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Title: The aneroid barometer: its construction and use

Author: George W. Plympton

Release date: December 10, 2022 [eBook #69513]

Language: English

Original publication: United States: D. Van Nostrand Company, 1884

Credits: deaurider and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive)

*** START OF THE PROJECT GUTENBERG EBOOK THE ANEROID BAROMETER: ITS CONSTRUCTION AND USE ***

THE

ANEROID BAROMETER:

ITS

CONSTRUCTION AND USE.

THIRD EDITION.

REVISED AND ENLARGED.

NEW YORK:

D. VAN NOSTRAND COMPANY,

23 MURRAY AND 27 WARREN STREET.

1890.

COPYRIGHT, 1884,

BY D. VAN NOSTRAND.

CONTENTS.

Page.

CHAPTER I.—The Atmosphere

5

CHAPTER II.—Barometric Measurements of Altitudes

27

CHAPTER III.—Aneroid Barometers: Their Construction

39

CHAPTER IV.—The Use of Aneroid Barometers

52

CHAPTER V.—Suggestions in Regard to the Selection and Systematic Use of an Aneroid

77

TABLE I.—Prof. Airy’s Table of Altitudes

88

TABLE II.—Logarithmic Table

106

TABLE III.—Metric Altitude Table

121

TABLE IV.—Corrections for Mercurial Barometer

125

TABLE V.—Boiling Point of Water corresponding to Different Barometric Pressures

126

PREFACE TO SECOND EDITION.

The fact that the first edition of this little manual is entirely exhausted is a sufficient indication that it supplied a want. As the use of the Aneroid Barometer is on the increase, the presumption is that there will be a further demand for this book of tables and instructions.

It has been thought advisable to rearrange the matter and to increase it by fuller descriptions of different instruments; and what is of more importance to the novice in measuring altitudes, to add a number of examples.

Another table has also been added to the collection of the previous edition.

THE ANEROID BAROMETER:

ITS CONSTRUCTION AND USE.

CHAPTER I.

THE ATMOSPHERE.

The gaseous envelope which surrounds our globe, and to which we give the name of atmosphere, is subject to many and varied changes. In the relative amount of the two gases which chiefly compose it, it remains marvelously constant; yielding upon analysis the same ratio of oxygen to nitrogen for all latitudes and all altitudes. It is only within a few restricted and generally confined areas where the natural chemical processes of respiration, combustion or fermentation are active, that the free oxygen is found to be notably deficient, and the product, carbonic dioxide, which exists normally to the extent of one twenty-fifth of one per cent., is, to a corresponding extent, in excess.

When, however, we regard the conditions which arise from its physical properties, no such constancy is observable. Indeed, it seems the most fitting type of a transitory state, and whether we regard the temperature, the moisture, the pressure resulting from its weight, or the direction and velocity of its motions, we can only acquaint ourselves with the limits within which these conditions have been known to vary. The nature of the changes within these limits we cannot, in the present state of our knowledge, assume to predict for the future, except for very limited periods; and even then the prediction is set forth only as a “probability.”

Certain average conditions are noticeable as belonging to certain areas or zones of the earth, and differing somewhat among themselves, especially as to greater or less range in temperature, moisture, etc. To such general conditions we apply the term climate.

The department of science which regards the physical phenomena arising from these varying conditions is called meteorology. The instruments employed with which to indicate or measure the extent of these changes, are of various kinds. Thus the thermometer indicates the relative temperature, the hygrometer the humidity, the anemometer the force or the velocity of the wind, and the barometer the pressure of the air which arises directly from its weight.

It is with the last of these instruments that we are especially concerned in the present essay. It has two quite distinct uses: One to indicate the varying pressures of the air at some fixed point for meteorological purposes, and the other to indicate difference in altitude of points to which the instrument is carried by affording a measure of the greater or less amount of atmosphere above it. Before using the instrument to measure altitudes it is important to become somewhat familiar with its use as a stationary instrument. The barometer most frequently employed for such use is the one invented by Toricelli in 1643. It is too well known to require description here. It will be sufficient to say that it measures the varying pressure of the air by the varying length of a column of mercury which balances the pressure.

When the barometer is employed for the purposes of meteorology only, the following facts are taken into consideration. We quote from Buchan’s “Handy Book of Meteorology.”

Variations of the Barometer.—The variations observed in the pressure of the air may be divided into two classes, viz., periodical and irregular; the periodical variations recurring at regular intervals, whilst the irregular variations observe no stated times. The most marked of the periodical variation is the daily variation, the regularity of which in the tropics is so great that, according to Humboldt, the hour may be ascertained from the height of the barometer without an error of more than 15 or 17 minutes on the average. This horary oscillation of the barometer is masked in Great Britain by the frequent fluctuations to which the atmosphere is subjected in these regions. It is, however, detected by taking the mean of a series of hourly observations conducted for some time. The results show two maxima occurring from 9 to 11 A.M. and from 9 to 11 P.M., and two minima occurring from 3 to 5 A.M. and from 3 to 5 P.M. (See Table, page 10.)

The maxima occur when the temperature is about the mean of the day, and the minima when it is at the highest and lowest respectively.

This daily fluctuation of the barometer is caused by the changes which take place from hour to hour of the day in the temperature, and by the varying quantity of vapor in the atmosphere.

TABLE SHOWING THE DAILY VARIATIONS AND RANGE OF THE BAROMETER IN DIFFERENT LATITUDES.

LAT.

A.M.

P.M.

RANGE.

MIN.

MAX.

MIN.

MAX.

Inches.

Inches.

Inches.

Inches.

Inches.

Atlantic Ocean

0.0

-.056

+.069

-.045

+.045

.125

Pacific Ocean

0.0

-.032

+.040

-.045

+.028

.085

Sierra Leone

8.28 N.

-.022

+.032

-.038

+.031

.070

Lima

12.3  S.

-.071

+.065

-.067

+.050

136

Calcutta

22.36 N.

-.017

+.052

-.038

+.018

.090

Pekin

39.53 N.

-.038

+.047

-.052

+.014

.099

Great St. Bernard

45.51 N.

-.010

+.005

-.003

+.012

.022

Plymouth (England)

50.21 N.

-.007

+.006

-.010

+.010

.020

St. Petersburg

59.58 N.

-.003

+.008

-.004

+.002

.012

The surface of the globe is always divided into a day and night hemisphere, separated by a great circle which revolves with the sun from east to west in twenty-four hours. These two hemispheres are thus in direct contrast to each other in respect of heat and evaporation. The hemisphere exposed to the sun is warm, and that turned in the other direction is cold. Owing to the short time in which each revolution takes place, the time of greatest heat is not at noon, when the sun is in the meridian, but about two or three hours thereafter; similarly, the period of greatest cold occurs about four in the morning. As the hemisphere under the sun’s rays becomes heated, the air, expanding upwards and outwards, flows over upon the other hemisphere where the air is colder and denser. There thus revolves round the globe from day to day, a wave of heat, from the crest of which air constantly tends to flow towards the meridian of greatest cold on the opposite side of the globe.

The barometer is influenced to a large extent by the elastic force of the vapor of water invisibly suspended in the atmosphere, in the same way as it is influenced by the dry air (oxygen and hydrogen). But the vapor of water also exerts a pressure on the barometer in another way. Vapor tends to diffuse itself equally through the air; but as the particles of air offer an obstruction to the watery particles, about 9 or 10 A.M., when evaporation is most rapid, the vapor is accumulated or pent up in the lower stratum of the atmosphere, and being impeded in its ascent its elastic force is increased by the reaction, and the barometer consequently rises. When the air falls below the temperature of the dew-point, part of its moisture is deposited in dew, and since some time must elapse before the vapor of the upper strata can diffuse itself downwards to supply the deficiency, the barometer falls—most markedly at 10 P.M., when the deposition of dew is greatest.

Hence, as regards temperature, the barometer is subject to a maximum and minimum pressure each day—the maximum occurring at the period of greatest cold, and the minimum at the period of greatest heat. And as regards vapor in the atmosphere, the barometer is subject to two maxima and minima of pressure—the maxima occurring at 10 A.M., when, owing to the rapid evaporation, the accumulation of vapor near the surface is greatest, and about sunset, or just before dew begins to be deposited, when the relative amount of vapor is great; and the minima in the evening, when the deposition of dew is greatest, and before sunrise, when evaporation and the quantity of vapor in the air is least.

Thus the maximum in the forenoon is brought about by the rapid evaporation arising from the dryness of the air and the increasing temperature. But as the vapor becomes more equally diffused, and the air more saturated, evaporation proceeds more languidly; the air becomes also more expanded by the heat, and flows away to meet the diurnal wave of cold advancing from the eastwards. Thus the pressure falls to the afternoon minimum about 4 P.M. From this time the temperature declines, the air approaches more nearly the point of saturation, and the pressure being further increased by accessions of air from the warm wave, now considerably to the westward, the evening maximum is attained. As the deposition of dew proceeds, the air becomes drier, the elastic pressure of the vapor is greatly diminished, and the pressure falls to a second minimum about 4 A.M.

The amount of these daily variations diminishes from the equator towards either pole, for the obvious reason that they depend, directly, or indirectly, on the heating power of the sun’s rays. Thus, while at the equator the daily fluctuation is 0.125 inch, in Great Britain it is only a sixth part of that amount. It is very small in the high latitudes of St. Petersburg and Bossekop; and in still higher latitudes, at that period of the year when there is no alternation of day and night, the diurnal variation probably does not occur. In the dry climate of Barnaul, in Siberia, there is no evening maximum; the lowest minimum occurs as early as midnight, and the only maximum at 9 A.M.

Since the whole column of the atmosphere, from the sea level upwards, expands during the heat of the day, thus lifting a portion of it above all places at higher levels, it is evident that the afternoon minimum at high stations will be less than at lower stations, especially when the ascent from the one to the other is abrupt. Thus, at Padua, in Italy, the afternoon minimum is 0.014 inch, but at Great St. Bernard it is only 0.003 inch.

Annual Variation.—When it is summer in the one hemisphere, it is winter in the other. In the hemisphere where summer prevails, the whole air being warmer than in the other hemisphere, expands both vertically and laterally. As a consequence of the lateral expansion there follows a transference of part of the air from the warm to the cold hemisphere along the earth’s surface; and, as a consequence of the vertical expansion, an overflow in the upper regions of the atmosphere in the same direction. Hence, in so far as the dry air of the atmosphere is concerned, the atmospheric pressure will be least in the summer and greatest in the winter of each hemisphere. But the production of aqueous vapor by evaporation being most active in summer, the pressure on the barometer will be much increased from this cause. As the aqueous vapor is transferred to the colder hemisphere it will be there condensed into rain, and being thereby withdrawn from the atmosphere, the barometer pressure will be diminished; but the dry air which the vapor brought with it from the warm hemisphere will remain, thus tending to increase the pressure.

In the neighborhood of the equator there is little variation in the mean pressure from month to month. Thus, at Cayenne, the pressure in January is 29.903 inches, and in July 29.957 inches.

