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MEASUREMENT OF HEIGHTS BY THE BAROMETER.

ter. When going on such an expedition, it is well to take also a hypsometer, and other instruments, so as to determine the dewpoint, solar radiation, temperature of the air, etc. These will be described in detail under Meteorological Instruments. On reaching the foot of the mountain, observations should be taken, and again on the return, and the mean of these compared with those taken at the top. Or better, one observer with a barometer is left below to take readings at regular intervals, as every quarter of an hour, during the whole time of the ascent. These are afterwards compared with those taken at the same time at the summit. Of course the lower barometer is compared carefully with the others at the beginning and end of the trip, and the errors corrected. If only one barometer is at hand, and time allows, a series of observations should be taken before and after the ascent, a curve constructed, and the intermediate readings obtained by interpolation. Accuracy is to be expected only from a long series of observations above and below, by which accidental errors are eliminated; any sudden change in the weather, as a thunder-storm, is especially liable to affect the result.

A small aneroid which may be easily carried in the pocket, is often very serviceable in preliminary surveys; by using it in connection with a pedometer, an approximate profile of the country may be constructed. In the same way the variations in the grade of a railway may be determined. The delicacy of these barometers is such that they will show the difference of the level of the different parts of a house, or even the rise and fall of a vessel at sea. For such observations the height is obtained with sufficient accuracy by allowing 87 feet for every tenth of an inch fall of the barometer.

MEASUREMENT OF HEIGHTS BY THE BAROMETER.

On ascending from the surface of the earth, the barometric pressure continually diminishes, and this is due to the fact that being caused by the weight of the superincumbent air, the greater the height the less the load to be borne. The law of diminution is easily deduced by the calculus; call p the pressure in inches at any height H. The decrease of pressure, or -dp, in any interval dÃ, is evi

MEASUREMENT OF HEIGHTS BY THE BAROMETER.

117

dently due to a column of air of this height, whose weight is pro

-dp

агат,

αρ

1

or H

a

log p

portional to p. Hence ―dpapd H, dH +C. The constant a equals the pressure due to a column of air of height unity and under pressure unity, or its reciprocal equals 60,300. The elevation E, or difference in height of two points Hand H' is therefore HH' 60,300 (log p' - log p).

In order to obtain the true height by the formula, it is necessary to apply several corrections, of which the most important are the following.

I. Capillarity. The effect of this force is to depress the mercury column by an amount dependent on the diameter of the tube. A constant quantity should therefore be added to each reading. Unfortunately this result is modified by the adhesion of the liquid to the tube, which renders this correction uncertain; sometimes, therefore, the height of the meniscus or curved portion is allowed for, but the best way is to use a very large tube, when the effect of capillarity becomes inappreciable.

p
1 + a T

II. Temperature of the Mercury. The standard pressure assumes the temperature to be 0° C.; at higher temperatures the mercury would be lighter, and the pressure less. Let Ρ be the observed height at temperature T, and P the true height with mercury at zero, then p = P (1 + a T′), or P in which a equals the expansion of the mercury per degree. As the scale expands. also, allowance must be made for this, which gives a = .00009, when the scale is of brass. The temperature T is given by the thermometer attached to the instrument, and this correction should always be applied to a mercurial barometer, but not to an aneroid, when the height is wanted.

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III. Temperature of the Air. In the above discussion the air also is supposed to be at zero. If warmer it will be lighter, and the elevation greater than that here assumed. Call t and t' the temperatures above and below, and their mean t" (t+t'). The true elevation E will then equal E (1 + a t'') in which a the coefficient of expansion of air. This is the most important correction of all, and should always be applied, or large errors will be introduced.

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IV. Latitude. Still another correction may be applied when great accuracy is required, owing to the diminution of the force of gravity as we approach the equator. The computed elevation should be multiplied by (1 + .0026 cos 27), in which is the latitude, since the force of gravity varies according to this law.

Introducing these corrections into the formula and reducing, it may be written in the following form,

E=120(log p-log p') (502 + t + t),

which may be applied directly to observations taken with an aneroid. For a mercurial barometer, p and p', must be corrected, first for capillarity, and then divided by (1 + .00009 T) and (1 + .00009 T'). The correction for latitude is always small, and becomes 0 at 45°.

