Of all the terms used by writers on mechanics, scarcely one has created more confusion and embarrassment to the young student than the one chosen for the caption of this article. What is momentum ? As defined by all writers on mechanics, it is the product of the mass of a body multiplied by its velocity. As understood by a majority of their readers, it conveys a different idea. Long before the youth becomes a student of mechanics, " momentum" is to him a household word. Does the strong tower yield to the heavy cannonade, he is told that the momentum of the cannon ball has done the work. A switch is misplaced, and a lightning express scatters destruction in its pathway ; on the fearful momentum of the iron horse is laid all the blame. A millstone bursts its bonds and, with resistless fcrce, crushes to a shapeless mass the engine which but a moment before was the source of its own power : the press itemizes on the wonderful effect of momentum. No wonder then that the youth, thus taught to regard momentum as the measure of the power stored up in a moving body, when he sees momentum defined as the product of mass and velocity (Mt>), comes to consider the product as the measure of the power of a moving body. But this (Mt>) is no measure of power! The true measure of the power of a moving body is the product of oue half its mass multiplied by the square of its velocity (MI)3-I-2). To this product physicists assign the term "vis viva," or living force. It would be deemed an exaggeration to state that of the popular articles written on the subject of mechanics, not one in ten uses the word " momentum" correctly ; yet perhaps it will be believed, when so well known a writer on scientific subjects as Professor Silliman, of Yale, in a recent work, falls into the same error, as is evidenced by the following quotation: "It is a fundamental principle of mechanics that the same force, acting upon different bodies, imparts velocities in the inverse ratio of the quantities of matter. If the same force successively projected balls whose masses were as the numbess 1, 2, 3, &c, it would impart to them the velocities 1, J, J, At, so that a mass ten times larger would acquire a velocity of only l-10th. The product of each of thse masses into its velocity is the same, for 1X1=1, 2X^=1, &c; and this product of the mass into the velocity of a body is called its momentum, moving force, or quantity of motion."Fi*st Principles of Philosophy, Silliman, Philadelphia, 1859, p. 81. Wrong ! all wrong from beginning to end. The same force, acting upon different bodies, imparts velocities in the inverse ratio of the square roots of their quantities of matter. If the same force acts successively, during equal portions of time, on two balls whose masses are the numbers 1 and'4, it imparts to them relative velocities of ^/4 and */\, or 2 and 1. What, then, is momentum? Mass is the measure of the resistance which a body offers to a force brought to bear upon it ! Velocity is the measure of the rapidity with which a body passes through space ! Vis viva is the measure of the power stored tip in a moving boely[! Has not momentum any such physical interpretation ? I know of none ; know of it only as a conventional term, used bj' physicists to express a certain product, often occurring in mechanical analysis, but not susceptible of direct interpretation as a measure of any phenomenal action. It has been the object of this article to point out facts rather than to prove their correctness. Those who feel suffi-cient interest in the matter to pursue it further will find in the issue of next week argument to prove that vis vira, not momentum, measures the amount of power stored up in a moving body. Jos. W. SPRAGUE. THE Arctic expedition of Dr. Hays has been heard from at Upernavik (North Greenland); all well. This expedition is fitted out for three years. Its object is to enter the polar sea discovered by Dr. Kane, and find out something more about it than has yet been discovered. THERE are fifty-seven cities in the world which contain from 100,000 to 200,000 inhabitants, twenty-three from 200,000 to 500,000, and twelve which contain above 500,000.