At Calcutta, 22° 36' N. lat., the pressure is 29.408 in July, and 30.102 in January, thus showing a difference of 0.694; and at Rio de Janeiro, 22° 57' S. lat., it is 29.744 in January (summer), and 29.978 in July (winter), the difference being 0.234. The large annual variation at Calcutta is caused jointly by the great heat in July, and by the heavy rains which accompany the south-west monsoons at this season; while in January the barometer is high, owing to the north-east monsoons, by which the dry cold dense air of Central Asia is conveyed southward over India.

At places where the amount of vapor in the air varies little from month to month, but the variations of temperature are great, the difference between the summer and winter pressures are very striking. Thus, at Barnaul and Irkutsk, both in Siberia, the pressures in July are respectively 29.243 and 28.267, and in January 29.897 and 28.865, the differences being upwards of six-tenths of an inch. The great heat of Siberia during summer causes the air to expand and flow away in all directions, and the diminished pressure is not compensated for by any material accessions being made to the aqueous vapor of the atmosphere; and, on the other hand, the great cold and little rain in that region during winter causes high pressures to prevail during that season. The same peculiarity is seen, though in a modified degree, at Moscow, St. Petersburg, and Vienna.

At Reykjavik, in Iceland, the pressure in June is 29.717, and in December 29.273; at Sandwich, Orkney, 29.775, and 29.586; and at Sitcha, in Russian America, 29.975, and 29.664. In all these places the distribution of the pressure is just the reverse of what obtains in Siberia, being least in winter and greatest in summer. The high summer pressures are due to the cool summer temperatures as compared with surrounding countries, thus causing an inflow from these regions, and to the large amount of vapor in the atmosphere, thus still further raising the barometric column. On the other hand, the low winter pressures are due to the comparatively high winter temperatures causing an outflow towards adjoining countries, and the large winter rainfall which, by setting free great quantitles of latent heat, still farther augments and accelerates the outflow.

The variations in mean pressure are very slight, and not marked by any very decided regularity in their march through the seasons, at Dublin, Glasgow, London, Paris, and Rome. As compared with Barnaul and Reykjavik their temperature is at no season very different from that of surrounding countries, and the vapor and rainfall are at no time much in excess or defect, but are more equally distributed over the different months of the year.

At the Great St. Bernard, 8174 feet above the sea, the pressure in summer is 22.364 inches, while in winter it is only 22.044. At Padua, there is scarcely any difference in the pressure between summer and winter. The increase in the summer pressure at the Great St. Bernard is no doubt due to the same cause already referred to in art. 65—viz., the expansion of the air upward during the warm summer months, thus raising a larger portion of it above the barometer at the highest station. But at St. Fe de Bogota, 8615 feet high, near the equator, and where, consequently, the difference between the temperature in July and January is very small, the difference in the pressures of the same months is also very small, being only 0.035.

Distribution of Atmospheric Pressure over the globe, as determined by the Annual Means.—Though much additional observation is required, especially in Africa, Asia, and South America, before the isobarometric lines can be laid down on a map of the world, yet many important conclusions regarding the mean barometric pressure have been arrived at from the results already obtained. We have seen that the daily and monthly variations of pressure observed at different places are modified by the variations of the temperature of the air, the amount of vapor, and the rainfall. Since these are in their turn greatly modified by the unequal distribution of land and water on the earth’s surface, we should expect to find the pressure, and the variations in the pressure, most regular in the southern hemisphere. Accordingly, there is a remarkable regularity observed in the distribution of the pressure from about 40° N. lat. southwards to the Antarctic Ocean, with the exception of the region of the monsoons in Southern Asia.

The mean pressure in the equatorial regions is about 29.90; at 20° N. lat. it rises to 30.00, and at 35° N. lat. to 30.20, from which northwards the pressure is diminished. The same peculiarity is seen south of the equator, but it is not so strongly marked. At 45° S. lat. it falls to 29.90, and from this southwards it continues steadily and rapidly to fall to a mean pressure of 28.91 at 75° S. lat. This extraordinary depression of the barometer in the Antarctic Ocean, being one inch less than at the equator and 1,326 inches less than at Algiers, is perhaps the most remarkable fact in the meteorology of the globe.

The pressure in the north temperate and frigid zones is in striking contrast to the above. From Athens, in a north-eastern direction, a high isobarometric line traverses Asia, passing in its course Tiflis, Barnaul, Irkutsk, and Yakutsk. To the east of the northern part of this area of high mean pressure, around the peninsula of Kamtschatka, there is a region of low barometer, the mean pressure being only 29.682. There is another remarkable area of low pressure around Iceland, the center being probably in the south-west of the island near Reykjavik, where the mean is 29.578. As observations are more numerous in Europe and North America, the dimensions of this depression may be defined with considerable precision by drawing the isobarometric of 29.90, which is about the mean atmospheric pressure. This line passes through Barrow Straits in North America, thence south-eastward toward Newfoundland, then eastward through the north of Ireland, the south of Scotland, and the south of Sweden, whence it proceeds in a north-easterly direction to Spitzbergen. The following mean annual pressures will show the nature of the depression: New York, 30.001; Paris, 29.988; London, 29.956; Glasgow, 29.863; Orkney, 29.781; Bergen, 29.804; Spitzbergen, 29.794; Reykjavik, 29.578; Godthaab, in S. Greenland, 29.605; Upernavik, in N. Greenland, 29.732; and Melville Island, 29.807. A depression also occurs in India, where the mean is only about 29.850, whereas in the same latitudes elsewhere it is about 30.100.

There are thus four areas of low pressure on the globe, the extent of each being nearly proportioned to the depth of the central depression—viz., Antarctic Ocean, the least pressure being 28.910; Iceland, 29.578; Kamtschatka, 29.682; and India, 29.850; and three areas of high pressure, one lying between latitudes 20° and 40° N., another between 15° and 35° S., and the third in Central Asia, from south-west to north-east. These low mean pressures are by no means constant in all cases during the months of the year. In the Antarctic Ocean they are nearly constant during the months, with perhaps a slight tendency to an increase in winter. In the region of low pressure around Iceland the pressure is a little less than elsewhere in summer; but in winter, when the rainfall is heaviest, it is very much less, being 0.251 inch less in winter than in summer at Reykjavik, and 0.189 at Sandwich, in Orkney. Similarly at Petropaulovski, in Kamtschatka, the pressure in winter is 0.323 less than in summer. Hence the low mean annual pressures in the North Atlantic and the North Pacific are chiefly brought about by the low pressure during the cold months of the year, and are doubtless caused by the copious rainfall during that season. On the other hand, in Southern Asia, the lowest pressures occur in summer. Thus, at Calcutta it is 29.408 in July, while in January it is 30.102—the average pressure for that degree of north latitude. Hence, in Hindostan, the low mean annual pressure arises from the very low pressure in summer caused by the heavy rains falling at that season, particularly on the south slope of the Himalayas. Generally the pressure is low wherever a copious rainfall prevails over a considerable portion of the earth’s surface, owing to the large quantity of caloric set free as the vapor is condensed into rain.

It is scarcely necessary to point out how important it is to keep in mind these facts of the pressure of the atmosphere, it being evident, for instance, that a pressure of 29.00 in the North Atlantic would portend stormy winds, while the same pressure south of Cape Horn, being the mean pressure there, would indicate settled weather.

The readings of the mercurial barometer are subjected in nice observations to several corrections:

1st. To 32° F. allowance being made for expansion of both mercury and scale for all observations above that temperature. A barometric pressure of thirty inches at 32° would be indicated by a height of 30⅒ inches at 70°.

2d. For decrease of gravitation at stations above the level of the sea, acting on both the mercury and the air.

3d. For increase of gravity with increase of latitude.

4th. For temperature of air; the density decreasing as temperature rises.

5th. For humidity of the air which also influences its density.

6th. For capillary attraction of the tube.

CHAPTER II.

BAROMETRIC MEASUREMENTS

OF ALTITUDES.

The text books in physics present formulas for computing heights from barometric observations, based on physical laws which we will briefly give.

If the density of the air were constant throughout, the measurement of heights would be a problem of the simplest character; for as mercury weighs 10,500 times as much as air at the sea level, the mercurial column would fall one inch for every 10,500 inches of ascent above the sea. But air is compressible, and, in accordance with Boyle’s law, its density varies with the pressure to which it is subjected.

Now suppose the atmosphere divided into layers of uniform thickness, but so thin that the density may be considered uniform throughout.

Let h = the thickness of each layer.

W = weight of a cubic foot of air at pressure H.

W₁ = weight of a cubic foot of air at H.

H₀ H₁, &c. = pressures measured in inches of mercury.

Then the pressure upon the unit of surface of any layer is greater than that upon the surface of next higher layer, by the weight of a volume of air whose base is the unit of surface and whose height is the thickness of the layer. If one foot be the unit of surface, then this quantity would be hW. And to express it by height of mercury column, it is necessary to multiply by

which gives

But W : W₀ : : H : 30.

W₀ being the weight of a cubic foot air at the level of the sea (=.0807 at 32°F).

We have from the above

,

and the above expression for diminution may be written

.

If H₀ H₁ H₂ represent the pressures at the surfaces of the successive layers, we shall have

Multiplying these equations and suppressing common factors, we get

If h be taken at one foot then n would represent the number of feet vertically between two stations at which the barometric pressures are Hn and H₀ respectively.

By substituting for W₀ its value and taking logarithms we have

whence

For use in accurate observations, corrections are required for temperature, humidity and variation in the force of gravity.

La Place’s formula which includes terms derived from the consideration of these conditions is obtained as follows:

Suppose a portion of the atmosphere included between two stations at different altitudes to be divided into very thin laminæ.

Let z be the distance of one of these from the surface of the globe and dz its thickness.

Let P be the pressure upon a unit of surface upon the lower side of this layer; and W the weight per cubic meter of the air at this pressure.

Then the pressure on the upper side will be less than P by an amount equal to the weight of a column of air whose base is a unit and height is equal to dz.

Whence

If W₀ be the weight of a cubic meter of air at the temperature 0°C and a barometric pressure of 0.ᵐ76, the weight of this same volume at pressure P and temperature ϴ would be

a being the coefficient of dilatation of air which is here taken at .004 in consequence of the constant presence of watery vapor.

This expresses the weight at the surface of the globe. If transferred to the height z, the weight would be diminished in the ratio of the squares of the distances from the center of the earth. We should then have

Substituting in equation 1, dividing by P and integrating between 0 and z, we get, by calling the pressure at the lower station P₀

the logarithm being Napierian.

From this we obtain

But the pressures P₀ and P are in direct ratio of the mercury columns which we will designate by h₀ and h. These columns also vary in weight in accordance with the law of inverse squares of distance from the earth’s center, so that

Substituting in the value of z, we have

But as z is so very small compared with R₁ we may replace by .

Also may be neglected.

We shall then have

The weight W₀ refers to the height h₁ the lower of the two stations. At the surface of the earth, this weight would be greater in the ratio of . But as h is always small compared with R this correction may be neglected.

