3d. To that quotient, add the fquare of half the referved remainder. 4th. From the fquare root of that fum, fubtra&t half the referved remainder and you obtain the time. In what time will an annuity of 250l. per annum mount to 20651. at 61. per cent? 2 Per ift. 33.3-1 .0633.3 and = 16. 16 2 4th. 536. 694 16. 16 536.694 = 7 years answer. Cafe 4th. Of present worths of annuities &c. to find the time. R ULE ft. Divide 2 by the ratio of the rate, and divide twice the present worth by the annuity; 2d. Subtract the latter quotient from the former, and fubtract 1 from the difference, then half the remainder referve. 3d. Divide twice the prefent worth, by the product of the annuity and ratio of the rate. 4th. To that quotient, add the fquare of the referved h: If remainder, and from the fquare root of that fum, fubtract that half remainder reserved, and you have the time. For what time may a falary of 250l. per annum be purchafed for 14541. 4s. 6d. at 6 per cent? 1454.225 X 2 11.6338. 2d. 33.3-11.6338=21.69953 and 21.69953—1= 20.69953 half of which is 10.34976 referved. T Extraction of the Cube Root. O extract the cube root, is to find from a given power fuch a number, as when fquared and multiplied into itself, may produce the propofed power, a the cube root of 216 is 6, for 6 X6 X6: = 216. A Table of Roots, Squares, and Cubes. Directions for extracting the cube root. ift. Point your propofed power, beginning at units place, over every third figure integers and decimals. Thus, {. 4768473.alfo.7689347218 2847.689340 2d. Take the cube root of the first period by means of the preceeding table of powers, which put in the quotient, and fubtract its cube from the first period to the left hand, and to the remainder bring down the next period for a dividend. 3d. Multiply the fquare of the quotient figure or figures by 300 for a divifor. 4th. Confider how often the new divifor will go in the dividend, and place the refulting figure in the quotient or root. 5th. Draw a line under the dividend, and multiply the divifor by the figure laft put in the quotient, to which product you must add 30 times the fquare of the laft figure multiplied by the other figure or figures in the root or quotient, and alfo the cube of the last figure put in the root. 6th. Subtract that fum from the dividend, and to the remainder bring down another period for a new divi dend dend, which divide as has been directed in article 3d: 4th. and 5th. to the end, and if the propofed power be a furd, there will be a remainder, and the root may be continued at pleafure, by annexing three cyphers to the remainder, and proceeding as before directed. If the cube root of a vulgar fraction be required, it may be reduced to a decimal, and the root of that decimal extracted as before directed. The Ufe of the Cube Root. ift. To find two geometrical means between two given numbers. RULE. The cube root, of the product of the greater, into the fquare of the lefs, is the less mean; and the cube root of the product of the less, into the fquare of the greater, is the greater mean. Required the two geometrical means between 8 and 27? 2d. To find the dimenfions of a veffel or folid. fimilar to a given one; either greater or less. ULE. As the weight or folidity of the given body: the cube of its fide, diameter, length, &c. :: the weight or folidity of another fimilar body, and of fimilar matter: the cube of its like fide, diameter length, &c. If a ball twenty inches diameter weighs 555.5lb. what is the diameter of one of the fame metal that weighs pouds? 3 As 555-320 X 20 X 20 :: 15 : 216 and √2166 answer. Admit a cubical ciftern, each fide 40 inches, required the fide of another that may contain 5 times as much? As 1: 40 X 40 X 40 ::.5 : 40 X 40 X 40 X 5 = 3.20000,. And If a ball of 6 inches diameter weighs 15lb. required the weight of another of the fame metal whofe diameter is 20 inches? anfwer. 555.5lb. E 3d. From a proof of any cable, to find the ftrength of any other. RULE. The ftrength of cables, and confequently the weights of their anchors, are as the cubes of their peripheries. If a cable 12 inches about requires an anchor 18 C wt. what weight muft an anchor be for a 15 inch cable. As 12 X 12 X 12 18:15 X 15 X 15: 35.15625 anfwer. If a 15 inch cable requires an anchor 35.15625 Cwt. how thick muft a cable be for an anchor 18. Cwt. As 35.15625 15 X 15 X 15. 18: 1728. 3 And 1728 12 anfwer.. 4th. The proportions of the following metals. If a brafs ball weighs 64lb. what is the weight of a leaden one of the fame bulk. 894: 1. As 98 94 56.7 if of iron. |