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 12 days, how many men will large in one-fifth of the time? perform a piece of work in accomplish another thrice as 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 14 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 morn ing, 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 with it, that he promised him any reward he should ask; on which Sessa requested that he might be allowed one grain of wheat for the first square on the chess board, 2 for the second, 4 for the third, and so on,,doubling continually, to 64, the whole number of squares. Now, supposing, a pint to contain 7680 of these grains, and one quarter or 8 bushels to be worth 27s 6d, it is required to compute the value of all the corn? Ans. 6450468216285/ 17s 3d 327570 QUEST. 28. A person increased his estate annually by 100% more than the part of it; and at the end of 4 years found that his estate amounted to 103421 38 9d. What had he at first? Ans. 4000/. QUEST. 29. Paid 1012/ 10s for a principal of 7504, taken in 7 years before: at what rate per cent. per annum did I pay interest? Ans. 5 per cent. QUEST. 30. Divide 1000/ among A, B, C ; so as to give A 120 more, and B 95 less than c. Ans. A 445, B 230, c 325. QUEST. 31. A person being asked the hour of the day, said, the time past noon is equal to night. What was the time? ths of the time till midAns. 20 min. past 5. 16 QUEST. 32. Suppose that I have of a ship worth 1200/ what part of her have I left after selling of of my share, and what is it worth? Ans. 37 worth 1851. QUEST 33. Part 1200 acres of land among A, B, C ; sơ that в may have 100 more than A, and c 64 more than B. Ans. A 312, B 412, c 476. QUEST. 34 What number is that, from which if there be taken of, and to the remainder be added off, the sum will be 10? Ans. 979 QUEST. 35. There is a number which if multiplied by of of 14, will produce 1: what is the square of that number Ans. 1. QUEST. 36. What length must be cut off a board, 8 inches broad, to contain a square foot, or as much as 12 inches in length and 12 in breadth? Ans. 16 inches. QUEST. 37 What sum of money will amount to 138/ 2s 6d, in 15 months, at 5 per cent. per annum simple interest? Ans. 1307. QUEST. 38. A father divided his fortune among his three sons, A, B, C, giving a 4 as often as в 3, and c 5 as often as B6; what was the whole legacy, supposing a's share was 4000%. Ans. 9500. QUEST. 39. A 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 101 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 each 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 15389d per annum. The prudent officer has to spend 4377 128 1124379d per annum. And the latter has saved, to dispose of, 7521 1989-1896 END OF THE ARITHMETIC OF LOGARITHMS*. LOGARIT OGARITHMS are made to facilitate troublesome calcu lations in numbers. This they do, because they perform multiplication by only addition, and division by only subtracttion, 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 expoments of ratios; or they are a series of numbers in arith metical * 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 Arst published by the inventor at Edinburgh, 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 Logas rithmica, with directions for supplying the intermediate parts. metical progression, answering to another series of numbers in geometrical progression. Thus, {0 Or Or 0, 1, 2, 3, 4, 5, 6, Indices, or logarithms. 16, 32, 64, Geometric progression. 4, 5, 6, Indices, or logarithms. 81, 243, 729, Geometric progression. So, 1, 2, 4, Indices, or logs. 21, 10, 100, 1000, 10000, 100000, Geom progress. Where it is evident, that the same indices serve equally for any geometric series; and consequently there may be an 3, 5, This Canon was again published in Holland by Adrian Vlacq, in the year 1628, together with the Logarithms of all the numbers which Mr Briggs had omitted; but he contracted them down to 10 places of decimals. Mr. Briggs also computed the Logarithms of the sines, tangents, and secants, to every degree, and centesm, or 100th part of a degree, of the whole quadrant; and annexed them to the natural sines, tangents, and secants, which he had before computed, to fifteen places of figures. These Tables, with their construction and use, were first published in the year 1633, after Mr. Briggs's death, by Mr. Henry Gellibrand, under the title of Trigonometria Britannica. Benjamin Ursinus also gave a Table of Napier's Logs. and of sines, to every 10 seconds. And Chr. Wolf, in his Mathematical Lexicon, says that one Van Loser had computed them to every single second, but his untimely death prevented their publication. Many other authors have treated on this subject; but as their numbers are frequently inaccurate and incommodiously disposed, they are now generally neglected. The Tables in most repute at present, are those of Gardiner in 4to, first published in the year 1742; and my own Tables in 8vo, first printed in the year 1785, where the Logarithms of all numbers may be easily found from 1 to 10000000; and those of the sines, tangents, and secants, to any degree of accuracy required. Also, Mr. Michael Taylor's Tables in large 4to, containing the common logarithms, and the logarithmic sines and tangents to every second of the quadrant. And, in France, the new book of logarithms by Callet; the 2d edition of which, in 1795, has the tables still farthe extended, and are printed with what are called stereotypes, the types in each page being soldered together into a solid mass or block. Dodson's Antilogarithmic Canon is likewise a very elaborate work, and used for finding the numbers answering to any given logarithm. endless |