But there is another of more importance which should be taken into account. On account of the spheroidal form of the globe weight varies with the latitude. If G represent the weight of a body at latitude 45°, then at any other latitude l, its weight, is found by multiplying G by

This factor is to be applied to W₀ in the formula. This is accomplished by multiplying the above value of z by

In order to simplify the expression we will substitute for the mean between the temperatures of the upper and lower stations, designated by t₀ and t. The factor then becomes

and the value of z may be written

If M be used to represent the modulus of the Napierian logarithms we may write

in which the logarithms are of the common kind.

This is La Place’s formula. h in the expression is not the barometric height directly observed at the upper station, but this height reduced to the temperature of the lower station.

The value of has been determined by trial of the formula upon known altitudes. Ramond in his survey of the Pyrenees determined its value to be 18336.

The unknown term z in the second member is determined by successive approximations.

The first value being

This being substituted, we may have

Finally, these being substituted in the above value of z we get

The terms of this formula are generally reduced to tabular form for practical use.

Guyot’s formula which is derived from this, reducing meters to feet and the constants depending on temperature being changed to accord with Fahrenheit’s scale, is

The three terms after the first are the corrections. The first being that for the temperature at the two stations. The second is the correction for the force of gravity depending on the latitude.

The third contains, first the correction for action of gravity on the mercury column at the elevation z, and second a correction required for decrease in density of air owing to decrease in action of gravity at the greater elevation. The factor s being the approximate difference in altitude of the stations.

Plantamour’s formula, which has been much used, differs slightly from Guyot’s. The first coefficient is 60384.3. The denominator of temperature term is 982.26 and a separate correction is used for humidity of the air.

To use either of these formulas tables are necessary, of which those prepared by Lieut. Col. Williamson[1] are the most elaborate.

For the Aneroid in ordinary practice, formulas of much less complexity may be profitably used. The corrections depending upon the gravity of the mercury column would, in any case, be omitted. The other corrections may in very nice work be retained. But a correction depending on the effect of changes of temperature on the metallic work of the instrument should be carefully remembered. First-class Aneroids claim to be compensated, but a greater portion will need a correction which the purchaser can determine for himself, by subjecting the instrument to different temperatures while the pressure remains constant.

A modification of Guyot’s formula adapted to aneroid work was suggested in an excellent paper on the use of the aneroid, read before the American Society of Civil Engineers, in January, 1871.

It is

D is the difference of altitude in feet. H and h are the barometric readings in inches.

T and t are the temperatures of the air at the two stations.

Table II is prepared for the use of this formula.

Other formulas will be given in another chapter.

[1] The use of the Barometer on Surveys and Reconnoisances. By R. S. Williamson. New York: D. Van Nostrand. London: Trubner & Co.

CHAPTER III.

ANEROID BAROMETERS:

THEIR CONSTRUCTION.

The general principle of construction of all aneroids is the same. A box with flexible sides, hermetically sealed, the air having been first exhausted, changes its form as the pressure of the atmosphere varies.

The chief differences in the various kinds lie in the mechanical devices, by which the motions of the box are rendered apparent to the eye, and also measured in such a manner as to allow the corresponding pressures to be expressed in inches of mercury.

Fig. 1.

The aneroid was invented about the beginning of this century, but was first made of a serviceable form by Vidi, in 1848. It is substantially the form most used to-day. The vacuum box is a thin low cylinder, and the motion of the thin flexible head of the cylinder is conveyed by suitable mechanism to the index hand. Vidi’s aneroid is shown in Fig. 1. D is the vacuum box, supporting the upright pillar M upon its center. As M rises or falls, a corresponding motion is given to the plate C. A counter-pressure is afforded by the spiral spring S. The motion of C is conveyed by the links 1 and 2 to a little rocker shaft, shown in the figure. An arm, 3, attached to this shaft is connected by a minute chain with the shaft which carries the index pointer. It is kept wound to the proper tension about this shaft by a fine spiral hair spring.

Fig. 2.

Fig. 3.

A modification of this is shown in Figs. 2 and 3. (See, also, frontispiece). This is Naudet’s aneroid, and is the one chiefly employed now. It differs from Vidi’s in the substitution of the thin laminated spring (B in frontispiece) for the spiral spring (S in Fig. 1).

Fig. 4.

One of the oldest forms of box barometer and the one to which the name aneroid is restricted by some writers, is represented in Fig. 4. A rectangular tube, from which the air has been perfectly exhausted, is sealed hermetically, and, having been bent into the form represented in the figure by cbd, is made fast at the middle point b. The varying pressure of the atmosphere causes the extremities c and d to approach or recede from each other. This motion is converted into a to-and-fro traverse of the index, by a mechanism sufficiently well exhibited by the diagram.

This is known as Bourdon’s form. It is not now employed for delicate work. The forms of Vidi and Naudet are, by some writers, designated the holosteric barometers.

The graduation of these instruments is made to correspond with the height of the mercurial barometer, and is expressed as inches or millimeters.

The difficulties to be met by the maker, in securing accuracy of working, are those which arise chiefly from the varying elasticity of the several metallic elements under change of temperature. Greater simplicity of construction might be presumed to be attended with a smaller liability to a kind of error, for which it is exceedingly difficult to compensate. This is the theory of the Goldschmid Aneroid.

The instrument designed for ordinary engineering use is represented by Fig. 5. The size recommended by the present makers for this service is 3⅛ inches in diameter and 2½ inches high.

Fig. 5.

Fig. 6.

Fig. 7.

The construction is exhibited by Fig. 6. The vacuum box, constructed as before described, is shown at aa. The motions of the box, caused by variations of atmospheric pressure, are conveyed directly to the lever, whose fulcrum is at e″, and whose free end is at e. This end, projecting through the side of the casing and working freely through a slot, is observed with a magnifying lens, and the reading on the index ff taken. But it is evident that the lever, working with proper ease on its fulcrum, must be supplied with a certain amount of counter-pressure. This is ingeniously done by aid of the delicate spring e', which is attached to the lever near the fulcrum. Bearing on the spring is the point of the micrometer screw M, whose head is graduated to hundredths and forms the top of the case. Both lever and spring are furnished at their extremities with bright metal heads, whose end surfaces lie in the same plane. The head e' is, under ordinary conditions, higher than e, as shown in Fig. 6. When a reading is to be taken the top of the case is turned until e' and e are side by side; the horizontal marks borne on the metallic heads being brought to an exact coincidence by aid of a lens (P in Fig. 5). The reading of the inches is taken from the scale ff, and of the hundredths from the divisions on the scale around the top of the box T; a fixed point c being marked on the cylinder. In figure 7 the indices exhibit a reading of 29.75 inches.

The thermometer F is an important part of the instrument.

In some of these instruments the scale ff bears no reference to the inches of the mercurial barometer, but is of an arbitrary character, and is different for different instruments. The value of the divisions is determined by comparison with standard instruments, and is carefully expressed in tabular form on the cover of the box.

Some corrections for temperature and pressure are required in the use of these instruments which, although desirable in the more common forms of aneroid, have not heretofore been considered necessary. In the latter instruments, however, when of the best construction, a compensation has been effected which renders a correction for temperature unnecessary. In the Goldschmid aneroids no compensation is attempted, but each instrument is furnished with a table of corrections which have been prepared from observation on standard instruments.

Thus, aneroid No. 3187, imported last year, bears on the cover the following:

CORRECTION TABLE.

For Division.

For Temperature.

26.0″ = -0.02

28° to 48° = 0

26.5″ = -0.03

52° = +0.01

27.0″ = -0.03

56° = +0.015

27.5″ = -0.02

60° = +0.025

28.0″ = 0

64° = +0.035

28.5″ = +0.03

68° = +0.04

29.0″ = +0.06

72° = +0.05

29.5″ = +0.10

76° = +0.07

30.0″ = +0.14

80° = +0.09

30.5″ = +0.19

84° = +0.11

31.0″ = +0.25

92° = +0.15

The temperatures are, of course, taken from the thermometer that forms a part of the instrument, and which, when the latter is carried slung from the shoulder, may exhibit a temperature considerably higher than that of the air.

A smaller and ruder instrument called the Pocket Aneroid is made by the Zurich manufacturers. It is only 1½ inches in diameter and 1¼ inches high. A bar fastened to the top of the vacuum box takes the place of the lever in the larger instrument.

A larger size is also made in which the movements of the vacuum box are directly observed with a compound microscope.

Fig. 8.

Fig. 9.

There is no doubt that all aneroids need a careful comparison with standard instruments or a series of trials upon known altitudes, in order to determine the proper corrections. Such trials should be made at different temperatures and under different conditions as to rising or falling at the time of observation. The tables of corrections furnished by the maker cannot well be substituted for those made by a careful observer deduced from systematic work. The air pump, the hot chamber and the freezing box are convenient, but inadequate substitutes for a large number of trials under normal conditions.

CHAPTER IV.

THE USE OF ANEROID BAROMETERS.

The Aneroid, like the Mercurial barometer may be used either as a weather indicator or in the measurement of altitudes. When used in the former capacity, the Aneroid, especially at sea, possesses some obvious advantages. Aside from its superior compactness of form and its portability, it responds more readily to the changes in atmospheric pressure than the Mercury column, and thereby serves more efficiently to warn the mariner of sudden tempests.

The words Rain—Change—Fair seen stamped or engraved on the dial of many barometers have, of course, no special significance, and are now rarely seen on first-class instruments of either kind. The probable changes of weather indicated by changes of the barometer are briefly set forth in the following:

RULES FOR FORETELLING THE WEATHER.

A Rising Barometer.

A “rapid” rise indicates unsettled weather.

A “gradual” rise indicates settled weather.

A “rise” with dry air, and cold increasing in summer, indicates wind from Northward; and if rain has fallen better weather is to be expected.

A “rise” with moist air, and a low temperature, indicates wind and rain from Northward.

A “rise” with southerly wind indicates fine weather.

A Steady Barometer.

With dry air and seasonable temperature, indicates a continuance of very fine weather.

A Falling Barometer.

A “rapid” fall indicates stormy weather.

A “rapid” fall, with westerly wind, indicates stormy weather from Northward.

A “fall,” with a northerly wind, indicates storm, with rain and hail in summer, and snow in winter.

A “fall,” with increased moisture in the air, and the heat increasing, indicates wind and rain from Southward.

A “fall” with dry air and cold increasing (in winter) indicates snow.

A “fall” after very calm and warm weather indicates rain with squally weather.

It does not require the highest quality in the mechanism of an Aneroid to serve the purpose indicated in the above rules.

For the accurate measurement of differences of altitude, however, the best skill in construction and the most careful adjustment of the parts is indispensably necessary. The use of an Aneroid of even medium quality will frequently lead to considerable errors in estimating heights. It may also be added here that instruments of the best manufacture in the hands of observers unacquainted with the principles involved, will often lead to erroneous conclusions. This is owing in many cases to a method adopted by some makers of adding a circle marked feet outside of the common graduation to inches of mercury.

Many tourists carry Aneroids of the pocket size, and consult them frequently while traveling, relying upon a single observation of the index for the determination of their altitude.

