(57) A block of ice, the volume of which is a cubic yard, is observed to float with ths of its volume above the surface, and a small piece of granite is seen embedded in the ice; find the size of the stone, the specific gravities of ice and granite being respectively '918 and 2.65.

(58) A cubical block of wood weighs 12 lbs.; the same bulk of water weighs 320 oz.; what part of the wood will be below the surface when it floats in water?

(59) A board 3 inches thick sinks 24 inches in water: what will a cubic foot of the same wood weigh, if a cubic foot of water weigh 1000 oz. ?

(60) The specific gravity of beech-wood is '85. What portion of a cubic foot of that wood will be immersed in sea water whose specific gravity is 1·03 ?

(61) A cubical iceberg is 100 feet above the level of the sea, its sides being vertical. Given the specific gravity of sea water=1.0263 and of ice=9214, find the dimensions of the iceberg.

(62) If a body of weight W float with three-quarters of its volume immersed in fluid, what will be the pressure on a hand which just keeps it totally immersed?

(63) Two hydrometers of the same size and shape float in two different fluids with equal portions above the surfaces; and the weight of one hydrometer: that of the other :: mn; compare the specific gravities of the fluids.

(64) A hydrometer, loaded with 40 grains, sinks 4 inches lower when floating in a fluid whose specific gravity is 3 than in water; without the weight it rises in the water one-twelfth of an inch higher: find the weight of the hydrometer.

(65) If the volume between two successive graduations on the stem of a hydrometer be 10th part of its whole bulk, and it floats in distilled water with 20 divisions, and in sea water with 46 divisions, above the surface; find the specific gravity of sea water.

(66) A piece of lead is found to weigh 13 lbs. in water, and when a block of wood weighing 6lbs. is attached to it the two together weigh 8 lbs. in water. Find the specific gravity of the wood.

(67) What is the weight of a hydrometer which sinks as deep in rectified spirits, specific gravity '866, as it sinks in water when loaded with 67 grains?

(68) The weight of a body A in water of specific gravity =1 is 10 oz., of another body B in air whose specific gravity ='0013 is 15 oz.; while A and B connected together weigh 11 grains in water: shew that the specific gravity of B is '0713.

(69) A substance weighs 20 oz. in water and 25 oz. in alcohol, the specific gravity of which is 7947 times that of water; find the number of cubic inches in the substance, taking the weight of a cubic foot of water as 1000 oz.

8. H.

CHAPTER V.

On the Properties of Air.

69. THE thin and transparent fluid which surrounds us on all sides, and which we call the Air or the Atmosphere, is a material body which possesses weight and resists compression. We can prove by experiment that even a small mass of air has an appreciable weight, by exhausting the air from a glass vessel (by a process which we shall describe in the next article). We then find that the vessel weighs less than it weighed before the air was taken out of it.

That the air resists compression is evident from the force required to drive down the piston of a syringe when the open end is closed.

Every body exposed to the atmosphere is subject to a pressure of nearly 15 pounds on each square inch of its surface. We feel no inconvenience from this great pressure, because the solid parts of our bodies are furnished with incompressible fluids, capable of supporting great pressures, while the hollow parts are filled with air like that which surrounds us. Also, since the atmosphere acts equally on all parts of our bodies, we have no difficulty in moving.

AB and DE are two pistons with valves opening upwards, which are worked up and down two cylindrical barrels by means of the toothed wheel W in such a way that one piston descends as the other ascends. The barrels communicate, by means of valves at C and F opening upwards, with a pipe leading into a strong glass vessel V called the receiver.

Suppose B to be at its lowest position and therefore E at its highest position. Then as B ascends the valve at B closes, and the air in the receiver and pipe opens C and expands itself in the barrel. As soon as B begins to ascend E begins to descend, the valve at E opens, the valve at F remains closed.

The air which before occupied the receiver and pipe, now occupies the receiver, the pipe, and one of the barrels, and is therefore rarefied.

Now let the wheel be turned back: then as E ascends the valve at E closes and F is opened, and meanwhile B is opened as it descends, and C being closed, a quantity of the rarefied air is taken from the receiver and pipe.

This process may be continued till the air in the receiver is so rarefied that it cannot lift the valves at C and F, and then the action of the instrument must cease.

71. Smeaton's Air Pump.

A

B

C

D

AC is a cylindrical barrel communicating with a strong vessel D called the receiver. At A and C, the ends of the barrel, are valves opening upwards.

A piston with a valve B opening upwards works up and down the barrel. Suppose the piston to be in its lowest position. Then as the piston ascends, the pressure of the air being removed from the upper surface of the valve at C, the air in DC opens C and expands into the barrel, while the valve at B is closed by the pressure of the atmosphere.

Thus a quantity of air is drawn away from the receiver. As soon as the piston begins to descend, the valve at A is closed, B opens and C is closed, and no external air comes into the barrel or receiver.

When the piston again ascends the air in the barrel is again drawn out.