9. A lever of the third kind is 8 ft. long, the power amounts to 16 lbs., and the weight is 14 lbs. ; where must the power be placed, so as to sustain the weight?

10. If the weight of a steelyard is suspended 1 inch from the fulcrum, at what distance from the fulcrum must a poise weighing 1 lb. be placed, to balance a weight of 1 lb. A weight of 2 lbs.? 2 lbs. ? 3 lbs.? 11 lbs. ? If the first notch is 1 inch from the fulcrum, and the notches are of an inch apart, how many pounds and ounces will the poise balance, when placed in the 2d notch? 3d notch? 4th notch? 5th notch? 8th notch? 16th notch? 64th notch? 72d notch? 80th notch?

LESSON 187.

For the Slate.

1. A weight of 2000 lbs. is on the end of a lever of the first kind, 1 ft. from the fulcrum; how many pounds as a power must be placed 10 ft. from the fulcrum to balance the weight? Answer, 200.

2. A lever of the second kind being 12 ft. long, where must a weight of 720 lbs. be placed, so that a power capable of lifting 50 lbs. shall sustain it?

Answer, 10 in. from the fulcrum. 3. A lever of the third kind is 15 ft. long, with a weight at the end of 80 lbs.; if a power be applied 11 ft. from the weight, how many pounds must it be capable of lifting in order to sustain the weight? Answer, 100.

4. A lever of the first kind, 11 ft. long, has a weight of 1500 lbs. at one end, and a power equal to 150 lbs. can be applied at the other; where must the fulcrum be placed so that the power shall balance the weight?

Answer, 1 ft. from the end. 5. I wish to sustain 933 lbs. on a lever of the second kind, 14 ft. long, the fulcrum of which is 3 ft. from the weight; what power must I employ?

Answer, a power capable of raising 200 lbs. 6. If you have a lever of the third kind 10 ft. long, with a weight at the end of 145 lbs., where must you apply a power equal to 900 lbs. to sustain the weight?

Answer, 1 ft. 7 in. from the fulcrum.

7. If the place of suspending the weight in a steelyard be 2 inches from the fulcrum, what weight will a poise weighing 4 lbs. balance, if placed 3 ft. from the fulcrum ? Answer, 72 lbs.

8. The place of suspending the weight in a steelyard being 1 inches from the fulcrum, at what distance from the fulcrum must a poise weighing 4 lbs. be placed, so as to balance a weight of 56 lbs. ? Answer, 1 ft. 9 in.

Observations on the Lever.-We have regarded the lever as very light; the weight of it, however, in prac tice, will increase or diminish the power a little. By examining figures 22, 23 and 24, lesson 185, we see that the weight of the lever in the first kind, will generally increase the power, and that the weight of the levers of the second and third kinds, will generally diminish the power.

When the power and weight balance each other, the power must be increased a little in order to raise the weight, as there is some rubbing or friction on the ful

crum.

The lever is a very important instrument, and is used in a great many different forms; when you employ your weight on the end of a handspike to overturn a log, the handspike is a lever of the first kind; but if you place your shoulder beneath the handspike to roll over the log, the handspike is a lever of the second kind. A man who loads hay with a pitchfork, employs a lever of the third kind, one hand being the fulcrum, and the other the power. A common tongs are double levers of the third kind; blacksmiths tongs are double levers of the first kind, the fulcrum being at the pivot.

What will the weight of the lever do in practice? What do we see by examining figures 22, 23 and 24, lesson 185?

When the power and weight balance each other, what must be done in order to move the weight? Why?

What is an example of a lever of the first kind? Second kind? Third kind? What are common tongs? Blacksmith's tongs; and where is the fulcrum?

Therefore, to balance the weight,

tance of the power from the fulcrum.

The power must be to the weight as the radius of the axle is to the radius of the wheel.

1. What power must be applied to the circumference of a wheel 6 ft. in diameter, to balance 350 lbs., suspended from the axle, which is ,5 of a foot in diameter? Answer, 29 lbs. 2 oz. 2. The diameter of the wheel being 7 ft., and that of the axle being 9 in., what weight will a power equal to 12 lbs. balance? Answer, 112 lbs.

3. What must the diameter of a wheel be so that a power equal to 40 lbs. may balance a weight of 500 lbs., the axle being 1 ft. in diameter ? Answer, 124 ft.

4. There are 2 axles, side by side, 1 ft. in diameter, each of which has a wheel 10 ft. in diameter; a belt passes round the first axle and the second wheel; how many pounds on the second axle, will a power equal to 25 lbs. on the first wheel balance? Answer, 2500 lbs.

Observations on the wheel and axle.-When the power and weight balance each other, the power must be increased a little in order to overcome the friction on the

What principle is employed in the wheel and axle? Explain how. How must the power be to the weight in order to balance it?

axis, and raise the weight; the power may also be diminished a little before the weight will overcome the friction and descend.

The wheel and axle are used in a great many different forms; the crank of the windlass with which water is sometimes drawn, turns round in a circle, and acts as a wheel, while the body of the windlass acts as an axle; the windlass of a vessel acts as a wheel and axle ; the capstan of a vessel is, in effect, a wheel and axle, where the wheel, represented by the levers, is horizontal, &c.

When the power and weight balance each other, what must be

done in order to move the weight? Why? Name some of the forms in which the wheel and axle are used.

A pulley with an immovable block like figure 26, is called a fixed pulley. A pulley with a movable block, like figure 27, is called a movable pulley. With a fixed pulley, like figure 26, the power must evidently be equal to the weight in order to balance it; this pulley merely serves to change the direction in which the power operates. With a movable pulley, like figure 27, the weight must be 2 times the power in order to be balanced, for the weight is supported equally by the power and that end of the rope which is fixed. Let us now examine figures 28 and 29, where several pulleys are used. When one end of the rope is fastened to the block of the fixed pulleys, as in figure 28, we see that the weight is supported by 2 times as many ropes as there are movable pulleys. When one end of the rope is fastened to the block of the movable pulleys, as in figure 29, we see that the weight is supported by 1 more than 2 times as many ropes as there are movable pulleys. It is so in all cases, no matter how the pulleys are arranged.

Therefore, to find what weight the power will balance,

When one end of the rope is fastened to the block of the fixed pulleys, multiply the power by 2 times the number of movable pulleys; but when the end of the rope is fastened to the block of the movable pulleys, multiply the power by 1 more than 2 times the number of movable pulleys.

1. If you have 2 movable pulleys, and the end of the rope is fastened to the block of the fixed pulleys, what weight will a power equal to 80 lbs. balance?

Answer, 320 lbs. 2. There are 3 movable pulleys, and the end of the rope is attached to the block which contains them; what power will be necessary to balance a weight of 420 lbs. ! Answer, 60 lbs.

What is called a fixed pulley? A movable pulley? How is the power to the weight in a fixed pulley? What does the fixed pulley serve for? How is the power to the weight in a movable pulley? Why?

By examining figures 28 and 29, lesson 189, what do we find to be the case when one end of the rope is fastened to the block of the fixed pulleys? Of the movable pulleys? Is it always so?

What is the rule to find what weight the power will balance?