QUEST. 19. A person, looking on his watch, was asked what was the time of the day, who answered, It is between 5 and 6; but a more particular answer being required, he said that the hour and minute hands were then exactly together: What was the time? Ans. 27 min. past 5. QUEST. 20. If 20 men can perform a piece of work in 12 days, how many men will accomplish another thrice as large in one-fifth of the time? Ans. 300. QUEST. 21. A father devised of his estate to one of his sons, and of the residue to another, and the surplus to his relict for life. The children's legacies were found to be 514 68 8d different: Then what money did he leave the widow the use of? Ans. 1270/ 18 911d. QUEST. 22. A person, making his will, gave to one child 13 of his estate, and the rest to another. When these legacies came to be paid the one turned out 1200/ more than the other: What did the testator die worth? Ans. 4000/. QUEST. 23. Two persons, A and B, travel between London and Lincoln, distant 100 miles, A from London, and B from Lincoln, at the same instant. After 7 hours they meet on the road, when it appeared that A had rode 1 miles an hour more than B. At what rate per hour then did each of the travellers ride? Ans. A 72, and в 611 miles. QUEST. 24. Two persons, A and B, travel between London and Exeter. A leaves Exeter at 8 o'clock in the morning, and walks at the rate of 3 miles an hour, without intermission; and в sets out from London at 4 o'clock the same evening, and walks for Exeter at the rate of 4 miles an hour constantly. Now, supposing the distance between the two cities to be 130 miles, whereabouts on the road will they meet? Ans. 694 miles from Exeter. QUEST. 25. One hundred eggs being placed on the ground, in a straight line, at the distance of a yard from each other: How far will a person travel who shall bring them one by one to a basket, which is placed at one yard from the first egg? Ans. 10100 yards, or 5 miles and 1300 yds. QUEST. 26. The clocks of Italy go on to 24 hours: Then how many strokes do they strike in one complete revolution of the index? Ans. 300. QUEST. 27. One Sessa, an Indian, having invented the game of chess, shewed it to his prince, who was so delighted Ans. 5 oz of 15, of 17, and of 18 caracts fine, and 25 oz of 22 caracts fine*. Ex. 2. A vintner has wine at 4s, at 5s, at 58 6d, and at 6s a gallon; and he would make a mixture of 18 gallons, so that it might be afforded at 58 4d per gallon; how much of each sort must he take? Ans. 3 gal. at 48, 3 at 5s, 6 at 58 6d, and 6 at 6s. A great number of questions might be here given relating to the specific gravities of metals, &c. but one of the most curious may here suffice. Hiero, king of Syracuse, gave orders for a crown to be made entirely of pure gold; but suspecting the workman had debased it by mixing it with silver or copper, he recommended the discovery of the fraud to the famous Archimedes, and desired to know the exact quantity of alloy in the crown. Archimedes, in order to detect the imposition, procured two other masses, the one of pure gold, the other of silver or copper, and each of the same weight with the former; and by putting each separately into a vessel full of water, the quantity of water expelled by them determined their specific gravities; from which, and their given weights, the exact quantities of gold and alloy in the crown may be determined. Suppose the weight of each crown to be 101b, and that the water expelled by the copper or silver was 921b, by the gold 521b, and by the compound crown 641b; what will be the quantities of gold and alloy in the crown? The rates of the simples are 92 and 52, and of the compound 64; therefore 28 of gold And the sum of these is 12+28 40, which should have been but 10; therefore by the Rule, = 40: 10: 12: 3lb of copper? the answer. RULE B6; what was the whole legacy, supposing A's share was Ans. 95004 4000/. QUEST. 39. Α young hare starts 40 yards before a greyhound, and is not perceived by him till she has been up 40 seconds; she scuds away at the rate of 10 miles an hour, and the dog, on view, makes after her at the rate of 18: how long will the course hold, and what ground will be run over, counting from the outsetting of the dog? Ans. 60 sec. and 530 yards run. QUEST. 40. Two young gentlemen, without private fortune, obtain commissions at the same time, and at the age of 18. One thoughtlessly spends 10 a year more than his pay; but, shocked at the idea of not paying his debts, gives his creditor a bond for the money, at the end of every year, and also insures his life for the amount; each bond costs him 30 shillings, besides the lawful interest of 5 per cent. and to insure his life costs him 6 per cent. The other, having a proper pride, is determined never to run in debt; and, that he may assist a friend in need, perseveres in saving 101 every year, for which he obtains an interest of 5 per cent. which interest is every year added to his savings, and laid out, so as to answer the effect of compound interest. Suppose these two officers to meet at the age of 50, when cach receives from Government 400 per annum; that the one, seeing his past errors, is resolved in future to spend no more than he actually has, after paying the interest for what he owes, and the insurance on his life. The other, having now something before hand, means in future, to spend his full income, without increasing his stock. It is desirable to know how much each has to spend per annum, and what money the latter has by him to assist the distressed, or leave to those who deserve it? Ans. The reformed officer has to spend 66/ 198 13.5389d per annum. The prudent officer has to spend 437 128 113.4379d per annum. And the latter has saved, to dispose of, 752/ 19s 9.1896c. END OF THE ARITHMETIC. 155 OF LOGARITHMS*. LOGARITHM OGARITHMS are made to facilitate troublesome calculations in numbers. This they do, because they perform multiplication by only addition, and division by only subtraction, and raising of powers by multiplying the logarithm by the index of the power, and extracting of roots by dividing the logarithm of the number by the index of the root. For, logarithms are numbers so contrived, and adapted to other numbers, that the sums and differences of the former shall correspond to, and show, the products and quotients of the latter, &c. Or, more generally, logarithms are the numerical exponents of ratios; or they are a series of numbers in arithmetical *The invention of Logarithms is due to Lord Napier, Baron of Merchiston, in Scotland, and is properly considered as one of the most useful inventions of modern times. A table of these numbers was first published by the inventor at Edingburgh, in the year 1614, in a treatise entitled Canon Mirificum Logarithmorum; which was eagerly received by all the learned throughout Europe. Mr. Henry Briggs, then professor of geometry at Gresham College, soon after the discovery, went to visit the noble inventor; after which, they jointly undertook the arduous task of computing new tables on this subject, and reducing them to a more convenient form than that which was at first thought of. But Lord Napier dying soon after, the whole burden fell upon Mr. Briggs, who, with prodigious labour and great skill, made an entire Canon, according to the new form, for all numbers from 1 to 20000, and from 90000 to 10100, to 14 places of figures, and published it at London in the year 1624, in a treatise entitled Arithmetica Logarithmica, with directions for supplying the intermediate parts. EXAMPLES. 1. A person after spending and of his money, has yet remaining 601; what had he at first? Then, 50 120 :: 60: 144, the Answer. per question. 2. What number is that, which being multiplied by 7, and the product divided by 6, the quotient may be 21? Ans. 18. 3. What number is that, which being increased by 1,1, and of itself, the sum shall be 75 ? Ans. 36. 4. A general, after sending out a foraging and of his men, had yet remaining 1000; what number had he in command? Ans. 6000. 5. A gentleman distributed 52 pence among a number of poor people, consisting of men, women, and children; to each man he gave 6d, to each woman 4d, and to each child 2d moreover there were twice as many women as men, and thrice as many children as women. How many were there of each? Ans. 2 men, 4 women, and 12 children? 6. One being asked his age, said, if of the years I have lived, be multiplied by 7, and product, the sum will be 219. of them be added to the What was his age? Ans. 45 years. DOUBLE |