E. 9 A garrifon confifting of 1500 men, being befieged, have provifions only for three months, but it being neceffary they should stand out five months, how many men muft depart, that the faid provifions may serve that time? E, 10. What weight will a man be able to raife, who preffes with the force of a hundred and half on the end of an equipoised hand-spike, 100 inches long, which is to meet with a convenient prop exactly 7 inches above the other end of the machine ? A leaver of the firft order, equally divided and juftly poifed, is the balance-beam; to this, if a power be applied at one end, it will always move an equal weight at the other: in like manner, a leaver equally poised, and unequally divided, having a power applied at one end, will move a weight at the other which will be reciprocally proportionable to the diftances of thofe ends from the fulcrum, or point fupported; of this kind is the steelyard. E. 11. What weight, hung at 70 inches diftance from the fulcrum of a fteel-yard, will equipoife a hogfhead of tobacco weighing 9cwt. freely fufpended at two inches diftance on the contrary fide? In the above Figure ce=70 inches, Ac=2, H the hogfhead, and w the weight. E. 13. A body weighing 200lb. is impelled by fuch a force, as to fend it 100 feet in a fecond; with what velocity would a body of 8. move, if it were impelled by the fame force? In comparing the motion of bodies, the ratio, or proportion between their velocities, will be compounded of the direct ratio of the forces wherewith they are moved, and the reciprocal of their quantities of matter they contain. E. 15. Suppofe that in a room where two men, A. and B. are fitting, there is a fire, from which A is three feet and B fix feet diftant, it is required to find how much hotter it is at A's feat than B's? To answer this question, it must first be philofophically confidered and learnt, that the effects or degrees of light, heat, and attraction, are reciprocally proportional to the fquares of their diftances, from the centre whence they are propogated. A's distance is 3 feet X 3=9; and B's distance is 6 feet, which X by 6 36; then As 36 9)36 Answer 4 So that it is evident A's place is 4 times as hot as B's. XIV. COMPOUND PROPORTION: OR, The RULE of FIVE, S fo called, from its having five numbers or terms given to find a a proportion to the fourth and fifth, as the third bears to the first and fecond. But if the proportion is inverfe, then the fixth term must bear fuch proportion to the fourth and fifth, as the first bears to the second and third, or as the second bears to the firft and third. The three first terms are a fuppofition, the two last a demand. RULE. 1. Let the principal cause of gain, lofs, or action, &c. be put in the first place. 2. Let that which denotes time, diftance of place, &c. be in the fecond place, and the remaining one in the third place. 3. Place the other two terms which move the question, underneath thofe of the fame name. 4. If the blank, or term fought, fall under the third term, multiply the two firft terms together for a divifor, and the three last for a dividend, the quotient arifing from them will be the answer, or fixth term. 5. If the blank fall under the first or second term, multiply the third and fourth terms together for a divifor, and the other three for a dividend; the quotient arifing from them will be the answer. PROOF. Is by two ftatings in the fingle rules of three. N E. 1. E. 1. If 6 men can mow 72 acres of grafs in 12 days, how many men can mow 120 acres in 4 days? d. a. : 72 120 120 12 1440 288)8640(30 Men, Answer, E. 2. A ufurer put out 120l. to receive intereft for the fame; but when it had continued 9 months he took it up, and received for the principal and intereft 1257. 8s. I demand at what rate per cent. per annum he received? E. 5. If a fack of coals be the allowance of 7 poor people for a week, how many poor belonged to that parish, which, when coals were 36s. per chaldron, had 417, to pay in fix weeks on that account? Firft, 365.12 (the facks in a chaldron) 3s, what the coals coft per week, and 417.820s, then, N = 820 18)5740(318 Poor, Answer, XV. |