EXAMPLES. 1. Required the solidity of the prolate spheroid ACBD, whose axes are AB 50, and CD 30. 2. What is the content of an oblate spheroid, whose axes are 50 and 30? Ans. 39270. 3. What is the solidity of a prolate spheroid, whose axes are 9 and 7 ? Ans. 230°9076. PROBLEM XXII. To find the solidity of a segment of a spheroid. CASE I. When the base is circular or parallel to the revolving axis. ど RULE. Multiply the difference between triple the fixed axe and double the height of the segment by the square of the height, and the product again by *5236. Then, ་ Then, as the square of the fixed axis is to the square of the revolving axe, so is the last product to the content of the segment. EXAMPLES. 1. Required the content of the segment of a prolate spheroid, the height AG being 5,, the fixed axe AB 50, and the revolving axe CD 30. 2. If the axes of a prolate spheroid be 10 and 6, required the area of a segment, whose height is 1, and its base parallel to the revolving axe. Ans. 5.277888. 3. The axes of an oblate spheroid being 50 and 30, what is the content of a segment, the height being 6, and its base parallel to the revolving axe? Ans. 4084 07. CASE II. When the base is perpendicular to the revolving axé: RULE. Multiply the difference between triple the revolving axe and double the height of the segment by the square of the height, and the product again by 15236. Then, as the revolving axe is to the fixed axe, EXAMPLES. 1. In the prolate spheroid ACBD, the fixed axe AB is 50, and the revolving axe CD 30; required the solidity of the segment CEF, its height CG being 6. Then, as 30 : 50 :: 1470*2688: 2450*448. S 3)7351*3440 2450 4480 answer. 2. In an oblate spheroid, whose axes are 50 and 30; required the content of the segment, whose height is 5, its base being perpendicular to the revolving axe. Ans. 1099'56. PROBLEM XXIII. To find the content of the middle frustum of a spheroid. CASE I. When the ends are circular, or parallel to the revolving axe. RULE. To double the square of the middle diameter add the square of the diameter of one end; multiply this sum by the length of the frustum, and the product by 2618 for the content. EXAMPLES. 1. Required the solidity of the middle frustum EGHF of a spheroid, the greatest diameter CD being 30, the di ameter of each end EF or GH 18, and the length AB 40. 18 VOL. II. R 2. What is the solidity of the middle frustum of an ob late spheroid, having the diameter of cach circular end 40, the middle 50, and the length 18? Ans. 3110184. CASE II. When the ends are elliptical, or perpendicular to the revolving axe. RULE. To double the product of the transverse and conjugate diameters of the middle section add the product of the transverse and conjugate of one end; multiply the sum by the |