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3. In the RULE of THREE or PRoportion. . Add the Logarithms of the second and third numbers, and from their sum subtract the Logarithm of the first. Erample. If 13ib. of tea cost 71.12s. what will 66;fb. cost 2
fb. Answ. 138.8769 Log. 1.5896919
Or this may be done something easier yet, if instead of the Log of the first term be taken its complement Arithmetical, or the difference of that Logarithm and the number 10.0000000, which is done by setting down the difference between each figure of the Logarithm, and the figure 9; for then, if the Arithmetical complement be added with the other two Logarithms, and if unity, which is the last, be taken away or erased from the sum, the remaining figures will be the Logarithm of the fourth term sought.
4. In INvolution or raising Powers. Multiply the Logarithm of the root by the index of the power, i.e. by 2 for the square : 3 for the cube, &c.
What is the square and cube of 12?
Mult. by 2 3
2. What is the square of 24 Answ. 576.
5. In Evolution or Ertracting Roots. Divide the Logarithm of the power by its index, i. e. the Log. of a square by 2, of a cube by 3, &c. and the quotient is the Logarithm of the root.
Find the square root of 144? 144 Log. 2)2 1583626 - * 1.0791812 Log. of 12. 2. Find the cube root of 1728? Ans. 12; of 729, Ans. 9. 3. The square root of 160 Answ. 12.6491. 4. 225? - .4743. 5. The cube root of 123456? 49,7982.
6. In Compound INTEREST.
, To find the amount of any sum for any time at compound interest. Multiply the Logarithm of the ratio (i.e. the amount of 1l, for 1 year) by the number of years, and to the product add the Logarithm of the principal; the sum will be the Logarithm of the amount.
What will 201. amount to, forborne 7 years, at 6 op' cent. ‘ts” annum, compound interest?
Log, of 1.06, the ratio is — 0.0253059
Multiply by the time 7
, 0.1771418 Add Log, of 20 the princ.—1.3010299
The sum is — — — 1.478 1712 Which is the Logarithm of 307, or 30l. 14s, the amount sought.
." From the Legarithm of the sum to be discounted, subtract the Logarithm of the rate multiplied by the time; the remainder is the Log. of the present worth.
What present money will pay a debt of 20l., due 7 years hence, at 5 #2 cent. #' annum compound interest? From Log. of 20l. — — — . — 1.3010300 Subt.. pro. of the Log. ratio + time —0.1483251 The reinainder is — — 1.1527049 Which is the Logarithin of 14.219 or 141. 4s. 43d. And thus may the other questions before delivered in Compound Interest be resolved.
A COLLECTION OF QUESTIONS
Person dying left his widow 1780l. and 1250l. to each of his four children, 30 guineas a piece to 15 of his poor relations, and 150l. in charities; he had been 254 years in trade, and at an average has cleared 126l. a year. What had he to begin with ? Answ. 4228l. 17s. 6d. 2. The globe of the earth, under the line, is 360 degrees in circumference, each degree 694 miles; and this body being turned on its own axis, in 23 hours, 56 min. At what rate an hour are the inhabitants of Bencoolen situate under the line, carried about from west to east by this rotation? Answ. 1045}}# miles. 3. A fellow was saying, that when he told over his basket of chesnuts 2 by 2, 3 by 3, 4 by 4, 5 by 5, or 6 by 6, there still came an odd one; but when he told them 7 by 7 they came even : how many had he Answ 721. 4. What number multiplied by 57 will produce just what 134 multiplied by 7 I will do Answ. 16633. 5. There are two numbers, whose product is 1610, the greater is given 46; what is the sum of their squares, and what the cube of their difference 2 Answ. Sum of sq. 33 11. The cube of their difference 1331. 6. A, B, and C trade in company: and at making up accounts, it appears that A and B together gained 131. 10s. B and C together 121. 10s. and A and C together gained . 1 11, 16s. 6d. what did they severally gain P - Answ. A 61.7s. 3d. B 71. 2s. 9d, and C 5l. 9s. 3d. - ) - 7. Some
