A Treatise on Mechanics: Intended as an Introduction to the Study of Natural Philosophy

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Pr. for T. Cadell and W. Davies, 1814 - Mathematics - 228 pages
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Page 231 - The simple machines, or what are commonly called the MECHANICAL POWERS, are six in number; viz. 1. The Lever; 2. The Wheel and Axle; 3. The Pulley; 4. The Inclined Plane; 5. The Screw; 6. The Wedge.
Page 42 - Ans. lOf feet per sec. 3. The space described by a heavy body in the 4th second of its fall was to the space described in the last second except 4, as 1 to 3 : What was the whole space described by the body...
Page 172 - Ans. 39.110, or 39TV inches nearly, from L, or the pendulum must be shortened. The theorem alluded to in the 3d example, therefore, gives this rule : Multiply twice the length of the pendulum by the number of seconds gained or lost, and divide the result by the number of seconds in a day ; the quotient will give the number of inches or parts of an inch by which the pendulum is to be lengthened or shortened.
Page 24 - ABCD, abed, become similar curves, in falling down which no velocity is lost. Suppose the curves to be circular arcs; then, since similar circular arcs are to each other as the radii of the circles to which they belong, the times of descending through these arcs will be to each other as the square roots of their radii.
Page 232 - ... power and weight with the different parts of the machine ; for the mechanism of the wheel and axle, and of the pulley, merely combines the principle of the lever with the tension of cords ; the properties of the screw depend entirely on those of the lever and the inclined plane ; and the case of the wedge, so far as it is capable of mathematical demonstration, is very analogous to that of a body sustained between two inclined planes.
Page 152 - ... stone materials, the hardness of the former will be found to be greatly inferior to that of the latter, and the error of the advocates of smooth-looking gravel roads will be immediately made manifest. By referring to works of science, it will be seen that hardness is defined to be that property of a body by which it resists the impression of other bodies which impinge upon it} and the degree of hardness is measured by the quantity of this resistance. If the resistance be so complete as to render...
Page 180 - If bodies are imperfectly elastic, shew that the sum of the product of each body into the square of its velocity, before impact, is greater than the sum of the product of each body into the square of its velocity after impact. 17- If the sun's apparent diameter at the extremity of the latus rectum were to his apparent diameter at perigee as 100 : 101, what would be the excentricity of the solar ellipse ? . 18.
Page 55 - Art. 41, the body at the end of that given time would be found in the point Q ; having described, not the diagonal PQ, but some curve line POQ.* In PN take any point M, and let T, t represent the times of describing PN, PM respectively ; make PL equal to the space through which a body would fall by gravity in the time t, and complete the parallelogram PMOL ; then...
Page 170 - Let ?-=the radius of the Earth, then since the force of gravity varies inversely as the square of the distance from the Earth's center, the force which accelerates the pendulum whose length is (L) : 1 the force which accelerates the pendulum whose length is (/): :-— -, __ :=-, :: r+rf|f : r+Dj1; but by Art.

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