Further, let _m_ be the mean temperature of the stratum of air between the stations. Now, if the mean temperature is less than 32, the column of air will be shorter; and if greater, longer than at 32. According to Regnault, air expands 1/49113 or 002036 of its volume at 32, for each degree increase of heat. Calling the correction due to the mean temperature of air _C_, its value will be found from the equation,

_C_ = _H_ (_m_ - 32) 002036

Calling the corrected height _H'_, it will be found from the formula,

_H'_ = _H_ + _H_ (_m_ - 32) 002036 that is, _H'_ = _H_ { 1 + (_m_ - 32) 002036 }

and subst.i.tuting the value of _H_,

_H'_ = _f_(_B_ - _b_) { 1 + (_m_ - 32) 002036 }

Strictly, according to theoretical considerations, there is a correction due to lat.i.tude, as in the determination of heights by the barometer; but its value is so small that it is practically of no importance.

If a barometer be observed at one of the stations, the table of vapour tensions (p. 62) will be useful in converting the pressure into the corresponding boiling-point, or _vice versa_; so that the difference of height may be found either by the methods employed for the boiling-point thermometer or the barometer.

In conclusion, it may be remarked that observers who have good instruments at considerable elevations, as sites on mountains or plateaus, would confer a benefit to science, by registering for a length of time the barometer along with the boiling temperature of water, as accurately as possible. Such observations would serve to verify the accuracy of theoretical deductions, and fix with certainty the theoretical scale with the barometer indications.

_Example, in calculating Heights from the Observations of the Boiling-point of Water._--1. At Geneva the observed boiling-point of water was 209335; on the Great St. Bernard it was 19764; the mean temperature of the intermediate air was 635; required the height of the Great St. Bernard above Geneva.

Method by formula:--

_H'_ = _f_ (_B_ - _b_) { 1 + (_m_ - 32) 002036 }

In this case _f_ is between 530 and 550, or 540.

_B_ = 209335 _m_ = 635 _b_ = 19764 32 ------- ----- 11695 315 _f_ = 540 002036 ------- --------- 63153 00641340 1064 1 ------- ----- _H'_ = 67195 feet. 1064 ======

Method by Tables supplied with boiling-point apparatus made by Messrs.

Negretti and Zambra:--

209335 gives 1464 in Table I.

19764 " 7736 "

---- 6272 635 " 107 in Table II.

---- Height 6711 ====

=96. Thermometers for Engineers.=--_1st. Salinometer._--Under the circ.u.mstances at which fresh water boils at 212, sea water boils at 2132. The boiling temperature is raised by the chemical solution of any substance in the water, and the more with the increase of matter dissolved.

From a knowledge of this principle, marine engineers make use of the thermometer to determine the amount of salts held in solution by the water in the boilers of sea-going steamers. Common sea-water contains 1/33 of its volume of salt and other earthy matters. As evaporation proceeds, the solution becomes proportionally stronger, and more heat is required to produce steam. The following table from the work of Messrs. Main and Brown, on the Marine Steam-Engine, shows the relation between the boiling-point under the mean pressure of the atmosphere, or 80 inches of mercury, and the proportion of matter dissolved in the water:--

Proportion of Salt in 100 parts of water 0 Boiling-point 212 " " 1/33 " 2132 " " 2/33 " 2144 " " 3/33 " 2155 " " 4/33 " 2166 " " 5/33 " 2179 " " 6/33 " 2190 " " 7/33 " 2202 " " 8/33 " 2214 " " 9/33 " 2225 " " 10/33 " 2237 " " 11/33 " 2249 " " 12/33 " 2260

When the salts in solution amount to 12/33, the water is saturated. It has also been ascertained that, when a solution of 4/33 is attained, incrustation of the substances commences on the boiler. Hence, it is a rule with engineers to expel some of the boiling water, when the thermometer indicates a temperature of 216, and introduce some more cold water, in order to prevent incrustation, which not only injures the boiler, but opposes the pa.s.sage of heat to the water. The thermometer used for this purpose should be very accurately graduated, and the scale must be considerably higher than, though it need not read much below 212.

_2nd. Pressure Gauge._--The elasticity of gases augments by increase of temperature, and _vice versa_; it follows, therefore, that when steam is generated in a closed boiler, its temperature rises beyond the boiling temperature of 212, owing to the increased pressure upon the water. The law connecting the pressure and the corresponding temperature of steam is the same as that upon which the boiling of fluids under diminished atmospheric pressure takes place. Hence, the indications of the thermometer become exponents of steam pressure. Engineers are furnished, in works on the steam-engine, with tables, from which the pressure corresponding to a given temperature, or the converse, can be obtained by mere inspection.

[Ill.u.s.tration: Fig. 74.]

Fig. 74 represents the thermometer employed as a steam-pressure gauge. It is fitted in a bra.s.s case, with screw-plug and washers for closing the boiler when the thermometer is not in use. The scale shows the pressure corresponding to the temperature, from 15 to 120 lbs., above the atmospheric pressure, which is usually taken as 15 lbs. on the square inch.

CHAPTER XI.

INSTRUMENTS FOR ASCERTAINING THE HUMIDITY OF THE AIR.

