the end of an equipoised handspike 100 inches long, which. is to meet with a convenient prop exactly 7 inches above the other end of the machine? Answ. 184 Cwt.

13. What weight hung at 70 inches distance from the fulcrum of a steel yard, will equipoise a hogshead of tobacco, weighing 9 Cwt freely suspended at two inches distance on the contrary side?

Answ. 30 6oz. 6ždrs. nearly.

MOTIONS of BODIES with their VELOCITIES.

In comparing the motion of bodies, the ratio or propertion between their velocities will be compounded of the direct ratio of the forces wherewith they are moved, and the reciprocal of the quantities of matter they contain.

Examples.

14. The battering ram of Vespasian weighed, suppose 100,000 and was moved, let us admit, with such a velocity, by strength of hands, as to pass through 20 feet in one second of time, and this was found sufficient to demo-lish the walls of Jerusalem: with what force must a bullet that weighs about 30. be moved in order to do the same execution? Answ. 66,666 feet, 8 inches second.

15. A body weighing 200lb. is impelled by such force as to send it 100 feet in a second; with what velocity would a body of 8lb move, if it were impelled by the same force? Answ. 2500 feet 4 second.

T

CHAP. IX.

THE DOUBE RULE OF THREE.

HIS probably is called the Double Rule of Three, because questions therein may be solved by two statings of the Single Rule of Three. It is likewise by some called the Rule of Five, because generally, five numbers are given to find a sixth, of which five given numbers, 3 are conjoined in form of supposition; and upon that supposi

tion a question is raised of the other two, which with the number sought, are respectively like the former three.

I. To solve questions in this rule by two statings of the Single Rule of Three, this is the Rule:

1. Let either of the two numbers of which the question is raised, be put in the third place, and the correspondent number of the same name or kind in the first, the second will be that which hath no correspondent number given.

2. Three of the first given numbers being thus stated, find a fourth proportional.

3. Put this fourth number resulting from the work of the first stating, for the second number of a second stating, the remaining number of which the question is raised the third, and its corresponding number of the same name the first, and the fourth number resulting will be the answer.

Application.

Let this question be proposed, viz.

If the carriage of 25 stone weight for 16 miles cost 157. 10s. what will 40 stone cost for 9 miles?

Here of the five given numbers 25 stone, 16 miles, and 157. 10s. are conjoined in form of a supposition, and thereupon a question is

raised concerning

Sto. l. S.

Sto.

40 stone for nine 1...25-15 10-40

miles: wherefore

let either of the Miles 1. s. Miles two numbers, 40 2...16-24-16-9 stone or 9 miles

be put for the

1. s.

Answ. 24 16

l. d.

Answ. 13 19

Or thus:

7. S. d.

Answ. 8 144

third number of Miles 1. s. Miles the first stating 1...16-15 10-9 and its corres

ponding term, 25 Sto. l. 8. d. Sto. stone or 16 miles. 2...25-8 14 101-40

1, s. Answ: 13 9

Such questions as being stated) are found to have both the statings in direct proportion, may be solved more readily by one compound stating and operation, thus: Place the two terms of which the question is raised under one another in the third place; their corresponding terms under each other in the first; and the remaining term in the mid

dle:

dle; then multiply both these first terms and third terms into each other, and so the double stating is reduced to a simple stating of the Rule of Three Direct, viz. the product of the two first terms is the first of a simple stating; the second term is the second; and the product of the third term is the third number to find a fourth proportional.

Questions in this Rule may be contracted as in the Rule of Three, particularly if any of the first and last terms have a common measure we may divide them, and use the quotients instead of the numbers themselves, by which means the last question will stand thus, viz.

Questions belonging to this Rule are such as follow:

1. If 4 students spend 197. in 3 months; how much will

serve 8 students 9 months?

Answ. 1147.

2. If the carriage of 8 Cut. 128 miles cost 48 shillings, for how much may I have 4 Cwt. carried 32 miles after the same rate? Answ. 6s.

3. If 2407. in 16 months gain 647. how much will 607. gain in 6 months? Answ. 61.

4. A merchant agrees with a carrier to carry 15 Cwt. of goods 40 miles for 10 crowns, each crown 65 pence; how much must one pay in proportion to have 3Cwt. carried 32 miles? Answ. 17s. 4d.

5. If 20 Cut. is to be carried 50 miles for 5l. how much will 40Cwt. cost if it was to be carried 100 miles?

Answ. 201.

6. With how many pounds sterling could I gain 57. annum, if with 4507. I gain in 16 months 301.

Answ. 100%.

7. If 87. is gained in 12 months with 1007. with how much money can I gain 8l. 12s. in 5 months?

Answ. with 258%

8. If 60l. in 6 months gain 67. what will 2401. gain in 16 months? Answ. 641.

9. If 1 pound of thread makes 3 yards of linen 5 quarters broad; how many pounds of thread would be wanted to make a piece of linen 45 yards long, and 1 yard broad? Answ. 12 pounds.

10. If 200. of merchandize is carried 40 miles for 3 shillings, how many pounds may be carried 60 miles for 221. 14s. 6d. ? Answ. 20200b.

11. If for 3 shillings 200. of goods are carried 40 miles; how many miles might 20200. be carried for 221. 14s. 6d. Answ. 60 miles._

12. If 2001. are carried 40 miles for 3 shillings; how much must be paid for carrying 20200. 60 miles?

Answ. 221. 14s. 6d.

13. If 3 of worsted make 10 yards of stuff of 1 yd. 2qrs. broad, how many pounds will be wanted to make a piece Answ. 15b. 100 yds. long and 3 qrs. broad?

14. If a footman travel 240 miles in 12 days when the day is 12 hours long; in how many days may he travel 720 miles when the day is 16 hours long?

Answ. 27 days.

15. If 12 men in 8 days gain 81. 8s. what will 21 men gain in 15 days? Answ. 271. 11s. 3d.

find

17. If 80,000 Cwt. of ammunition was to be removed from a place in 9 days, and that in 6 days time 4500 Cut. is carried away by 18 horses, how many horses would be wanted to carry away the remainder in 3 days?

Answ. 604 horses.

18. A and B are on opposite sides of a wood, 134 fathoms about, they begin to go round it both the same way at the same instant of time; A goes 11 fathoms in two minutes, and B 17 in 3: the question is, how many times will they surround this wood, before the nimbler overtakes the slower?

17 times by A.
by B.

17

19. A weight of 1. laid on the shoulders of a man is no greater burthen to him than its absolute weight; what difference will he feel between the said wt. applied near his elbow, at 12 inches from the shoulder, and in the palm of his hand 28 inches therefrom; and how much more must his muscles then draw to support it at right angles; that is, have his arm extended right out?

Answ. 24.

BOOK