If such a circle of feet be engraved on the dial plate with the zero mark made to correspond with 30 inches of the mercury column, of course every estimate of altitude made as above mentioned assumes that at the moment of observation; the barometer at the level of the sea would stand exactly at 30 inches; a condition only realized occasionally. And the further condition is also assumed, that the temperature of the air is of no account in estimating heights; an assumption equally at variance with fact.

It is only an inferior class of Aneroids that bear a fixed graduated circle of feet, with the zero of altitude corresponding to 30 inches of pressure.

Prof. Airy, the former Astronomer Royal of Great Britain, prepared a table for the use of barometer makers—a scale from which is now engraved on many English Aneroids. It places the zero of altitude at 31 inches of pressure. This affords such large numbers for slight elevations that the proper use of the rule is suggested to the observer. He is led to subtract the two readings of feet to get difference in height. But this again assumes that the average temperature is 50° F.

Table I exhibits Prof. Airy’s series of heights.

Some makers, designing to improve upon the simple construction just described, have engraved the outer circle of feet on a movable ring encircling the dial, so that when an observer is at any locality whose height is known, he may bring the proper mark of the altitude scale against the index pointer. Then if the observer travels about over a section of country, the pointer will indicate with fair approximation for some hours the altitude of the new positions.

FIELD’S ENGINEERING ANEROID.

For description, see page 57.

This device is convenient to a skilled observer who only requires rapid and approximate results, but to the novice it is misleading in two ways; first, because the temperature is left out of the calculation, and furthermore, such a use of the movable scale will, at times, involve a large error, as it is not a scale of equal parts.

Mr. Rogers Field, C. E., in 1873, applied the movable scale to the Aneroid, so as to convert it from a source of inaccuracy into an aid towards accuracy. He employs the altitude scale proposed by Sir G. Airy for temperature 50°, but he makes it movable so as to adjust it for any other temperature. The shifting of the scale into certain fixed positions, is made to answer the same purpose as if the original scale were altered to suit various temperatures of the air. In the Journal of the Meteorological Society for 1874, January, Mr. Field says:

“The object aimed at in designing this improved form of Aneroid was, to simplify the correct determination of altitudes in cases such as ordinarily occur in England, and the instrument is therefore arranged to suit moderate elevations, say of 2000 feet and under, and is not intended for more considerable heights.

“The Aneroid is graduated for inches in the usual way on the face, but the graduation only extends from 31 inches to 27 inches so as to preserve an open scale. The outer movable scale is graduated in feet for altitudes, and this graduation is laid down by fixing the movable scale with the zero opposite 31 inches. This is the normal position of the scale and it is then correct for a temperature of 50°. For temperatures below 50° the zero of the scale is moved below 31 inches; for temperatures above 50°, the zero of the scale is moved above 31 inches. The exact position of the scale for different temperatures has been determined partly by calculation and partly by trial, and marked by figures engraved on the outside of the Aneroid. In order to insure the altitude scale not being shifted, after it has once been set in its proper position there is a simple contrivance for locking it in the various positions. This consists of a pin, which fits into a series of notches on the outside of the ring carrying the glass. By slightly raising the glass it is freed from this locking pin, and can be turned until the figures corresponding to the air temperature are opposite to the pin, when the glass should be depressed so as to relock it, and the scale becomes correct for that temperature. The altitudes are in all cases determined by taking two readings, one at each station, and then subtracting the reading at the lower station from that at the upper.

“It will be seen from the foregoing description that the movable scale of the instrument requires to be set for temperatures before taking any observations, and must not be shifted during the progress of the observations.

“This may appear at first sight as a defect, inasmuch as the temperature of the air may alter during the progress of the observations; but practically it will not be found to be any drawback in the case of moderate altitudes, as small variations of temperature will not appreciably affect the result. A variation of 5° of temperature gives only about 1 per cent. variation in the altitude, an amount that would under ordinary circumstances be inappreciable, so that as long as the temperature does not vary during the course of the observations more than 5° from that at which the instrument is set, the results may be accepted as correct, and, generally speaking, even a greater variation than this, say 6° or 8°, would be practically of no importance. Of course, if it should be found at any time that the temperature has varied considerably, during the course of the observations, from that at which the instrument was set, this variation can be allowed for by calculation in the usual way.”

The principle of allowing for variation of temperatures of the air by shifting the altitude scale is not theoretically accurate, but sufficiently so for practical purposes. For altitudes within the range of the instrument (say 3000 feet and under) and temperatures between 30° and 70°, the maximum error from using the shifted scale, instead of the calculation, is only 2 feet, which is inappreciable on the scale. The same principle might even be applied to altitudes up to 6000 feet, as the maximum error would be only 10 feet. For considerable elevations, however, the variations of the temperature between the base and the summit would interfere with the application of the principle.

Nevertheless, the best plan is to dispense with altitude scales, whether fixed or movable, and to calculate the heights. Simple rules, giving more reliable results than the attached scales, are at the service of those who need easy processes. Among these are the following:

Note the rise or fall of the barometer in hundredths of an inch, in passing from one station to the other; multiply by 9. The product is the difference of altitude in feet.

This is for ordinary temperatures and pressures. If the pressure is below 26 inches or the temperature above 70°, use 10 for a multiplier.

A higher degree of accuracy is obtained by using the multiplier obtained from the following table prepared by Mr. G. J. Symons:

Mean temperature

30°

40°

50°

60°

70°

80°

Mean pressure,   27in.

9.7

9.9

10.1

10.3

10.6

10.8

”         ”      28in.

9.3

9.5

9.8

10.0

10.2

10.4

”         ”      29in.

9.0

9.2

9.4

9.6

9.8

10.0

”         ”      30in.

8.7

8.9

9.1

9.3

9.5

9.7

To find the difference in height between two stations: Find the mean pressure; also the mean temperature. The number in the table corresponding to these two means, if multiplied by the difference of the barometric pressures in hundredths of an inch, will give the difference in altitude very nearly.

In the absence of a table to aid in computation, but having an Aneroid with the scale of feet, use the formula,

adding of the estimated altitude for every degree, the average temperature is above 55°, and subtracting a like amount when it is below. D, is the difference of altitude in feet; H and h are the readings in feet from the Aneroid scale. This gives fair approximations up to 3000 feet.

For accurate results use one of the following methods: Having Airy’s table (Table 1) and an Aneroid carefully graduated to inches; Take the reading in inches of the barometric scale at both lower and upper stations; also the temperature at both stations. Find from the table the heights in feet corresponding to the barometer readings. Subtract them and multiply the remainder by

The complete formula is

T and t are the observed temperatures; H and h are the heights in feet taken from the table.

In the absence of this table, but with a table of logarithms at hand, the barometric heights in inches are to be taken, and the following formula used:

B and b are the barometric readings in inches; D, T and t as in the other formulas. (See Table II.)

To avoid error from the constant changes in barometric pressure, the observations should be simultaneous. This is accomplished in the best manner by using two instruments, and requires, when the distance between the stations is considerable, two observers. With one instrument only, large errors are avoided by repeating the observation at the first station after taking that at the 2d station, and assuming that any change in barometric pressure that has occurred has been gradual during the absence.

When it is impracticable to repeat the observation at the first station, the error which, in case of a changing pressure, might be a large one, may be reduced if the observation at the 2d station be continued for an hour or two, or until the rate of change can be estimated and a proportionate correction applied.

Many Aneroids marked “compensated” exhibit a sensible change when the temperature is varied; such instruments may be serviceable and quite accurate if allowance be made for the error of the instrument. This correction the owner had better determine by experiment. It is easy to subject the Aneroid to such variation of temperature as shall embrace the range at which it is likely to be used, and the movement of the index for each 10° or 20° of temperature recorded.

Aneroids require to be compared from time to time with a good mercurial barometer. While making such comparisons, it is well to remember that the mercurial column and the scale by which it is measured both require correcting, and that during times of rapid changes, in atmospheric pressure, the Aneroid shows such changes more readily than the mercurial barometer. (See Table IV.)

In measuring heights with the Aneroid care should be taken that the instrument is not influenced by the heat of the hand nor by the direct rays from the sun.

The instrument should always be tapped gently with the finger at the moment of taking an observation. It should also be held in the same position for both observations; preferably with the face horizontal.

Considerable care is also required to determine exactly where the index points. It is best accomplished by sighting along the pointer, using one eye only for the purpose.

The following example will illustrate the use of the tables.

Barometer at Station A

30.04

Thermometer  78°

”       ”   ”   B

28.68

”          65°

From Table I we find height corresponding to reading at A is 857 feet. The height for B is 2120 feet.

The approximate height is 2120-857 = 1263 feet; but the sum of the temperatures is 143°. An additional correction of is, therefore, to be applied to the above difference; this is 54 feet. The total estimated difference of altitude is then 1263 + 54 = 1317 feet.

The formula directly applied is

Applying the logarithmic formula we have:

As before remarked, the Goldschmid Aneroid requires that both the temperature of the air and of the instrument be carefully taken. Two examples of altitudes taken with the instrument previously referred to (No. 3187) will serve to show the kind of correction necessary, and as both examples apply to the same mountain (Kiarsarge of Conway, N. H.,) they will together indicate the character of the instrument

EX. I.—JULY 9TH, 1881.

Station.

Time

Bar.

Reading.

Temp.

Correct’ns

Corrected

Reading.

Air.

Inst.

Temp.

Press.

Freyb’g.

6.00 A.M.

29.51

66°

66°

+.04

-.10

29.65

Mt. Kiarsarge.

1.00 P.M.

26.75

74°

74°

+.06

-.03

26.78

EX. II.—AUGUST 9TH, 1881.

Station.

Time

Bar.

Reading.

Temp.

Correct’ns

Corrected

Reading.

Air.

Inst.

Temp.

Press.

Freyb’g.

7.00 A.M.

29.34

60°

65°

+.03

+.09

29.46

Mt. Kiarsarge.

1.20 P.M.

26.48

65°

75°

+.06

-.03

26.51

In both these examples another reading would have been taken at Fryeburg on the return, if the better alternative of securing hourly readings of a stationary barometer at Fryeburg had not been followed. On July 9th there was no change in the Fryeburg barometer. On August 9th the following readings were taken at Fryeburg:

7

A.M.

29.53

8

”

29.52

10

”

29.515

12

”

29.46

1

P.M.

29.46

2

”

29.455

3

”

29.40

As this set of observations indicates a fall of .07 in the interval between the base and summit readings, it becomes necessary to make another correction to the last column.

Correcting the first reading to accord with the fall indicated by the stationary barometer, we get after all corrections:

Fryeburg,

29.39

Mt. Kiarsarge,

26.51

The logarithmic formula for estimating heights from barometric observations is

in which

D

=

difference in altitude in feet.

B

=

height of barometer in inches at lower station.

b

=

height of barometer in inches at upper station.

T and t are the temperatures of the air in Fahrenheit degrees.

Applying this formula to our first example we have:

The second example gives:

As the station at Fryeburg is 434 feet above the sea, the estimated total height of Kiarsarge would be, in one case, 3321 feet, and in the other 3315 feet.

Prof. Airy’s table gives 3319 and 3314 from the same data.

