached a somewhat similar conclusion, when he asserts that, " as he understands ' vis viva/ it relates only to change in velocity, and does not apply to the maintenance of a uniform velocity after it has been once attained." Now, change in velocity is purely and simply the subtraction from, or addition to, the motion of a body of motion considered as quantity and as (if the views of the identity of motion and force be correct) this, of necessity, implies force and its correlative, resistance, we see how " vis viva " can only relate to diange of velocity. There is little doubt that the differences which arise upon topics like these, between those who attempt their discussion, originate more from the inefficiency of language than from the real views entertained respecting them. The language of scientific discussion should be cleared of many terms that now are only sources of embarrassment. Some of these may be noticed, more especially, in a future article.
This article was originally published with the title "Time as a Measure of Force" in Scientific American 20, 16, 249 (April 1869)