7. Some others advance in trade, as follows, viz. W, X and Y raised 350l. 10s. W, X and Z 3441. 10s. X, Y and Z made up a stock of 400l. and W, Y and Z contribute 37.8l. 4s. In the conclusion, they parted with their joint property for 450 guineas. What did they gain or lose by their adventure ? Answ. If the guineas are computed according to the English currency at 21s. they lost 18l. 1 1s. 4d. but at 22s. 9d. they gained 20l. 16s. 2d. 8. There is a mast or pole, ; of its length stands in the ground, 12 feet of it in the water, and # of its length in the air, or above water: I demand the whole length . Answ. 216 feet. 9. A and B traded together, and gained 100]. A put in 640l. B put in so much tha the must receive 60l. of the gain; I demand how much B put in Answ. 960l. 10, What quantity of water must I add to a pipe of mountain wine value 331. to reduce the first cost to 4s. 6d. gallon Answ. 20; gallons. 11. What difference is there between the interest of 500l. at 5 #2 cent. for 12 years, and the discount of the same sum, at the same rate and for the same time * Answ. 1121. 10s. advantage to the interest. 12. If 12 apples are worth 21 pears, and 3 pears cost £d. what is the price of 4 score and 4 apples Answ. 2s. Oţd 13. Three merchants, A, B and C have gained 2341. which they are to divide so that when the profit of A is multiplied by 2, that of B by 3, and C’s by 4; their products are to be equal; I demand how much each of them is to receive Answ. A 1081. B 721. C 541. 14. There are 2 pieces of linen, the one is 9 yards shorter than the other, and cost 31. 1;s. the other piece at the same price cost 31. 12s. I demand how many yards were in both pieces, and the price of 1 yard 2 Answ. I 11 yards, at 1:s. #2 yard. :5. A piece of satun cost a certain sum, and being sold for 31. 10s. there is lost 3 in a shilling. I demand the first cost 2 Answ. 5l. 16s. 8d. 16. With 13 gallons of Canary at 6s. 8d. the gallon, I mingled 20 gallons of white wine, at 5s. a gallon; and to these add 10 gallons of cyder, at 3s, dip” gallon: at what rate must I sell a quart of this mixture so as to clear 10 45° cent. Answ. 1633d. 17. It is a rule in some parishes, to assess the inhabitants in proportion to *s of their rents: What is the year'y - - - - rest rest of that house, which pays 81. 10s, to the king under this limitation, at 5s. # 1..? Answ. 421. 10s. 18. If by selling hops at 31. 10s. d?' Cwt. the planter clears 30 dp' cent what was his gain per cent, when the same goods sold for 41. 5s. ? Answ. 571. 17s. 1 #d. 19. If by remitting to Holland, at 31s. 9d. Flemish op” 1. sterling, 5 #2 cent. is gained ; how goes the exchange when by remittance I gain 10 of cent. Answ. 33s. 3; d. - 2. 20. If when port wine is 17 guineas the hogshead, a company of 45 people will spend 20I.. therein in a certain time; what is wine a pipe when 13 persons more will spend 631, in twice the time, drinking with equal moderation * Answ. 431. 12s. 6d. nearly, the guineas being taken as English, which is 471. 5s. 24d. Irish. 21. A is dispatched on a commission from London to Fdioburgh, distant by computation, say 350 miles, and his rout is settled at 22 miles a day : 4 days after B is sent after him with fresh orders, and is to travel 32 miles a day ; whereabout on the road will B overtake Af Answ. 68.2 miles on this side Edinburgh. 22. If 6H5, of pepper be worth 13fb. of ginger, and 195. of this be worth 435, of cloves, and 10th of cloves be equivalent to 63fb. of sugar, at 5d. p’ fo. what is the value of 1 Cwt. of pepper? Answ. 7]. 19s. 3d. - 23. If 30 men can perform a piece of work in 11 days; how many will accomplish another, 4 times as big in onefifth of the time * Answ. 600. 24. A may-pole 50 feet, 11 inches long, at a certain time of the day, will cast, a shadow 98 feet, 6 inches long, I would hereby find the breadth of a river, that runnin 20 feet 6inches from the foot of a steeple, 300 feet 8 inches high, the extremity of the shadow of the steeple reaches 30 feet 9 inches beyond the stream? Answ. 330 feet. 5 inches nearly. 25. In 81034 rundlets of brandy, each 18 gallons; how inany gross of bottles, each $of a quart?. Answ. 455.81 gross 7 dozen and 6. 26. Bought hose in London for 4s. 3d. ts” pair, and sold them in Dublin for 6s. a pair: now taking the charges at an average to be 8d., a pair, and the exchange is known to be 8. cent, disadvantage; what do I gain cent. b this it: of trade 2 Ausw. 1334}. gain P y - Ee