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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 edition. Excerpt: ...the circle.. In 11. sector of:1 circle, the centre of gravity is two-thirds of the distance of that of an are, from the centre of the circle. Or, multiply the radius by twice the chord of the arc, and divide by three times the length of the arc; the quotient is the distance of the centre of gravity from the centre of the circle. In a semicircle, multiply the radius by '42-14; the product is the distance of the centre of gravity from the centre of the circle. In a solid hemisphere, the centre of gravity is at a distance of three-eighths of the radius from the centre. For a solid spherical segment, deduct half the versed sine from the radius, and square the difference; multiply this square by the square of the versed sine and by 31416; and divide by the content of the segment. The quotient is the distance of the centre of gravity from the centre of the segment. In a hemispherical surface, spherical-segment surface, or spherical-zone surface, the centre of gravity is at half the height of the axis. In a parabola, the centre of gravity is in the axis, at a. distance of three-fifths of the height from the vertex. In a semiparabola, the centre of gravity is at the same height as in a parabola, but it is situated at a distance from the axis, of three-eighths of the semibase. In a paraboloid, the centre of gravity is in the axis, at a distance of two-thirds of the axis from the vertex. For two bodies, fixed one at each end of a straight bar, the common centre of gravity is in the bar, at that point which divides the distance between their respective centres of gravity in the inverse ratio of the weights. In this solution, the weight of the bar is not reckoned for. But it may be taken as a third body, and allowed for as in the following...
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