60 9.9984639.998187 110 0.017672 0.020327 160 0.036881 0.041393 210 0.056090 0.061484

Logarithmic Coefficients.

EXPLANATION OF THE BAROMETRIC TABLES.

1. Table I. contains the depression of mercury in glass tubes, arising from capillary action, and must always be added to the observed height of the mercury in the barometer in those instruments which, from their construction, require it.

2. Table II. contains the corrections arising from temperature, in order to reduce the observed height of the mercury within a moderate range, to what it would be at the freezing-point, and when above that point it is always to be subtracted, but when below it must be added to get the true height at 32° Fahrenheit. When the temperature is below 32°, subtract it from 32°, and the difference added to 32° will be the argument above 32°, to obtain the correction to be added to reduce the height of the mercury in the barometer to that point of temperature when Part I. only is employed, which for general purposes is sufficiently correct.

Part II. was deduced from the following formula:—

Let the observed height on the scale of brass be represented by ß, the dilatation of mercury for one degree of the thermometer by A, the dilatation of brass for one degree of temperature also by d, the normal temperature, (the freezing-point), to which all heights of the barometer are to be reduced by 7, then it will be found, that to reduce the height of the barometer, at any temperature t common to the scale and mercury, the correction must be

C=ß

A(t—)-d(t―0)
1+A(t)

(C)

in which is the standard temperature, 62° Fahrenheit, at which the brass scale shows English inches.

The table was calculated on the supposition, that the dilatation from the freezing to the boiling points were

the

Brass

0.0018782, Mercury

0.018018*

3. Table III. contains the expansion of mercury in volume, for purpose of reducing the upper and lower barometers to the same temperature, as shown in the computation of heights by the baro

meter.

4. Table IV. contains the elastic force of aqueous vapour, and its use is shown in the computations.

Let

Correction for Pressure and Temperature.

Ρ be the actual barometric pressure, f the tabular elastic force, t the temperature, and d the dew-point; then if f' be the correct

pf
30

t-d

elastic force, f' (1+4418+)

5. Table V. contains the expansions of dry air according to the hypothesis of Dalton, which, from the computations that I have made, seems to give accurate barometric heights. Should any computer prefer that of Dulong and Petit, of an equable expansion, there is given a column for that purpose.

6. Table VI. contains the effects arising from a variation of the force of gravity according to the latitude on the mercurial column.

0.0001004 (t—32°) — 0.0000098 (t—62°) 1+0.0001004 (t—32°)

* Hence, on this supposition, E = which would be rather more accurate than Table III. for mercury alone, when very great nicety is required.

7. Table VII. contains the logarithmic coefficients deduced from the principles previously explained according to the situations of the barometers relative to one another, and that of the lower above the level of the sea.

The usual formulæ given by Roy, Shuckburgh, and Laplace may give the height as near the geometrical method in certain cases, such as in a mean state of the atmosphere, as that which we have given, though there is no doubt but that the circumstances which have induced us to give a new method, involving considerations not usually attended to in such measurements, are more conformable to the laws of nature, and will in time become more accurate as those branches of physical science on which they depend are rendered more perfect.

The dew-point is supposed to be found by Daniell's hygrometer. If that instrument is not at hand, the dew-point may be found by two good thermometers, one of which has its ball covered with moistened tissue-paper, as proposed by Mr Anderson, Rector of the Academy of Perth, who also gives a formula for the barometric measurement of altitudes, in which in some of the corrections I have been anticipated.

Let F, the elastic force of vapour by Table IV. be thus reduced to f according to the difference between the naked and covered 0.028dt XP_F_0.00092dt × p, in which thermometers, then f-F

30

t is the difference between the temperatures of the thermometers, and p the barometric pressure.

Now let be the elastic force at the dew-point, then

F-0.00092 pdt

1+0.002084(t-d)1+0.0021(t-d)

Here d, the temperature of the dew-point, is unknown, but may be determined, first approximately from the numerator of the formula, and then substituted in the denominator, and a second approximation obtained, which will generally be sufficiently correct.

To exemplify this, let the thermometer with the dry ball show 60° F, and that covered with moistened tissue-paper

T-t or St.

5111

Now if the barometer be at 30.1 inches we have from the numera-
tor of formula (1) ƒ=0.524–0.00092 × 8 × 30.4-0.524-0.238-
0.286. This f corresponds, by the table of Dalton, to 42° nearly,
which being substituted for d in the denominator of the formula
0.286
0.286
gives 0=1+0.0021(60—42) 1.0378
=0.2756, which finally gives
d=41°.3, the dew-point. This is perhaps one of the best methods
of determining the point of deposition, as the instruments are not,
like the hygrometers of Deluc and Saussure, liable to be deteriorated
by time, and, besides, may still answer other purposes
which none
of the usual hygrometers can.

Cor. From the same principles may be derived a formula to
determine the weight of moisture in 100 cubic inches of air, or
0.6854
W=
at the freezing-point. When =.2756 and
1+0.0021 (d-32)
d=41.3, we get from the expression W=0.1837 grains when the air
is completely saturated with humidity. But when the temperatures

1

0.1837
1+0.0021 (60—41)

are 60° and 41° the W= 0.1767 grains in 100 cubic inches. Perhaps this method may be conveniently compared with Mr Daniell's, to show their relative accuracy and consistency. It may be added, that Mr Dalton states from experiments at moderate heights, that an elevation of 240 feet gives a depression of 1° temperature Fah. and an elevation of 390 feet gives a depression of 1°F. of the dew-point. Hence, if t be the temperature and D the dew-point ΔΗ At= and AD= 240'

ΔΗ 390

To determine the height from the given temperature. Let h be the height in feet, and n the change of temperature in degrees of Fahrenheit's thermometer, then h={251.5+ (n-1)} n,

h

also n=251.5+0.005 h very nearly,

If t be the temperature, and a the latitude,

t=97.08 cos * r—(10.534

h

—(10°.53+251.5+0.005 h.
h)

(1.) (2.)

(3.)

This last formula agrees very well with the continent of America where the latitude is considerable, but gives results generally too great near the equator.

In Europe and Asia t=81°.5 cos à very nearly,

Method II.

(4.)

For ordinary heights, such as those usually met with in Britain, the following method, requiring no tables, and easily recollected, is subjoined.

Let B be the barometric altitude at the lower situation, and b that at the upper corrected for the difference of temperature in the usual manner, the atmosphere being in its mean state with regard to aqueous vapour, &c.

Then H=13100

t+t'

(B+b) (B—b) { 1 + 0.00244 ("+" 32°) } =

Bb

{ 12100+16(1+t') } (B+b) (B—6)

Bb
Bar. In.

Ex.-Leith Pier, 29.567

Arthur's Seat, 28.704

2

28.704 x 0.0001 x3.5-0.010, and 28.704+0.010-28.714-b 12100+(54°+50°.5)16=104.5 × 16+12100=13772

=

806 feet.

803

3 feet.

Method III.

Mr Alexander Adie, optician in Edinburgh, has lately invented a very convenient and delicate instrument called a sympiesometer, to supply with advantage, in several cases, the mercurial barometer. It consists of a glass tube about 18 inches long, terminated above with a bulb filled with hydrogen gas, and having the lower extrem

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