The instrument employed in the above measurements has been used in many other cases of altitudes from 3000 to 4000 feet. An error of about 2 per cent. in excess has been detected in those cases where the altitude has been measured by more accurate means. It seems likely that the special correction needs some slight revision.

The following measurement was made with an aneroid only 1½ inches diameter, made by Casella.

Neversink, Sullivan Co., N. Y.,

and Slide Mountain, Ulster Co.

Time.

Bar.

Readings

T.

Ht.

Tab. I.

Neversink.

7 A.M.

28.64

61°

2158

Fly Club Camp.

11  ”

27.92

78°

2853

Slide Mountain.

4 P.M.

25.87

69°

4931

As Neversink had been satisfactorily determined to be 1350 feet above the sea, the total height of Slide Mountain is estimated from this observation to have an altitude of 4206 feet.

(NOTE).—Return observations were made only at the camp of the Fly Club. Between 11 A.M. and 9 P.M., no change occurred in the barometer.

The Tribune report, however, indicates a rise on this date of .07 between 7 and 11 A.M. If such a change was felt in this region, then the calculated height of the mountain is too low by at least 60 feet. On the other hand, a height given by railway survey in this vicinity, (Johnson’s Mill) near the camp, seems to confirm the figures given here.

Also, the height of Helsinger Notch, taken incidentally on this excursion, was estimated at 2660 feet. Guyot makes the Notch 2677 and the summit of Slide Mountain 4205 feet.

The height of the base at Neversink was established by four observations, between New York Bay and this base, and was confirmed by comparison with the height of the railway track at Liberty, six miles south-west.

Neversink to Blue Mountain,

August 18, 1880.

Time.

Bar.

Readings

T.

Cor.

Rd’g.

Ht.

Tab. I.

Neversink.

10:30 P.M.

28.90

60°

28.87

1941

Blue Mt.

3   P.M.

27.47

60°

27.47

3295

Neversink

6      ”

28.85

64°

The corrected reading would be 28.875, if the second reading had been midway in point of time between the first and last.

This mountain is in Ulster Co., N. Y. Long. 74° 35 W, and Lat. 41° 52 N.

Neversink and Denman Mountains (Casella Aneroid).

September 11, 1880.

Time.

Bar.

Readings

T.

Cor.

Rd’g.

Ht.

Tab. I.

Neversink.

12:30 A.M.

28.86

70°

28.84

1969

D. Mt.

4:30 ”

27.13

63°

27.13

3634

Neversink

9       ”

28.82

55°

This mountain is S. S. W. of Slide Mountain, and near Claraville. Long. 74° 28'; Lat. 41° 53' N.

Fryeburg, Me., and Kiarsarge Mountain, N. H.—Fryeburg base 434 feet above the sea, July 9th, 1881.

(Casella Aneroid)

Time.

Bar.

Readings

T.

Ht.

Tab. I.

Fryeburg

6 A.M.

29.63

66°

1233

Kiarsarge

1 P.M.

26.83

74°

3938

(Note)—Barometer at Fryeburg remained stationary.

Fryeburg, Me., and Mt. Kiarsarge, N. H. (second survey) August 17th, 1881.

(Casella Aneroid.)

Time.

Bar.

Readings

T.

Ht.

Tab. I.

Fryeburg

9 A.M.

29.70

59°

1169

Mt. Kiarsarge

3 P.M.

26.81

53°

3958

(Note)—Barometer at Fryeburg stationary till 4 P.M.

Diff. = 2,789 × 1.012 = 2822 feet.

Total ht. = 3256 feet above the sea.

Height of this summit according to the Geological Survey is 3251 feet.

Liberty Hill, N. H. (near Laconia), and Mt. Belknap.—The base station was at Mr. Rowe’s 1130 feet above the sea, July 9th, 1878.

(Casella Barometer.)

Bar.

Readings

T.

Ht.

Tab. I.

Liberty Hill

28.75

82°

2054

Mt. Belknap

27.53

79°

3235

As the interval between the observations was very short, and the general pressure sensibly stationary, no record was made of the time nor the return reading.

(Note)—An average of three measurements of this mountain gave 2392 feet. The other observations yielding 2369 and 2425 ft. respectively.

The height given in the Guide Books quoted from the Geological Survey is 2394 feet.

CHAPTER V.

SUGGESTIONS IN REGARD TO THE

SELECTION AND SYSTEMATIC

USE OF AN ANEROID.

Dealers in good aneroids are generally prepared to testify in regard to the performance of their instruments when tested by the air pump. Comparison tables frequently accompany first-class instruments which show the differences between the aneroid referred to and a standard mercurial barometer submitted to the same exhaustion.

The buyer may reasonably ask, therefore, that such a test may be made if it has not been previously done.

The best English aneroids are now marked compensated, and are presumably free from error arising from changes of temperature in the instrument itself. Whether such be the case can readily be determined, by the owner of the instrument subjecting it to the action of a freezing mixture and then of a drying oven, while the normal pressure remains the same. A thermometer should be placed beside the aneroid during the trial. A range of temperature from 15° F. to 175° F. may easily be produced, and a coefficient of correction if the instrument is not compensated, may be determined.

The graduations of a good instrument are neatly engraved on the dial.

The divisions corresponding to the inches and fractions of a mercurial barometer are the only essential ones. The circle of feet, whether movable or fixed, is a convenience of secondary importance.

If an aneroid bears a fixed circle of feet with the zero mark corresponding to the 30-inch point of the other scale, the probabilities are that the instrument is not from one of the best makers.

Excellent aneroids are now made with dial plates only 2½ inches in diameter. The Casella barometer referred to in the examples has a diameter of only 1¼ inches. Of course the smaller fractions of an inch are more easily read on dials of 4 inches in diameter; but the portability of the smaller instruments recommends them for the use of the topographer, and the medium size, which is from 2¼ to 2½ inches, is now most in demand for surveyor’s work.

The aneroids in any considerable collection will be found to be variously graduated; some of them capable of indicating a fall of pressure to 20 inches, corresponding to a height of over 11,000 feet, while many are designed for continual use below 3,000 feet of altitude. In two instruments of the same diameter, but differing as above, it is clear that the latter will have the larger scale divisions, and will, therefore, be the better instrument to use at the lower altitudes.

It should be carefully remembered that all aneroids vary in their readings, with the position in which they are held; reading always a little higher with the dial horizontal (face uppermost), than when it is vertical. The difference is clearly owing to the direct weight of the mechanism exerted on the vacuum box. There is no objection to allowing this weight to be always added, but the practice of the observer should be uniform, and to read from the horizontal dial is probably the most convenient practice.

A tap with the finger just before taking the reading is required to bring the springs to their proper bearing. Also, in case of rapid ascents, as some aneroids will not, at the moment of attaining an altitude, indicate the entire fall of pressure, a few minutes’ delay is necessary.

The pointer should be fine and very close to the graduated scale, and the reading should be taken by looking along the direction of the pointer.

For ordinary work it should not be considered important to adjust the aneroid to an absolute agreement with the mercurial barometer. The difference between the readings may be noted, but to force the aneroid to an agreement by aid of the adjusting screw is a questionable practice.

Whenever comparison with the mercury column is made, the reduction for the latter by Table 4 should be carefully observed.

In the use of either form of Aneroid, whether it has been furnished with a correction or not, the observer should take early means to become acquainted with its limits of error under various conditions of temperature or pressure. Repeated measurements of a known altitude afford good data for such information, but direct comparisons, for a long time, with a standard cistern barometer will yield, with a minimum of labor, the greatest number of comparisons.

For the method of dealing with such data to determine correction coefficients, the reader is referred to the larger treatises, the most exhaustive of which, probably, is “Die Aneroide,” by Josef Höltschl (Alfred Holder, Vienna, 1872).

For ordinary use of a single instrument, however, the corrections, if any are necessary, are determined with sufficient accuracy by the exercise of ordinary skill and patience; skill here implying, also, systematic trial.

Some of the sources of error in measuring altitudes, which are not to be eliminated by any adjustment or correction of instruments, are clearly stated by Prof. Elias Loomis, in a paper read before the National Academy of Sciences, April 19, 1881.

“The Laplace formula assumed that the atmosphere has attained a condition of equilibrium, and in such a case it gives the reduction to sea level with tolerable accuracy. The average of a long series of observations represents approximately such a condition of equilibrium; but in the daily observations this equilibrium is very much disturbed. The mean between the temperatures at the upper and lower stations does not represent the average temperature of the intermediate column of air; and when the atmosphere is in rapid motion the downward pressure is modified by the earth’s rotation, in a manner not represented by the Laplace formula. There is no doubt that the formulæ of reduction now employed may be considerably improved; but it does not seem possible that any single formula, with constant coefficients, should provide for the immense variety of conditions which prevail in the neighborhood of mountain stations; and we may be compelled for each mountain region to adopt tables founded upon a direct comparison of observations made at stations of different elevations and not very remote from each other.”

The following remarks bearing upon the same subject are from an article by J. Allan Brown, F. R. S., on “Periodic Oscillations of Barometric Pressure,” published in Nature in April, 1881:

Sedgwick has said: [“To explain difficulties in these questions” (relating to pressure and temperature) “the atmospheric strata have been shuffled in accordance with laboratory experience.”]

“If we suppose that the attraction of gravity is not the only attraction which affects the pressure of the atmosphere, but that this pressure varies through some other attracting force—such as an electric attraction of the sun depending upon the varying humidity of the air, and this again depending on its temperature, we should find another method of relating the two variations which does not exist if gravitation alone is employed. It is quite certain that many physicists will not admit the idea of an electric attraction on our atmosphere in the present state of our knowledge, hence the efforts to make expansion, and a shuffling of the atmospheric strata suffice. We must not, however, in our ignorance, attempt to force conclusions in opposition to facts, and if these can be satisfied more easily and with greater probabilities in its favor by the aid of the hypothesis of an electric attraction of the sun, that hypothesis will have a better claim to acceptance than the other. I shall here note a few facts which cannot be explained by thermic actions.

“1. I have shown that, on the average of many years’ observation in our latitudes, the mean pressure diminishes at the rate of 0″.038 of mercury for every one hundred miles we proceed toward the north. This has been called a gradient from the similar term used in railway slopes: but it is no slope, it is a level of a surface of equilibrium like that of the sea. It is the mean heights of the barometer at the sea level which indicate the form, if we may so say, of the equilibrating atmosphere.

“2. In India we have seen that the atmospheric pressure oscillates at each station even when these are quite near to each other, independently of the known laws of equilibrium of gases. When we turn to the semi-diurnal oscillation of the barometer we are only amused at the attempts made to explain it by shuffling the atmospheric strata. Nothing can be more certain than that the theories of expansion, or resistance to expansion and overflow, are the vain efforts to make the laws of nature agree with a theory. Over the great ocean within the tropics, where the diurnal variations of temperature are small and the air is absolutely without perceptible currents for days together, the barometer rises and falls a tenth of an inch twice in twenty-four hours with the regularity of the solar clock. The action of the sun on the whole atmosphere which produces this movement varies chiefly during the day hours at inland stations with the temperature oscillation, so that, as in the case of the annual variation, the fall of the barometer at 4 P.M. is greater in the same latitude as the temperature is higher. This variation occurs during the most complete calms; the smoke rises vertically from the plain of Tinnevelly; no current is visible in the motion of the clouds; yet the barometer falls at four in the morning as it did at four in the afternoon, only it falls less.”

