the length of the frustum, and the product by •2618 for the content. 1 EXAMPLES. 1. In the middle frustum EFHG of an oblate spheroid, the diameters of the middle or greatest elliptic section AB are 50 and 30, and of one end EF or GH 40 and 24; required the content, the height IK being 9. 2. In the middle frustum of an oblate spheroid, the axes of the middle ellipse are 50 and 30, and those of each end are 30 and 18 ; required the content, the height being 40. Ans. 37070-88. PROBLEN PROBLEM XXIV. RULE. To the square of the greatest diameter add the square of double the diameter at of the length ; multiply the sum by the length, and the product by "1309 for the solidity, very nearly NOTE. This rule will also serve for any other solid, formed by the revolution of any conic section. EXAMPLE. What is the solid content of an elliptic spindle, whose length is 20, the greatest diameter 6, and the diameter at 3 of the length 4*74773 ? 4°74773 90'16375 square of double diameter. diameter. 36'00000 square of out 126 16375 sum. 20 length. 2523:27500 9031 or 1309 inverted, 2523 757 22 3302 the solidity nearly. PROBLEM PROBLEM XXV. To find the solidity of a frustum, or segment, of an elliptic spindle. RULE. Proceed, as in the last rule, for this, or any other solid, formed by the revolution of a conic section about an axis ; namely, Add together the squares of the greatest and least diameters, and the square of double the diameter in the middle between the two; multiply the sum by the length, and the product by 1309 for the solidity. NOTE. For all such solids, this rule is exact when the body is formed by the conic section, or a part of it,, revolved about the axis of the section. And it will always be very near the truth when the figure revolves about another line to form the body. EXAMPLES. 1. Required the content of the middle frustum EGHF of any spindle, the length' AB being 40, the greatest or middle diameter CD 32, the least or diameter at either end EF or GH 24, and the diameter IK in the middle between EF and CD 30-157568. + 2. What is the content of the segment of any spindle, the length being 10, the greatest diameter 8, and the middle diameter 6? Ans. 272*272 3. Required the solidity of the frustum of a hyperbolic conoid, the height being 12, the greatest diameter 10, the least diameter 6, and the middle diameter 8 Ans. 667.59 4. What is the content of the middle frustum of a hyperbolic spindle, the length being 20, the middle or greate est diameter 16, the diameter at each end 12, and the diameter at of the length 141 ? 4. What Ans. 3248.938. Multiply the square of the diameter of the base by the altitude, and the product by '3927, for the content. EXAMPLES. 1. Required the solidity of a paraboloid, whose height BD is 30, and the diameter of its base AC 40. 2. What is the content of a parabolic conoid, whose altitude is 42, and the diameter of its base 24? Ans. 9500'1984. PROBLEM |