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These formula (2), (3), and (4) are only theoretically true as regards air in mines, the pressure or head of air-column required being from ten to twenty times. as much in order to overcome the friction and resistance of airways, etc., in underground workings; and, were it not for these resistances, very small pressure would suffice to produce great velocity.



10. MOTION in air is caused by pressure, or difference of pressure. When air becomes heated, it ascends, because it assumes a larger volume;



and, as the same volume of cold air is heavier, it pushes the warmer up, or out of its place. This phenomenon in the open air gives rise to winds and breezes, which vary in intensity, according as the cool air takes the place of the warm air, rapidly or slowly. Suppose we have two shafts (connected, as in the above figure) of equal depths, the air in them having



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§ 10.

the same temperature and density throughout. If no artificial means be used to cause a movement in either direction, — down one, and up the other, — the air will be in equilibrium, and be stagnant. If the tops of the shafts be not of the same height, as AB, the air AE, if of the same density and temperature, would have the same effect as if the shaft rose to E, and remain in equilibrium. Suppose, now, that the external air is of lower temperature than the air in the shafts, and the column AB lower in temperature than CD, a movement of the air then takes place from A towards C. On the contrary, if the external air be warmer than that of the shafts, the shaft AB will be the upcast, and circulation will be from C to A, on account of the heavier column of air CD.

This is the principle upon which furnaces are employed to ventilate mines. They are placed at the bottom, or near the bottom, of the upcast shaft. The heat given off by them raises the temperature of the air, which expands part of its volume for each degree of heat added, and hence becomes lighter. The cooler air of the downcast shaft is now able, owing to its greater density, to fall down the shaft, and push the air of the mine into the upcast, which becomes, in turn, heated by the furnace. Let us take an example to see in what manner this difference in density will cause

ventilation. Suppose the two shafts to be of equal depth, say 900 feet, and suppose the barometer to stand at 29 inches; also let the temperature in the downcast be assumed to be 42°, and that of the upcast 72°. From the table on p. 21, we find that 100 cubic feet of air at 42° weigh 7.67 pounds: therefore 900 cubic feet weigh 9 times as much, or 69.030 pounds. Again: we find 100 cubic feet of air at 72° weigh 7.236 pounds, and hence 900 cubic feet weigh 65.124 pounds. The difference between these weights will give the pressure that would cause circulation.


900 cubic feet at 42° = 69.030
900 cubic feet at 72° = 65.124

Difference in weight 3.906

This pressure in the open air would produce a velocity of wind between twenty-five and thirty miles per hour.

11. The "motive-column" is a "head of air" of such a height that it will equal the difference between the weight of the downcast and upcast columns of air.

Let M= the motive-column, or head of air,

D = the depth of the upcast in feet,

t = the temperature of the upcast in degrees,
t1 the temperature of the downcast in degrees,




M = DX


Problem.-Find the motive-column which would produce a pressure of 3.906 pounds when the upcast has a depth of 900 feet and a temperature of 72°, and the downcast has the same depth and a temperature of 42°. Substituting in formula 5 we have

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as the length of the motive-column.

The height of a column of this air, one foot in area, weighing one pound, may be found by dividing the motive-column by the pressure per square foot; thus:

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The relative diameters of the shafts make no difference upon the total pressure, so far as the consideraThis is tions regarding ventilation are concerned. termed "the pneumatic paradox;" for if we have one square foot area for a downcast, and an upcast of ten square feet, the pressure on each square foot of upcast will be the same as on the one square foot of the downcast, provided there is no friction.

When calculating the weight of the motive-column, we must bear in mind that it is not the total amount of air, or the total number of cubic feet, that we seek, but the length of an air-column which has for its base one square foot, and which weighs a certain amount for each cubic foot in height.

12. The temperature of the atmosphere varies at different seasons of the year. This variation causes

considerable increase and decrease in the ventilation of mines. To illustrate this, suppose we have a mine 900 feet deep, what will be the ventilating pressure, when the temperature in the downcast is, on an average, 42°, and in the upcast 202°, the barometer being 30" on an average in the two shafts, which are equal in length?

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Suppose, now, the temperature of the downcast to

be raised to 82° F., then

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