is 7 grains; the specific gravity of water being 1, and of air .0013, shew that the specific gravity of Q is .8237, and that it is as large as 17.023 grains of water.

6. The specific gravity of pure gold is 19.3, and of copper 8.62; required the specific gravity of standard gold, which is a mixture of eleven parts of gold and one of copper.

The weight of a vessel when empty being given, also when filled with water, and when filled with some other fluid, compare the specific gravity of water and of the fluid.

8. A life-boat contains 100 cubic feet of wood, specific gravity .8, and 50 feet of air, specific gravity .0013. When filled with water, what weight of iron ballast, specific gravity 7.645, must be thrown in before it will begin to sink?

9. A cylinder, placed with its axis vertical in a fluid, rests with an mth part immersed; when placed in another fluid it rests with the nth part immersed; to what depth would it sink in a mixture composed of equal quantities of these fluids?

10. A spherical bubble composed of matter the specific gravity of which is S, and filled with gas of the specific gravity s, just floats in air, specific gravity σ. Required the

11. A body weighs 4oz. in vacuum, and if another body which weighs 3 oz. in water be attached to it the whole in water weighs 24oz.; find the specific gravity of the former body.

12. If the specific gravity of air be called m, that of water being 1, and if W be the weight of any body in air, and W' its weight in water, its weight in vacuum will be

13. Compare the specific gravities of two bodies, one of which weighs 10lbs. in vacuum, and the other 3lbs. in

water; the bulks of the two bodies being respectively 48 and 72 cubic inches, and the weight of a cubic foot of water 1000 oz.

14. If three fluids, the volumes of which are 3, 4, 5, and specific gravities 2, 3, 4, be mixed together, determine the specific gravity of the compound.

15. A piece of wood weighs 12 lbs., and when attached to 22lbs. of lead and immersed in water the whole weighs 8lbs; the specific gravity of lead being 11 times that of water, determine the specific gravity of the wood.

16. A body weighs 14lbs. in vacuum and 9lbs. in water; another weighs 8lbs. in vacuum and 7lbs. in water; compare their specific gravities.

PRESSURE OF THE AIR.

1. In an imperfectly exhausted barometer, the depression below the true altitude is to the true altitude as the space which the air left in the tube occupied before immersion is to the space which it occupies after.

2. Find the height of the mercury in a barometer when a given quantity of air is allowed to remain in the tube.

3. Supposing the pressure of atmospheric air to be 12lbs. on the square inch, determine to what depth a piston of 3 tons weight will sink in a cylinder of radius 1 foot and height 3 feet, filled with atmospheric air.

4. A cylinder, the height of which is 6 inches, and the radius of the base one inch, is filled with atmospheric air; suppose a piston fitted into the cylinder and to be forced down through the space of 1 inch, determine the pressure of the air within the cylinder.

5. Two barometers are imperfectly filled; shew how by observations on two days to determine the quantity of air contained in each.

6. The height of the barometer at the foot of a mountain is 29.6 inches, on carrying the instrument to the summit the mercury falls 1.5 inches; taking the value of g to be 32.17, and assuming that, in the formula p = kp, 916.27 feet, find the height of the mountain.

=

Given that the density of the air at the height of 7

1

miles is

4

th

that at the earth's surface, calculate an approxi

mate value of the quantity k in the formula p = kp.

INSTRUMENTS AND MACHINES.

1. A body when put under the receiver of a common air-pump weighs a oz. and after n turns weighs b oz. Required the weight of the body in vacuum; and supposing the specific gravity of the body known, determine the density of the air in the receiver at first.

2. What will be the number of degrees indicated by a centigrade thermometer, when Fahrenheit's stands at 50", 18o, and — 12o respectively?

3. What will be the number of degrees Fahrenheit respectively corresponding to 49° and - 3o centigrade?

4. The altitude of the barometer placed in a given cylindrical diving bell is observed at the beginning and end of a descent; find the depth descended.

5. There are two air pumps, one with a receiver A and barrel B, the other with a receiver B and barrel A; compare the quantities of air exhausted by them in n turns.

6. Given the quantity of air (Q) contained in an air pump at first, it is required to determine after how many turns a given quantity (q) will be exhausted.

7. A barrel exhausts a receiver, but owing to some imperfection of the construction of the pump a given quan

tity of common air is forced back at every stroke. Find the density of the air in the receiver after n strokes.

8. Supposing the distance from the lower valve in a common pump to be just equal to the length of a column of water which can be supported by the atmospheric pressure, find the height to which the water rises in the pump after the first stroke.

9. A cylinder of known density and magnitude, floats with its axis vertical in a vessel of water placed under the receiver of an air pump; after how many strokes of the pump will the cylinder be depressed by a given quantity?

10. A portion of the receiver of an air pump is a plane valve opening inwards and kept in its place by a spring acting with a pressure P, less than that of the atmosphere; after how many turns will the pressure of the external air open the valve?

11.

In De Lisle's thermometer the boiling point is marked 0o, and the freezing point 150°. What degree of Fahrenheit corresponds to 138° of De Lisle ?

12. In Reaumur's thermometer the freezing point is marked 0o, and the boiling point 80o. What degree of Reaumur corresponds to 39° Fahrenheit?

13. In Bramah's press, given the sections of the two cylinders, and the force applied to the pump, determine the pressure produced.

14. In Bramah's press, suppose the radii of the cylinders to be 2 inches and 1 foot respectively, the length of the pump handle to be three feet, and the distance of the pump from the fulcrum of the handle 4 inches, determine in what proportion the power is increased.

MISCELLANEOUS PROBLEMS.

1. Three globes of the same diameter, and of given specific gravities, are placed with their centres in the same line. How must they be disposed that they may balance on the same point of the line in vacuum and in water?

2. Explain how it is, that a ship is able to sail in a direction making an angle less than a right angle with that of the wind. What is meant by the leeway of a vessel?

3. Explain the construction of the sails of a wind-mill.

4. Given the weight of a body corresponding to the altitudes h and h' of the barometer, find the weight corresponding to the altitude h".

5. Two masses of given specific gravities balance when suspended from the equal arms of a lever in a known fluid; what is the specific gravity of the fluid in which they balance when one of the masses is doubled?

6. A ship on sailing into a river sinks two inches, and after discharging 12,000 lbs. of her cargo rises one inch; find the weight of the ship and cargo.

Given that

the specific gravity of sea water

fresh.....

=

1.026.

7. Why is it necessary for a diamond merchant to have regard to the state of the weather in buying diamonds? Is it to his advantage to buy in dry or in wet weather?

8.

When two persons A and B descend together to the bottom of a lake in a cylindrical diving bell, it is observed that the water stands 1 inch lower within the bell than when A descends alone; the pressure of the atmosphere is equal to that of a column of water 34 feet high, the diameter of the bell is 4 feet, and the surface of the water within it, at the bottom of the lake, is 20 feet below the surface of the lake; find the volume of B.