A complete system of mensuration of superficies and solids, of all regular figures ...

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. 1834 Excerpt: ...decimal,5236 and the product will be the sohdity. EXAMPLES. 1. The transverse diameter of a prolate spheroid is 50 inches, and the conjugate 40--What is its sohdity 1 Ans. 24,2465 + cubic feet. 2. The two diameters of a prolate spheroid are 3 feet, and 2 feet--What is the solidity? ' Ans. 6,2832. 2. The two diameters of a prolate spheroid are 60 inches, and 40--What is the solidity? Ans. 29,0883 + cubic feet. 4. What is the solidity of a prolate spheroid whose diameters are 100, and 60 inches? Ans. 109,083 + cubic feet DEFINITION. An oblate spheroid is generated by the revolution of a semi-ellipsis about its conjugate diameter. Problem x. To find the solidity of an oblate spheroid. Rule--Multiply the shortest diameter by the square of the longest, and that product by,5236, the last product will be the solidity. EXAMPLES. 1. The two diameters of an oblate spheroid are 100, and 60--Required the solidity, Ans. 181,8--cubic feet. 2. The transverse and conjugate diameters of an oblate spheroid are 40, and 30 inches--What is its solidity? Ans. 14,544 + cubic feet. 3. If the transverse diameter of an oblate spheroid be 20 inches, and the conjugate 15, what will be the solidity of the spheroid? Ans. 1,818 4-cubic feet. PROBLEM XI. To find the solid content of the middle fijustrum of a spheroid, its length, the middle diameter,, and that of either of the ends being given: I.--When the ends are circular or parallel to the revolving axis. Rule--To twice the square of the middle diameter add the square of the diameter of either of the ends, and this sum multiplied by the length of the frustrum, and that product by,2618, will give the solidity. EXAMPLES. I. In the middle frustrum of a spheroid the middle r diameter is 50 inches, and that of either of the ends is 40, and...