It seems probable that the use of the Aneroid will soon become more widely extended, and that engineers, when made familiar with the qualities of well-made instruments, will welcome so valuable an aid in preliminary surveys. The conditions of satisfactory work with barometers are certainly peculiar, and to field workers familiar only with the level and transit, may seem unique. But when the conditions are fully understood, the engineer may easily take precautions which will avoid too large errors, and conduct surveys in hilly regions with a celerity not heretofore attained.

TABLE I.

FOR ESTIMATING HEIGHTS

BY THE ANEROID.

Take readings of the barometer and thermometer at both stations; find in the the heights corresponding to the barometric readings, and subtract them. Multiply the remainder by . T and t being the temperatures, the product will be the difference in altitude.

Barometer

Readings.

Heights.

Inches.

Feet.

31.00

00

30.99

9

30.98

18

30.97

27

30.96

35

30.95

44

30.94

53

30.93

62

30.92

71

30.91

80

30.90

88

30.89

97

30.88

106

30.87

115

30.86

124

30.85

133

30.84

142

30.83

151

30.82

160

30.81

168

30.80

177

30.79

186

30.78

195

30.77

203

30.76

212

30.75

221

30.74

230

30.73

239

30.72

247

30.71

256

30.70

265

30.69

274

30.68

283

30.67

292

30.66

301

30.65

310

30.64

318

30.63

327

30.62

336

30.61

345

30.60

354

30.59

363

30.58

372

30.57

381

30.56

390

30.55

399

30.54

407

30.53

416

30.52

425

30.51

434

30.50

443

30.49

452

30.48

461

30.47

470

30.46

479

30.45

488

30.44

497

30.43

506

30.42

515

30.41

524

30.40

533

30.39

542

30.38

551

30.37

559

30.36

569

30.35

578

30.34

587

30.33

596

30.32

605

30.31

613

30.30

622

30.29

631

30.28

640

30.27

649

30.26

658

30.25

667

30.24

676

30.23

685

30.22

694

30.21

703

30.20

712

30.19

721

30.18

730

30.17

740

30.16

749

30.15

758

30.14

767

30.13

776

30.12

785

30.11

794

30.10

803

30.09

812

30.08

821

30.07

830

30.06

839

30.05

849

30.04

857

30.03

866

30.02

875

30.01

884

30.00

893

29.99

903

29.98

911

29.97

920

29.96

929

29.95

938

29.94

947

29.93

956

29.92

965

29.91

976

29.90

985

29.89

994

29.88

1002

29.87

1012

29.86

1021

29.85

1030

29.84

1039

29.83

1049

29.82

1058

29.81

1067

29.80

1076

29.79

1085

29.78

1094

29.77

1103

29.76

1113

29.75

1122

29.74

1132

29.73

1141

29.72

1150

29.71

1159

29.70

1169

29.69

1177

29.68

1186

29.67

1195

29.66

1205

29.65

1214

29.64

1224

29.63

1233

29.62

1242

29.61

1251

29.60

1260

29.59

1269

29.58

1278

29.57

1287

29.56

1296

29.55

1305

29.54

1314

29.53

1324

25.52

1333

29.51

1342

29.50

1352

29.49

1361

29.48

1370

29.47

1379

29.46

1389

29.45

1398

29.44

1408

29.43

1417

29.42

1426

29.41

1435

29.40

1445

29.39

1454

29.38

1464

29.37

1473

29.36

1482

29.35

1491

29.34

1500

29.33

1509

29.32

1519

29.31

1528

29.30

1537

29.29

1546

29.28

1556

29.27

1565

29.26

1574

29.25

1583

29.24

1593

29.23

1603

29.22

1612

29.21

1621

29.20

1630

29.19

1639

29.18

1649

29.17

1658

29.16

1668

29.15

1677

29.14

1687

29.13

1696

29.12

1706

29.11

1715

29.10

1725

29.09

1734

29.08

1743

29.07

1752

29.06

1762

29.05

1771

29.04

1781

29.03

1790

29.02

1799

29.01

1809

29.00

1818

28.99

1827

28.98

1837

28.97

1846

28.96

1856

28.95

1865

28.94

1875

28.93

1884

28.92

1894

28.91

1903

28.90

1913

28.89

1922

28.88

1931

28.87

1941

28.86

1950

28.85

1960

28.84

1969

28.83

1979

28.82

1988

28.81

1998

28.80

2007

28.79

2016

28.78

2026

28.77

2035

28.76

2044

28.75

2054

28.74

2063

28.73

2073

28.72

2082

28.71

2091

28.70

2101

28.69

2111

28.68

2120

28.67

2129

28.66

2139

28.65

2148

28.64

2158

28.63

2168

28.62

2177

28.61

2186

28.60

2196

28.59

2205

28.58

2215

28.57

2224

28.56

2234

28.55

2243

28.54

2253

28.53

2263

28.52

2272

28.51

2282

28.50

2291

28.49

2301

28.48

2310

28.47

2320

28.46

2329

28.45

2339

28.44

2349

28.43

2358

28.42

2368

28.41

2378

28.40

2387

28.39

2397

28.38

2407

28.37

2416

28.36

2426

28.35

2435

28.34

2445

28.33

2455

28.32

2464

28.31

2474

28.30

2483

28.29

2493

28.28

2503

28.27

2512

28.26

2522

28.25

2531

28.24

2541

28.23

2551

28.22

2561

28.21

2570

28.20

2580

28.19

2590

28.18

2600

28.17

2609

28.16

2619

28.15

2628

28.14

2638

28.13

2648

28.12

2658

28.11

2667

28.10

2677

28.09

2687

28.08

2696

28.07

2706

28.06

2715

28.05

2726

28.04

2735

28.03

2745

28.02

2755

28.01

2765

28.00

2774

27.99

2784

27.98

2794

27.97

2804

27.96

2813

27.95

2823

27.94

2833

27.93

2843

27.92

2853

27.91

2863

27.90

2873

27.89

2882

27.88

2892

27.87

2901

27.86

2911

27.85

2921

27.84

2930

27.83

2940

27.82

2950

27.81

2960

27.80

2969

27.79

2979

27.78

2989

27.77

2999

27.76

3009

27.75

3019

27.74

3029

27.73

3039

27.72

3048

27.71

3058

27.70

3068

27.69

3078

27.68

3087

27.67

3097

27.66

3107

27.65

3117

27.64

3126

27.63

3136

27.62

3146

27.61

3156

27.60

3166

27.59

3176

27.58

3186

27.57

3196

27.56

3206

27.55

3216

27.54

3225

27.53

3235

27.52

3245

27.51

3255

27.50

3265

27.49

3275

27.48

3285

27.47

3295

27.46

3305

27.45

3315

27.44

3325

27.43

3335

27.42

3345

27.41

3355

27.40

3365

27.39

3375

27.38

3384

27.37

3394

27.36

3404

27.35

3414

27.34

3424

27.33

3434

27.32

3444

27.31

3454

27.30

3464

27.29

3474

27.28

3484

27.27

3494

27.26

3504

27.25

3514

27.24

3524

27.23

3534

27.22

3544

27.21

3554

27.20

3564

27.19

3574

27.18

3584

27.17

3594

27.16

3604

27.15

3614

27.14

3624

27.13

3634

27.12

3644

27.11

3654

27.10

3665

27.09

3675

27.08

3685

27.07

3695

27.06

3705

27.05

3715

27.04

3725

27.03

3735

27.02

3745

27.01

3755

27.00

3765

26.99

3775

26.98

3785

26.97

3795

26.96

3806

26.95

3816

26.94

3826

26.93

3836

26.92

3846

26.91

3856

26.90

3866

26.89

3876

26.88

3886

26.87

3897

26.86

3907

26.85

3917

26.84

3927

26.83

3938

26.82

3948

26.81

3958

26.80

3968

26.79

3978

26.78

3988

26.77

3999

26.76

4009

26.75

4019

26.74

4030

26.73

4040

26.72

4050

26.71

4060

26.70

4070

26.69

4081

26.68

4091

26.67

4101

26.66

4111

26.65

4122

26.64

4132

26.63

4142

26.62

4152

26.61

4163

26.60

4173

26.59

4183

26.58

4193

26.57

4203

26.56

4213

26.55

4223

26.54

4233

26.53

4244

26.52

4254

26.51

4264

26.50

4274

26.49

4284

26.48

4294

26.47

4304

26.46

4315

26.45

4326

26.44

4336

26.43

4347

26.42

4357

26.41

4368

26.40

4378

26.39

4388

26.38

4399

26.37

4409

26.36

4419

26.35

4430

26.34

4440

26.33

4450

26.32

4461

26.31

4472

26.30

4482

26.29

4492

26.28

4502

26.27

4513

26.26

4523

26.25

4533

26.24

4544

26.23

4554

26.22

4565

26.21

4575

26.20

4585

26.19

4596

26.18

4606

26.17

4617

26.16

4627

26.15

4638

26.14

4648

26.13

4658

26.12

4669

26.11

4679

26.10

4690

26.09

4700

26.08

4711

26.07

4721

26.06

4731

26.05

4742

26.04

4752

26.03

4763

26.02

4773

26.01

4784

26.00

4794

25.99

4805

25.98

4815

25.97

4826

25.96

4836

25.95

4847

25.94

4857

25.93

4868

25.92

4878

25.91

4889

25.90

4899

25.89

4910

25.88

4920

25.87

4931

25.86

4941

25.85

4952

25.84

4962

25.83

4973

25.82

4983

25.81

4994

25.80

5004

25.79

5014

25.78

5025

25.77

5036

25.76

5046

25.75

5057

25.74

5067

25.73

5078

25.72

5088

25.71

5099

25.70

5110

25.69

5121

25.68

5132

25.67

5142

25.66

5153

25.65

5164

25.64

5174

25.63

5185

20.62

5195

25.61

5206

25.60

5216

25.59

5227

25.58

5237

25.57

5248

25.56

5259

25.55

5270

25.54

5281

25.53

5291

25.52

5302

