Elements of natural philosophy, Volume 1

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A.S. Barnes, 1850 - Mechanics - 632 pages
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Page 182 - ... is equal to the sum of the moments of the forces which tend to turn the body in the opposite direction about the same point.
Page 516 - When a solid is immersed in a fluid, it loses a portion of its weight ; and this portion is equal to the weight of the fluid which it displaces; that is, to the weight of its own bulk of that fluid.
Page 85 - Then the work performed in accelerating it, being equal to the product of its mass into the increase of the half-square of its velocity, is also equal to the product of its mass into the square of its radius-vector, and into the increase of the half-square of...
Page 557 - FLUIDS. the shorter branch, and cause the air above it to be compressed into a smaller space, but the heights at which it will stand in. the two branches will be different. The difference between these two heights, added to 30 inches, will be the altitude of the column of mercury, whose weight is just sufficient to resist the expansive action of the confined air. Now it is found by trial, that when the air in the shorter branch is compressed into half its primitive volume, the difference of level...
Page 21 - These atoms are endowed with attractive and repulsive forces, varying both in intensity and direction by a change of distance, so that at one distance two atoms attract each other, and at another distance they repel.
Page 235 - ... consequently the resultant of an infinite number of forces, just as the weight of a body is the resultant of the forces separately impressed by gravity on its component molecules. LAPLACE has shown that the indefinitely small parts into which the current may be supposed to be divided, exert forces which are to each other in the inverse ratio of the squares of their distances from the pole, and that by the composition of these a resultant is produced, which varies in the inverse proportion of...
Page 326 - VIII, leads to the following remarkable conclusion, easily fixing itself in the memory, that with the unguents, hogs* lard and olive oil interposed in a continuous stratum between them, surfaces of wood on metal, wood on wood, metal on wood, and metal on metal, when in motion, have all of them very nearly the same co-efficient of friction, the value of that co-efficient being in all cases included between 0,07 and 0,08, and the limiting angle of resistance therefore between 4 and 4 35'.
Page 49 - ... to it, that is, they are the same at each instant ; it is constant. obvious, from what precedes, that the work produced will be proportioned to the length of the path described by the point of application of the effort — double, if the path is double, triple, if the path is triple, &c. ; so that, if we take for unity the work which consists in overcoming a resistance over a length of 1 foot, the total work will be measured by the number of feet passed over. But if for another work, the constant...
Page 194 - ... to its followers, who are attracted to it by the importance and beauty of the truths it contains ; and the complete absence of any material advantage to be gained by means of it, adds perhaps even another charm to its study. The late Prof. Benjamin Peirce denoted the base of the Napierian logarithms and the ratio of the circumference to the diameter of a circle by two special symbols turned opposite ways, somewhat resembling a 6 and a 6 reversed. The forms of these symbols would seem to imply...
Page 144 - G' 0" is one third of AC, and hence G G" is one third of AG, or one fourth of A G". The centre of gravity of a triangular pyramid is, therefore, on a line joining one of the angles with the centre of gravity of the opposite face, and at a distance from this face, equal to one fourth of the line. The same result may be obtained for the common centre of gravity of four equal balls, whose centres of gravity are situated at the four vertices of the pyramid.

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