# An Elementary Treatise on Rational Mechanics

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1866 edition. Excerpt: ...to their masses. For the acceleration due to gravity has the same value at a given station for all kinds of matter. 149. When the units of mass and force are so chosen that a force 1 applied to a mass 1 produces an acceleration 1, the force that acts upon any moving particle is measured by the product of mass and acceleration. The proportion established in the last article, m \$: nij/:: P: Q, is true for all values of n and Q. But if n = 1 and Q = 1, our hypothesis with reference to the units gives also i// = 1: .-. P = m i . P When the units are thus chosen, the force--which acts upon m the unit of mass is measured by the acceleration tjt. The forces m \$ and tjt are usually distinguished from each other as the moving force and the accelerating force respectively. Dynamical Measurement Of Forces. 150. We begin here by assuming a certain volume of a standard substance as unit of mass. Two instances will suffice: the English pound (avoirdupois), and the French kilogramme. A mass of one pound is the quantity of matter contained in the tenth part of a gallon (or 27.727 cubic inches) of distilled water at 62 Fahrenheit., A mass of one kilogramme is the quantity of matter contained in a cubic decimetre of distilled water at the temperature of' greatest density (4 centigrade or 39 Fahrenheit). i Def. The absolute unit of force is the force which, acting on a unit of mass, produces a unit of acceleration, or generates a unit of velocity per unit of tune. If To be the mass of a particle, P the applied force hu absolute units, i the acceleration, we have therefore (art. 149) Def. The gravitation-unit of force corresponding to any station is the weight of the unit of mass at that station. Prom the value of a force in absolute units to find its..