25.51

5312

25.50

5323

25.49

5333

25.48

5344

25.47

5355

25.46

5365

25.45

5376

25.44

5387

25.43

5397

25.42

5408

25.41

5419

25.40

5429

25.39

5440

25.38

5451

25.37

5462

25.36

5473

25.35

5483

25.34

5494

25.33

5505

25.32

5516

25.31

5527

25.30

5537

25.29

5548

25.28

5559

25.27

5570

25.26

5581

25.25

5592

25.24

5602

25.23

5613

25.22

5624

25.21

5635

25.20

5646

25.19

5657

25.18

5668

25.17

5679

25.16

5689

25.15

5700

25.14

5711

25.13

5722

25.12

5733

25.11

5744

25.10

5754

25.09

5765

25.08

5776

25.07

5787

25.06

5798

25.05

5809

25.04

5820

25.03

5831

25.02

5842

25.01

5853

25.00

5863

24.99

5874

24.98

5885

24.97

5896

24.96

5907

24.95

5918

24.94

5929

24.93

5940

24.92

5950

24.91

5962

24.90

5972

24.89

5983

24.88

5994

24.87

6005

24.86

6016

24.85

6027

24.84

6038

24.83

6049

24.82

6060

24.81

6071

24.80

6082

24.79

6093

24.78

6104

24.77

6115

24.76

6126

24.75

6137

24.74

6148

24.73

6159

24.72

6170

24.71

6181

24.70

6192

24.69

6203

24.68

6214

24.67

6225

24.66

6236

24.65

6247

24.64

6258

24.63

6269

24.62

6280

24.61

6291

24.60

6302

24.59

6313

24.58

6324

24.57

6335

24.56

6346

24.55

6357

24.54

6368

24.53

6379

24.52

6390

24.51

6401

24.50

6412

24.49

6424

24.48

6435

24.47

6446

24.46

6458

24.45

6469

24.44

6480

24.43

6491

24.42

6503

24.41

6514

24.40

6525

24.39

6536

24.38

6547

24.37

6559

24.36

6570

24.35

6581

24.34

6592

24.33

6603

24.32

6615

24.31

6626

24.30

6637

24.29

6648

24.28

6659

24.27

6671

24.26

6682

24.25

6693

24.24

6705

24.23

6716

24.22

6727

24.21

6738

24.20

6750

24.19

6761

24.18

6772

24.17

6783

24.16

6795

24.15

6806

24.14

6817

24.13

6828

24.12

6840

24.11

6851

24.10

6862

24.09

6873

24.08

6885

24.07

6896

24.06

6907

24.05

6919

24.04

6930

24.03

6941

24.02

6953

24.01

6964

24.00

6976

23.99

6987

23.98

6999

23.97

7010

23.96

7022

23.95

7033

23.94

7045

23.93

7056

23.92

7068

23.91

7079

23.90

7090

23.89

7101

23.88

7113

23.87

7124

23.86

7135

23.85

7146

23.84

7157

23.83

7168

23.82

7180

23.81

7191

23.80

7203

23.79

7214

23.78

7226

23.77

7237

23.76

7249

23.75

7261

23.74

7272

23.73

7283

23.72

7294

23.71

7305

23.70

7316

23.69

7327

23.68

7339

23.67

7350

23.66

7362

23.65

7374

23.64

7386

23.63

7398

23.62

7409

23.61

7421

23.60

7433

23.59

7445

23.58

7456

23.57

7468

23.56

7480

23.55

7492

23.54

7503

23.53

7515

23.52

7527

23.51

7539

23.50

7550

23.49

7562

23.48

7574

23.47

7585

23.46

7597

23.45

7609

23.44

7621

23.43

7633

23.42

7644

23.41

7656

23.40

7667

23.39

7679

23.38

7690

23.37

7702

23.36

7713

23.35

7725

23.34

7736

23.33

7748

23.32

7759

23.31

7771

23.30

7782

23.29

7793

23.28

7805

23.27

7817

23.26

7829

23.25

7841

23.24

7853

23.23

7865

23.22

7876

23.21

7888

23.20

7900

23.19

7912

23.18

7923

23.17

7935

23.16

7946

23.15

7958

23.14

7969

23.13

7981

23.12

7092

23.11

8004

23.10

8015

23.09

8027

23.08

8039

23.07

8051

23.06

8063

23.05

8075

23.04

8086

23.03

8098

23.02

8110

23.01

8122

23.00

8134

22.99

8146

22.98

8158

22.97

8170

22.96

8182

22.95

8194

22.94

8206

22.93

8218

22.92

8230

22.91

8242

22.90

8254

22.89

8266

22.88

8278

22.87

8290

22.86

8302

22.85

8314

22.84

8326

22.83

8338

22.82

8850

22.81

8362

22.80

8374

22.79

8386

22.78

8398

22.77

8410

22.76

8422

22.75

8434

22.74

8446

22.73

8458

22.72

8470

22.71

8482

22.70

8495

22.69

8507

22.68

8519

22.67

8531

22.66

8543

22.65

8555

22.64

8567

22.63

8579

22.62

8591

22.61

8603

22.60

8615

22.59

8627

22.58

8638

22.57

8650

22.56

8661

22.55

8673

22.54

8685

22.53

8697

22.52

8709

22.51

8721

22.50

8733

22.49

8745

22.48

8757

22.47

8769

22.46

8781

22.45

8793

22.44

8806

22.43

8818

22.42

8830

22.41

8842

22.40

8855

22.39

8867

22.38

8879

22.37

8891

22.36

8904

22.35

8916

22.34

8928

22.33

8941

22.32

8953

22.31

8965

22.30

8977

22.29

8090

22.28

9002

22.27

9014

22.26

9026

22.25

9039

22.24

9051

22.23

9063

22.22

9075

22.21

9088

22.20

9100

22.19

9113

22.18

9125

22.17

9138

22.16

9150

22.15

9162

22.14

9174

22.13

9187

22.12

9199

22.11

9212

22.10

9224

22.09

9236

22.08

9249

22.07

9262

22.06

9274

22.05

9286

22.04

9298

22.03

9311

22.02

9323

22.01

9336

22.00

9348

21.99

9360

21.98

9372

21.97

9384

21.96

9397

21.95

9410

21.94

9422

21.93

9435

21.92

9447

21.91

9460

21.90

9472

21.89

9485

21.88

9497

21.87

9510

21.86

9522

21.85

9535

21.84

9547

21.83

9560

21.82

9572

21.81

9585

21.80

9597

21.79

9610

21.78

9622

21.77

9635

21.76

9647

21.75

9660

21.74

9672

21.73

9685

21.72

9697

21.71

9710

21.70

9722

21.69

9735

21.68

9747

21.67

9760

21.66

9772

21.65

9785

21.64

9797

21.63

9810

21.62

9822

21.61

9835

21.60

9848

21.59

9861

21.58

9873

21.57

9886

21.56

9898

21.55

9911

21.54

9923

21.53

9936

21.52

9949

21.51

9962

21.50

9974

21.49

9987

21.48

9999

21.47

10012

21.46

10025

21.45

10038

21.44

10050

21.43

10063

21.42

10075

21.41

10088

21.40

10101

21.39

10114

21.38

10126

21.37

10139

21.36

10151

21.35

10164

21.34

10176

21.33

10189

21.32

10202

21.31

10214

21.30

10228

21.29

10241

21.28

10253

21.27

10266

21.26

10278

21.25

10291

21.24

10304

21.23

10317

21.22

10330

21.21

10343

21.20

10355

21.19

10368

21.18

10381

21.17

10394

21.16

10407

21.15

10420

21.14

10432

21.13

10445

21.12

10458

21.11

10471

21.10

10484

21.09

10497

21.08

10509

21.07

10522

21.06

10535

21.05

10548

21.04

10561

21.03

10574

21.02

10587

21.01

10600

21.00

10613

20.99

10627

20.98

10640

20.97

10654

20.96

10667

20.95

10681

20.94

10694

20.93

10707

20.92

10720

20.91

10733

20.90

10746

20.89

10759

20.88

10772

20.87

10785

20.86

10798

20.85

10811

20.84

10824

20.83

10837

20.82

10850

20.81

10863

20.80

10876

20.79

10889

20.78

10902

20.77

10915

20.76

10928

20.75

10941

20.74

10954

20.73

10967

20.72

10980

20.71

10993

20.70

11006

20.69

11019

20.68

11032

20.67

11045

20.66

11058

20.65

11071

20.64

11084

20.63

11097

20.62

11110

20.61

11123

20.60

11136

20.59

11149

20.58

11163

20.57

11176

20.56

11190

20.55

11204

20.54

11217

20.53

11230

20.52

11243

20.51

11257

20.50

11270

20.49

11284

20.48

11297

20.47

11311

20.46

11324

20.45

11338

20.44

11351

20.43

11364

20.42

11377

20.41

11391

20.40

11404

20.39

11418

20.38

11431

20.37

11444

20.36

11457

20.35

11470

20.34

11483

20.33

11496

20.32

11509

20.31

11523

20.30

11536

20.29

11550

20.28

11563

20.27

11577

20.26

11591

20.25

11605

20.24

11618

20.23

11632

20.22

11645

20.21

11659

20.20

11673

20.19

11687

20.18

11700

20.17

11714

20.16

11727

20.15

11741

20.14

11754

20.13

11768

20.12

11781

20.11

11795

20.10

11808

20.09

11821

20.08

11835

20.07

11859

20.06

11863

20.05

11877

20.04

11891

20.03

11905

20.02

11918

20.01

11932

20.00

11945

The following table is to be used when applying the modified formula of chapter II:

RULE.—Find in the table the logarithms of the barometer readings to hundredths of an inch. Subtract these logarithms and multiply the remainder by 60000. The product is the approximate difference in altitude between the two stations. To apply the corrections for temperature, add the temperatures of the two stations and subtract 60°. Increase the above approximate value by of itself for each degree of excess above 60°. If the sum of the temperature is less than 60° diminish the value by a like amount.

TABLE II.

Bar.

Height.

Log.