59. BUNSEN PUMP.

Apparatus. Fig. 46 represents a Bunsen filter-pump, such as is used in chemical laboratories. A is a valve in the supply-pipe, by which the water is admitted to the bulb B. From this it withdraws a portion of the air, which passes down the pipe E with the water. The vessel to be exhausted C, is connected with B by the long pipe CB, through which the air is drawn. Above C is placed a U mercury-gauge, and below it a wide tube, designed to prevent the pressure from exceeding a certain amount. A fine hole is made near the bottom of this tube, and it dips into a mercury-cistern D. As the pressure diminishes, the mercury rises in D and falls in the outer vessel until below this hole, and the air rushes in and increases the pressure; by varying the height of the cistern any pressure may be maintained. This device, though excellent in theory, often gives trouble in practice from the jumping of the mercury, unless the tube is large and the hole small. Instead, therefore, two or more valves may be used, or the tube nearly closed, and thus the air admitted so slowly as to keep up the required pressure. If too much water is passed through B it sometimes overflows into C. An arm and stop should therefore be attached to A, so that it cannot be opened too far. water escaping from E is received in a Florence flask, F, which is fitted with a second tube G, passing nearly to the bottom, while E opens near the top. To measure the amount of water expended, a balance and weights should be provided, or a large graduated vessel.

The

Experiment. Open A and the water will flow through B, and there encountering the air, will carry it in bubbles through E. If

now is closed, the air will gradually be carried out of B, producing a rarefaction, and the air-bubbles

in E will be found to occupy less and less space compared with the water, until the limit of exhaustion is reached, and the tube carries off nothing but water. The diminution in pressure thus obtained should nearly equal that of a column of water of height BE, or if this is made 40 feet, nearly all the air should be withdrawn. The aqueous vapor, however, always remains, and for other reasons the exhaustion is never perfect; it nevertheless forms a very convenient method of producing a partial vacuum.

Gf

Fig. 46.

D

مها

A

To test the working of the pump and its efficiency, the following experiment should be performed. Pour water through G until F is filled up to the end of the tube E. Empty it by blowing through E, collect the water escaping from G, and weigh it. The weight in grammes gives V, the volume in cubic centimetres of the portion of F included between the ends of E and G. Measure the temperature of the water and the height of the barometer. Fill Fas before, take out of the mercury, and open A slightly. A large amount of air and a small amount of water will now enter the flask. Water will flow from G until a volume of air equal to V has entered the flask, and air begins to bubble up through G. Collect the water that has escaped, and weigh it. Calling its volume V', the amount of water brought from B is evidently V' V, while in the same time V centimetres of air have been brought down. Record also the time required to empty F. Repeat the experiment several times with a larger flow of water. Try also the effect of a flow under pressure by connecting the end of C in the mercury, which will then rise in it when the water is turned on, and may be kept at any desired height by raising or lowering D. As in these experiments it takes some time for the mercury to attain its normal level, it is well to connect a third tube with the flask, which may then be filled without disconnecting it from B. It will be seen that the best results are attained when the smallest

amount of water is used, but as the exhaustion then takes place very slowly, it is often best to begin with a large flow, and diminish it as the air is withdrawn. The maximum amount of air that might be drawn out by the apparatus may be determined analytically, and dividing the observed amount by this, gives the efficiency.

This same apparatus may also be employed with advantage, to test aneroid barometers. C is attached to an air-tight chamber, formed of a tubulated receiver placed on an air-pump plate. When the water is turned on, the air is gradually withdrawn, and the barometer falls. The reading is compared with the true pressure found by subtracting the reading of the U gauge from the height of the standard barometer. Different results will be attained according as the barometer is placed vertically or horizontally, or if the friction is reduced by gently tapping on the instrument. To render the test more complete this experiment should be tried at different temperatures, which is best effected by a water jacket, which may be filled either with hot or cold water.

60. AIR-METER.

Apparatus. An organ bellows, such as is described in the next experiment, and an air-meter, of which a very convenient form is that manufactured by Casella. It consists of a very light fanwheel, like a wind-mill, with a counter to record the number of revolutions. The vanes are set at such an angle that the divisions of the dial shall represent the number of feet traversed by the air.

Experiment. Work the bellows and allow the air to escape through an orifice, so as to produce a constant current of air. Measure its velocity at intervals of ten inches from the orifice, until it becomes imperceptible. Measure also the velocity on each side of the central line. A spring catch serves to throw the gearing in or out of connection with the fan-wheel. To make an observation, therefore, the meter should be placed in the current, and when it has attained a uniform velocity thrown in gear for exactly one minute. As the hands move only during this time, the difference of readings taken before and after, give the distance. traversed, or dividing by 60, the velocity of the air per second.

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