NOTE. This rule will give the solidity of a cone when it is square, or parallelogramical, &c. Example. What is the solidity of the cone, figure third, case fifth; width of the large end 9, thickness 9, and length 21? Width of the edge Width of large end 9 X 2 = 18 18 reserved sum. 21 length X9 thickness=189 X 18=3402-6=567 Ans. CASE X. To find the solidity of a globe, or sphere. N. B. A globe or sphere is a round body bounded by a surface every point of which is equally distant from a point within called the centre; a line passing from one side to the other through the centre is called the diameter, or axis. RULE. Cube the diameter, or axis, and multiply its cube by 5236 the last product is the solidity. Examples. 1. What is the solidity of a globe, or sphere whose diameter is 113? 113X113x 113 x 5236768486-9422 solidity. 2. What is the solidity of the world which we inhabit, in miles; allowing its circumference to be 25000 miles? As 22 is to 7 so is 25000 to 7954 diam. nearly. (Fractions omitted.) 263485304337 solid miles Ans. 3. What is the solidity of a cannon ball that is 9 inches on its diameter ? Ans. 381.7044 solid in. 4. What is the solidity of a sphere whose diameter is 2 ft. 8 in. ? Ans. 9·92† ft. solidity. CASE XI. To find the solidity of a segment, or part of a globe, or sphere; or part of a globe cut off parallel to the diameter, as part D G F. RULE. Square the radius of its base, (as D o, or F o) multiply its square by 3, and reserve the product; square the depth o G, add the square and reserved product together; and multiply the sum by the depth; and the last product by 5236; the product is the solidity. Examples. 1. What is the solidity of the segment D G F, radius Do, or F 07 and depth o G 5? Radius 7×7×3-147 reserved product. 2. Required the solidity of a segment of a globe whose semi-diameter, is 9 in. depth 9 in.? Ans. 1526.8176 in. CASE XII. To find the solidity of the middle zone of a sphere, or globe; or the part of a sphere after two segments have been cut off, parallel to the diameter or axis, as C D E F, in case eleventh. RULE. Square the semi-diameter of both ends and add the squares together, and reserve the sum ; square the height, or distance of the two ends as o M, and add of its square to the reserved sum; multiply the sum by the height, or distance o M, and this product again by 1.5708; the last product is the solidity. Examples. 1. What is the solidity of the middle zone C DE F, (case eleventh); diameter C E, or D F, 14 and height o M, 3? N. B. In this example the diameters are alike which. is not always the case. 2. What is the solidity of the middle zone of a sphere whose greatest diameter is 12, and least 8, and height or length, 10? Ans. 1340-41 CASE XIII. To find the solidity of a spheroid, or elipsoid; and also to find the solidity of the middle frustum of a spheroid. NOTE. A spheroid is a solid generated by the revolution of an ellipse, or oval, about the transverse or conjugate diameter. [See the figure A B C D.] To find the solidity of the spheroid A B C D.. RULE. Multiply the revolving diameter B D, into itself, and the product by the fixed diameter A C, and the product again by 5236, the last product is the solidity. Examples. 1. What is the solidity of a spheroid whose revolving diameter B D 20, and fixed diameter A C 30? Revoly. diameter 20 X 20-400X 30 X 5236=6283.2 [Ans. 2. What is the solidity of a spheroid whose revolving diameter is 30, and fixed diameter 50? Ans. 23562. To find the solidity of the middle frustum of a RULE. To the square of the diameter of one end, add twice the square of the middle diameter, multiply this sum by the length, and the product again by 2618 the last product is the solidity. Examples. 1. What is the solidity of the frustum E F G H length 40, end diameters E G, or F H 24, and middle diameter B D 32. ? End diam. 24 X24 = 576 Mid. diam. 32×32×2=2048 add. 2624X40X 2618=27478·5280 [Ans. 2. What is the solidity of the middle frustum of a spheroid length 30, middle diameter 25, end 20? [Ans. 12959.1. CASE XIV. To find the solidity of an elliptic spindle. NOTE. An elliptic spindle is formed by any of the three conic sections revolving about a double ordi RULE. Find the diameter half way between the middle and end, multiply it by two, square the product and add the square to the square of the diame |