the sun, a distance of 597000000 miles, in 365 days 6 hours, how far on an average does it move in each hour?

40. The equatorial portions, by the diurnal rotation of the earth, moves about 24900 miles each day? is that in each hour?

How far Ans. 1037 miles.

41. If it require 10 years of 3654 days for light to pass from a fixed star to the earth, how many miles distant is it, on the supposition that light moves 192000 miles in one second? Ans. 60590592000000 miles.

42. If by a leak of a ship enough water run in, in 4 hours, to sink her, how long can she survive?

Ans. 6hr. 40m. 43. If I pay $25 for the masonry of 4000 bricks, how much ought I to pay for the work which requires 100000 bricks? Ans. $625.

44. If a steam-ship require 14 days to sail a distance of 3000 miles, what time, at the same rate of sailing, would she require to sail 24900 miles ?

Ans. 116 days 44 hours. 45. Admitting the diameter of the earth to be 8000 miles, and the highest mountain to be 5 miles, what elevation must be made on the globe of 16 inches diameter to represent accurately the height of such mountain? Ans. T of an inch. 46. If $100 in 12 months bring an interest of $7, how much will be the interest of $100 for 8 months?

Ans. $4.66.

47. If the interest of $100 for 12 months is $7, will be the interest of $75 for the same time?

what

Ans. $5.25.

48. If in 12 months the interest of $100 is $7, how long must $100 be on interest to gain $10?

Ans. 174 months. 49. If a glacier of 60 miles in length move 50 inches per annum, in what time will it move its whole length? Ans. 76032 years.

50. If a staff of 10 feet in length give a shadow of 15 feet, how high is that tree whose shadow measures 90 feet? Ans. 60 feet.

51. Suppose sound to move 1100 feet in a second; how many miles distant is a cloud, in which lightning is observed 16 seconds before the thunder is heard, no allowance being made for the motion of light? Ans. 31⁄2 miles.

52. If it require 30 yards of carpeting which is of a yard wide to cover a floor, how many yards of carpeting which is 14 yards wide will be necessary to cover the same floor? Ans. 18 yards.

53. If the earth move through 12 signs, or 360° in 365 days, how far will she move in a lunar month of 294 days? Ans. 29-37 degrees.

54. Suppose a steamboat capable of making 15 miles each hour, to move with a current whose velocity is 21 miles per hour, what will be the whole distance made during 13 hours? And what distance will the boat move in the same time against the same current ?

55. If the magnetic influence move through the telegraphic wires at the rate of 200000 miles in one second of time, how many times could it pass around the world in one second, allowing the circumference of the earth to be 24899 miles ? Ans. 8 times.

808 24899

56. If A can do a piece of work in 7 days, and B can do it in 8 days, what part of it can both do in 3 days? Ans. 1 of it.

57. A reservoir. whose capacity is 1000 hogsheads, has a supply pipe by means of which it receives 300 gallons each hour; it also has two discharging pipes, the first of which discharges of a gallon each minute, the second discharges 1 gallons per minute. The reservoir being empty, in what time will it be filled if the supply pipe alone is opened? In what time, if the supply pipe and the first discharging pipe are opened? In what time, if the supply pipe and the second discharging pipe? And in what time, if all three are opened ?

Supply pipe only opened, 210 hours 83 days.

110. When the quantity required depends upon more than three terms, the operation of finding it is called the Rule of Compound Proportion.

Suppose we have the following example:

If 6 men can mow 30 acres of grass in 5 days, by working 8 hours each day, how many acres can 4 men mow in 9 days of 10 hours each?

Had the number of days, as well as hours in each day, been the same in both cases, the question would have been quivalent to the following:

If 6 men mow 30 acres of grass, how many acres will 4 men mow?

It is evident the number of acres sought would be the same fractional part of 30 acres that 4 men is of 6 men; that is, the quantity required is

of 30 acres.

If, now, we take into account the number of days, still supposing the number of hours in each day to remain the same in both cases, our question would become:

If 4 of 30 acres can be mowed in 5 days, how much can be mowed in 9 days?

The answer in this case is obviously

of of 30 acres.

Now, taking into account the number of hours each day, our question will become as follows:

If of 4 of 30 acres can be mowed in a certain time, when 8 hours are reckoned to each day, how much could be mowed when 10 hours are reckoned to each day? This leads to the following final result:

of of 4 of 30 acres.

By cancelling, we reduce this last expression to 45 acres. From the above work we see that questions of Compound Proportion may be solved by the following

answer,

RULE.

Among the quantities given, there will be but one like the which one we will call the odd quantity. The other quantities will appear in pairs or couplets. Form ratios out of each couplet in the same manner as in the Rule of Three ; then multiply all the ratios and the odd quantity together, and this will give the answer in the same denomination as the odd quantity.

NOTE. Before forming ratios from the couplets, they must be

reduced to the same denominate value.

EXAMPLES.

1. If a person travel 300 miles in 17 days, traveling only 6 hours each day, how many miles could he have gone in 15 days, by traveling 10 hours each day?

In this example, the answer is required in miles, therefore our odd term is 300 miles?

The first couplet consists of days; and since in 15 days, other things being the same, he could not travel as far as in 17 days, we must divide 15 by 17, which gives 1 for the first ratio.

The second couplet consists of hours; and since in 10 hours he could travel farther than in 6 hours, we must divide 10 by 6, which gives for the second ratio.

Multiplying these two ratios and the odd term together, we get 300 miles ××0. Cancelling the 6 of the dencminator against 6, a factor of 300 (=30o) of the numer ator, we have 50 ××4441 miles, for the answer.

2. If a marble slab 10 feet long, 3 feet wide, and 3 inches thick, weigh 400 pounds, what will be the weight of another slab, of the same marble, whose length is 8 feet, width 4 feet, and thickness 5 inches?

In this example, the answer is required to be given in pounds; therefore 400 pounds is the odd term. The first couplet consists of the lengths; and since 8 feet in length will give less weight than 10 feet, we must divide 8 by 10, which gives for the first ratio.

The second couplet consists of the widths; and since 4 feet wide will give more weight than 3 feet, we must divide 4 by 3, which gives for the second ratio.