=97. Hygrometric Substances.=--The instruments devised for the purpose of ascertaining the humidity of the atmosphere are termed _hygrometers_. The earliest invented hygrometers were constructed of substances readily acted upon by the vapour in the air, such as hair, gra.s.s, seaweed, catgut, &c., which all absorb moisture, and thereby increase in length, and when deprived of it by drying they contract. Toy-like hygrometers, upon the principle of absorption, are still common as ornaments for mantel-pieces.

A useful little instrument of this cla.s.s, formed from the beard of the wild oat, is made to resemble a watch in external appearance, and is designed to prove the dampness or dryness of beds: a moveable hand points out on the dial the hygrometric condition of the clothes upon which the instrument is laid.

=98. Saussure's Hygrometer=, formerly used as a meteorologic instrument, but now regarded as an ornamental curiosity, is represented in fig. 75.

Its action depends upon a prepared hair, fixed at one end to the frame of the instrument, and wound round a pulley at the other. The pulley carries a pointer which has a counterpoise sufficient to keep the hair stretched.

By this means the shrinking and lengthening of the hair cause the pointer to traverse a graduated arc indicating the relative humidity.

[Ill.u.s.tration: Fig. 75.]

Such instruments, however ingenious, are not of scientific value; because they do not admit of rigid comparison, are liable to alter in their contractile and expansive properties, and cannot be made to indicate precisely alike.

=99. Dew-Point.=--The amount of water which the air can sustain in an invisible form increases with the temperature; but for every definite temperature there is a limit to the amount of vapour which can be thus diffused. When the air is cooled, the vapour present may be more than it can sustain; part will then be condensed as dew, rain, hail or snow, according to the meteorologic circ.u.mstances. The temperature which the air has when it is so fully saturated with vapour that any excess will be deposited as dew, is called the _dew-point_.

=100. Drosometer.=--"To measure the quant.i.ty of dew deposited each night, an instrument is used called a _Drosometer_. The most simple process consists in exposing to the open air bodies whose exact weight is known, and then weighing them afresh after they are covered with dew. According to Wells, locks of wool, weighing about eight grains, are to be preferred, which are to be divided [formed] into spherical ma.s.ses of the diameter of about two inches."--_Koemtz._

=101. Humidity.=--The proportion existing between the amount of vapour actually present in the air at any time, and the quant.i.ty necessary to completely saturate it, is called _the degree of humidity_. It is usually expressed in a centesimal scale, 0 being perfect dryness, and 100 complete saturation.

The pressure, or tension, of vapour at the dew-point temperature, divided by the tension of vapour at the air temperature and the quotient multiplied by 100, gives the degree of humidity. (Regnault's Tables should be used.)

Hence the utility of instruments for determining the dew-point.

=102. Leslie's Hygrometer.=--This instrument consists of a gla.s.s syphon tube, terminated with a bulb or ball at each end, turned outwards from each other, as in fig. 76. The tube is partly filled with concentrated sulphuric acid, tinged by carmine. One of the b.a.l.l.s is covered smoothly with fine muslin, and is kept continually moistened with pure water, drawn from a vase placed near it by the capillary attraction of a few strands of clean cotton-wick. The descent of the coloured liquid in the other stem will mark the diminution of temperature caused by the evaporation of the water from the humid surface. The drier the ambient air is, the more rapidly will the evaporation go on; and the cold produced will be greater.

When the air is nearly saturated with moisture, the evaporation goes on slowly; the cold produced is moderate, because the ball regains a large portion of its lost heat from surrounding bodies; and the degree of refrigeration of the ball is an index of the dryness of the air.

[Ill.u.s.tration: Fig. 76.]

"Should the water become frozen on the ball, this hygrometer will still act; for evaporation goes on from the surface of ice in proportion to the dryness of the air. Leslie estimates, that when the ball is moist, air, at the temperature of the ball, will take up moisture equal to the sixteen-thousandth part of its weight, for each degree of his hygrometer; and as ice in melting requires one-seventh of the caloric consumed in converting water into vapour, when the ball is frozen, the hygrometer will sink more than when wet by 1 in 7; and hence, in the frozen state, we must increase the value of the degrees one-seventh: so that each of them will correspond to an absorption of moisture equal to one-fourteen-thousandth part of the weight of the air.

"When this hygrometer stands at 15, the air feels damp; from 30 to 40, we reckon it dry; from 50 to 60, very dry; and from 70 upwards, we should call it intensely dry. A room would feel uncomfortable, and would probably be unwholesome, if the instrument in it did not reach 30.[8] In thick fogs it keeps almost at the beginning of the scale. In winter, in our climate, it ranges from 5 to 15; in summer often from 15 to 55; and sometimes attains 80 or 90. The greatest degree of dryness ever noticed by Leslie was at Paris, in the month of September, when the hygrometer indicated 120."--_Professor Trail, in "Library of Useful Knowledge."_

In estimating the value of the indications of this hygrometer, it should be borne in mind that the scale adopted by Leslie was _millesimal_, that is to say, from the freezing to the boiling-point of water was divided into a thousand parts; ten millesimal degrees are therefore equal to one of the scale of Celsius.

103. DANIEL'S HYGROMETER.