and this additional cubic centimeter can raise the level of the water there but Too centimeter. We see, therefore, that the product of the force acting by the distance moved is precisely the same at both ends of the machine. This important conclusion will be found in our future study to apply to every type of machine.

26. The hydraulic elevator. Another

very common use of the above principle of the transformation of pressure by liquids is found in the hydraulic elevator. The simplest form of such an elevator is shown in Fig. 16. The cage A is borne on the top of a long piston P, which runs in a cylindrical pit C equal in depth to the height to which the carriage must ascend. Water enters the pit either directly from the water mains, m, of the city's supply or,

if this does not furnish sufficient pressure, from a special reservoir on top of the building. When the elevator boy pulls up on the cord cc, the valve v opens so as to make connection from m into C. The elevator then ascends. When cc is pulled down, v turns so as to permit the water in C to escape into the sewer. The elevator then descends.

Where speed is required, the motion of the piston is communicated indirectly to the cage by a system of pulleys like that shown

Gas and oil are found in porous rocks having a nonporous covering;
for example, the porous rock may be limestone or sandstone, and
the nonporous covering may be shale. Frequently water is found
below, the oil and the gas being on top. The pressure of the gas
sometimes exceeds 1000 pounds to the square inch; hence if a boring
is made into the layer of water or oil, the boring tools and derrick
may be blown high in the air by the rushing water or oil. When
the pressure of the expanding gas falls too low to force the oil from
the boring, pumping must be resorted to. Natural gas is sometimes
piped for many miles to steel works, where millions of cubic feet of
it are burned daily. We have here an illustration of Pascal's law on
a grand scale in nature

in Fig. 17. With this arrangement a foot of upward motion of the piston P causes the counterpoise D of the cage to descend 2 ft.; for it is clear from the figure that when the piston goes up 1 ft., enough rope must be pulled over the fixed pulley p to lengthen each of the two strands a and b 1 ft. Similarly, when the counterpoise descends 2 ft., the cage ascends 4 ft. Hence the cage moves four times as fast and four times as far as the piston. The elevators in the Eiffel Tower in Paris are of this sort. They have a total travel of 420 ft. and are capable of lifting fifty people 400 ft. per minute. The cylinder C and the piston P are often not in a pit, but lie in a horizontal position. (Most modern elevators are electric rather than hydraulic.)

27. City water supply. Fig. 18 illustrates the method by which a city is often supplied with water from a distant

B

b

FIG. 18. City water supply from lake

source. The aqueduct from the lake a passes under a road r, a brook b, and a hill H, and into a reservoir e, from which it is forced by the pump p into the standpipe P, whence it is distributed to the houses of the city. If a static condition prevailed in the whole system, then the water level in e would of necessity be the same as that in a, and the level in the pipes of the building B would be the same as that in the standpipe P; but when the water is flowing, the friction of the mains causes the level in e to be somewhat less than that in a, and that in B less than that in P. It is on account of the friction of both the air and the pipes that the fountain ƒ does not rise nearly so high as the ideal limit shown in the figure. When the reservoir e requires cleaning, or in case of accident or need of repairs, the supply of water from the lake a may be partly or wholly cut off by a huge valve, or gate, at r.

SUMMARY. Pascal's law. Pressure applied anywhere to a body of confined liquid is transmitted undiminished to every portion of the surface of the containing vessel.

Hydraulic-press rule. The force exerted upon the large piston is as many times that applied to the small piston as the area of the large piston is times that of the small piston. Expressed as a formula,

F A D2

1. A jug full of water may often be burst by striking a blow on the cork. If the interior surface of the jug is 200 sq. in. and the cross section of the cork 1 sq. in., what total force acts on the interior of the jug when a 10-pound blow is struck on the cork?

2. Fig. 19 represents an instrument commonly known as the hydrostatic bellows. If the base C is 50 cm. square and the tube is filled with water to a depth of 1.5 m. above the top of C, what is the value of the weight in kilograms which the bellows can support?

3. The cross-sectional areas of the pistons of a hydraulic press were 3 sq. in. and 60 sq. in. How great a weight would the large piston sustain if 75 lb. were applied to the small one?

4. The diameters of the pistons of a hydraulic press were 2 in. and 20 in. What force would be FIG. 19. Hydroproduced upon the large piston by 50 lb. on the

small one?

static bellows

5. The water pressure in the city mains is 80 lb. to the square inch. The diameter of the piston of a hydraulic elevator of the type shown in Fig. 16 is 10 in. If friction could be disregarded, how heavy a load could the elevator lift? If 30 per cent of the ideal value must be allowed for frictional loss, what load will the elevator lift?

6. How does your city get its water? How is the pressure in the pipes maintained?