2200

3.34242

01

.34262

02

.34282

03

.34301

04

.34321

05

.34341

06

.34361

07

.34380

08

.34400

09

.34420

10

.34439

11

.34459

12

.34479

13

.34498

14

.34518

15

.34537

16

.34557

17

.34577

18

.34596

19

.34616

20

.34635

21

.34655

22

.34674

23

.34694

24

.34713

25

.34733

26

.34753

27

.34772

28

.34792

29

.34811

30

.34830

31

.34850

32

.34869

33

.34889

34

.34908

35

.34928

36

.34947

37

.34967

38

.34986

39

.35005

40

.35025

41

.35044

42

.35064

43

.35083

44

.35102

45

.35122

46

.35141

47

.35160

48

.35180

49

.35199

50

.35218

51

.35238

52

.35257

53

.35276

54

.35295

55

.35315

56

.35334

57

.35353

58

.35372

59

.35392

60

.35411

61

.35430

62

.35449

63

.35468

64

.35488

65

.35507

66

.35526

67

.35545

68

.35564

69

.35583

70

.35603

71

.35622

72

.35641

73

.35660

74

.35679

75

.35698

76

.35717

77

.35736

78

.35755

79

.35774

80

.35793

81

.35813

82

.35832

83

.35851

84

.35870

85

.35889

86

.35908

87

.35927

88

.35946

89

.35965

90

.35984

91

.36003

92

.36021

93

.36040

94

.36059

95

.36078

96

.36097

97

.36116

98

.36135

99

.36154

2300

3.36173

01

.36192

02

.36211

03

.36229

04

.36248

05

.36267

06

.36286

07

.36305

08

.36324

09

.36342

10

.36361

11

.36380

12

.36399

13

.36418

14

.36436

15

.36455

16

.36474

17

.36493

18

.36511

19

.36530

20

.36549

21

.36568

22

.36586

23

.36605

24

.36624

25

.36642

26

.36661

27

.36680

28

.36698

29

.36717

30

.36736

31

.36754

32

.36773

33

.36791

34

.36810

35

.36829

36

.36847

37

.36866

38

.36884

39

.36903

40

.36922

41

.36940

42

.36959

43

.36977

44

.36996

45

.37014

46

.37033

47

.37051

48

.37070

49

.37088

50

.37107

51

.37125

52

.37144

53

.37162

54

.37181

55

.37199

56

.37218

57

.37236

58

.37254

59

.37273

60

.37291

61

.37310

62

.37328

63

.37346

64

.37365

65

.37383

66

.37401

67

.37420

68

.37438

69

.37457

70

.37475

71

.37493

72

.37511

73

.37530

74

.37548

75

.37566

76

.37585

77

.37603

78

.37621

79

.37639

80

.37658

81

.37676

82

.37694

83

.37712

84

.37731

85

.37749

86

.37767

87

.37785

88

.37803

89

.37822

90

.37840

91

.37858

92

.37876

93

.37894

94

.37912

95

.37931

96

.37949

97

.37967

98

.37985

99

.38003

2400

3.38021

01

.38039

02

.38057

03

.38075

04

.38093

05

.38112

06

.38130

07

.38148

08

.38166

09

.38184

10

.38202

11

.38220

12

.38238

13

.38256

14

.38274

15

.38292

16

.38310

17

.38328

18

.38346

19

.38364

20

.38382

21

.38399

22

.38417

23

.38435

24

.38453

25

.38471

26

.38489

27

.38507

28

.38525

29

.38543

30

.38561

31

.38579

32

.38596

33

.38614

34

.38632

35

.38650

36

.38668

37

.38686

38

.38703

39

.38721

40

.38739

41

.38757

42

.38775

43

.38792

44

.38810

45

.38828

46

.38846

47

.38863

48

.38881

49

.38899

50

.38917

51

.38934

52

.38952

53

.38970

54

.38987

55

.39005

56

.39023

57

.39041

58

.39058

59

.39076

60

.39094

61

.39111

62

.39129

63

.39146

64

.39164

65

.39182

66

.39199

67

.39217

68

.39235

69

.39252

70

.39270

71

.39287

72

.39305

73

.39322

74

.39340

75

.39358

76

.39375

77

.39393

78

.39410

79

.39428

80

.39445

81

.39463

82

.39480

83

.39498

84

.39515

85

.39533

86

.39550

87

.39568

88

.39585

89

.39602

90

.39620

91

.39637

92

.39655

94

.39672

94

.39690

95

.39707

96

.39724

97

.39742

98

.39759

99

.39777

2500

3.39794

01

.39811

02

.39829

03

.39846

04

.39863

05

.39881

06

.39898

07

.39915

08

.39933

09

.39950

10

.39967

11

.39985

12

.40002

13

.40019

14

.40037

15

.40054

16

.40071

17

.40088

18

.40106

19

.40123

20

.40140

21

.40157

22

.40175

23

.40192

24

.40209

25

.40226

26

.40243

27

.40261

28

.40278

29

.40295

30

.40312

31

.40329

32

.40346

33

.40364

34

.40381

35

.40398

36

.40415

37

.40432

38

.40449

39

.40466

40

.40483

41

.40500

42

.40518

43

.40535

44

.40552

45

.40569

46

.40586

47

.40603

48

.40620

49

.40637

50

.40654

51

.40671

52

.40688

53

.40705

54

.40722

55

.40739

56

.40756

57

.40773

58

.40790

59

.40807

60

.40824

61

.40841

62

.40858

63

.40875

64

.40892

65

.40909

66

.40926

67

.40943

68

.40960

69

.40976

70

.40993

71

.41010

72

.41027

73

.41044

74

.41061

75

.41078

76

.41095

77

.41111

78

.41128

79

.41145

80

.41162

81

.41179

82

.41196

83

.41212

84

.41229

85

.41246

86

.41263

87

.41280

88

.41296

89

.41313

90

.41330

91

.41347

92

.41364

93

.41380

94

.41397

95

.41414

96

.41430

97

.41447

98

.41464

99

.41481

2600

3.41497

01

.41514

02

.41531

03

.41547

04

.41564

05

.41581

06

.41597

07

.41614

08

.41631

09

.41647

10

.41664

11

.41681

12

.41697

13

.41713

14

.41731

15

.41747

16

.41764

17

.41781

18

.41797

19

.41814

20

.41831

21

.41847

22

.41863

23

.41880

24

.41896

25

.41913

26

.41929

27

.41946

28

.41963

29

.41979

30

.41996

31

.42012

32

.42029

33

.42045

34

.42062

35

.42078

36

.42095

37

.42111

38

.42127

39

.42144

40

.42160

41

.42177

42

.42193

43

.42210

44

.42226

45

.42243

46

.42259

47

.42275

48

.42292

49

.42308

50

.42325

51

.42341

52

.42357

53

.42374

54

.42390

55

.42406

56

.42423

57

.42439

58

.42455

59

.42472

60

.42488

61

.42504

62

.42521

63

.42537

64

.42553

65

.42570

66

.42586

67

.42602

68

.42619

69

.42635

70

.42651

71

.42667

72

.42684

73

.42700

74

.42716

75

.42732

76

.42749

77

.42765

78

.42781

79

.42797

80

.42813

81

.42830

82

.42846

83

.42862

84

.42878

85

.42894

86

.42911

87

.42927

88

.42943

89

.42959

90

.42975

91

.42991

92

.43008

93

.43024

94

.43040

95

.43056

96

.43072

97

.43088

98

.43104

99

.43120

2700

3.43136

01

.43152

02

.43169

03

.43185

04

.43201

05

.43217

06

.43233

07

.43249

08

.43265

09

.43281

10

.43297

11

.43313

12

.43329

13

.43345

14

.43361

15

.43377

16

.43393

17

.43409

18

.43425

19

.43441

20

.43457

21

.43473

22

.43489

23

.43505

24

.43521

25

.43537

26

.43553

27

.43569

28

.43584

29

.43600

30

.43616

31

.43632

32

.43648

33

.43664

34

.43680

35

.43696

36

.43712

37

.43727

38

.43743

39

.43759

40

.43775

41

.43791

42

.43807

43

.48823

44

.43838

45

.43854

46

.43870

47

.43886

48

.43902

49

.43917

50

.43933

51

.43949

52

.43965

53

.43981

54

.43996

55

.44012

56

.44028

57

.44044

58

.44059

59

.44075

60

.44091

61

.44107

62

.44122

63

.44138

64

.44154

65

.44170

66

.44185

67

.44201

68

.44217

69

.44232

70

.44248

71

.44264

72

.44279

73

.44295

74

.44311

75

.44326

76

.44342

77

.44358

78

.44373

79

.44389

80

.44404

81

.44420

82

.44436

83

.44451

84

.44467

85

.44483

86

.44498

87

.44514

88

.44529

89

.44545

90

.44560

91

.44576

92

.44592

93

.44607

94

.44623

95

.44638

96

.44654

97

.44669

98

.44685

99

.44700

2800

3.44716

01

.44731

02

.44747

03

.44762

04

.44778

05

.44793

06

.44809

07

.44824

08

.44840

09

.44855

10

.44871

11

.44886

12

.44902

13

.44917

14

.44932

15

.44948

16

.44963

17

.44979

18

.44994

19

.45010

20

.45025

21

.45040

22

.45056

23

.45071

24

.45086

25

.45102

26

.45117

27

.45133

28

.45148

29

.45163

30

.45179

31

.45194

32

.45209

33

.45225

34

.45240

35

.45255

36

.45271

37

.45287

38

.45301

39

.45317

40

.45332

41

.45347

42

.45362

43

.45378

44

.45393

45

.45408

46

.45423

47

.45439

48

.45454

49

.45469

50

.45484

51

.45500

52

.45515

53

.45530

54

.45545

55

.45561

56

.45576

57

.45591

58

.45606

59

.45621

60

.45637

61

.45652

62

.45667

63

.45682

64

.45698

65

.45712

66

.45728

67

.45743

68

.45758

69

.45773

70

.45788

71

.45803

72

.45818

73

.45834

74

.45849

75

.45864

76

.45879

77

.45894

78

.45909

79

.45924

80

.45939

81

.45954

82

.45969

83

.45984

84

.46000

85

.46015

86

.46030

87

.46045

88

.46060

89

.46075

90

.46090

91

.46105

92

.46120

93

.46135

94

.46150

95

.46165

96

.46180

97

.46195

98

.46210

99

.46225

2900

3.46240

01

.46255

02

.46270

03

.46285

04

.46300

05

.46315

06

.46330

07

.46344

08

.46859

09

.46374

10

.46389

11

.46404

12

.46419

13

.46434

14

.46449

15

.46464

16

.46479

17

.46494

18

.46509

19

.46523

20

.46538

21

.46553

22

.46568

23

.46583

24

.46598

25

.46613

26

.46627

27

.46642

28

.46657

29

.46672

30

.46687

31

.46702

32

.46716

33

.46731

34

.46746

35

.46761

36

.46776

37

.46790

38

.46805

39

.46820

40

.46835

41

.46849

42

.46864

43

.46879

44

.46894

45

.46909

46

.46923

47

.46938

48

.46953

49

.46967

50

.46982

51

.46997

52

.47012

53

.47026

54

.47041

55

.47056

56

.47070

57

.47085

58

.47100

59

.47114

60

.47129

61

.47144

62

.47159

63

.47176

64

.47188

65

.47202

66

.47217

67

.47232

68

.47246

69

.47261

70

.47276

71

.47290

72

.47305

73

.47319

74

.47334

75

.47349

76

.47363

77

.47378

78

.47392

79

.47407

80

.47422

81

.47436

82

.47451

83

.47465

84

.47480

85

.47494

86

.47509

87

.47524

88

.47538

89

.47553

90

.47567

91

.47582

92

.47596

93

.47611

94

.47625

95

.47640

96

.47654

97

.47669

98

.47683

99

.47698

3000

3.47712

01

.47727

03

.47741

03

.47755

04

.47770

05

.47784

06

.47799

07

.47813

08

.47828

09

.47842

10

.47857

11

.47871

12

.47886

13

.47900

14

.47914

15

.47929

16

.47943

17

.47958

18

.47972

19

.47986

20

.48001

21

.48015

22

.48030

23

.48044

24

.48058

25

.48073

26

.48087

27

.48101

28

.48116

29

.48130

30

.48144

31

.48159

32

.48173

33

.48187

34

.48202

35

.48216

36

.48230

37

.48244

38

.48259

39

.48273

40

.48287

41

.48302

42

.48316

43

.48330

44

.48344

45

.48359

46

.48373

47

.48387

48

.48402

49

.48416

50

.48430

51

.48444

52

.48458

53

.48473

54

.48487

55

.48501

56

.48515

57

.48530

58

.48544

59

.48558

60

.48572

61

.48586

62

.48601

63

.48615

64

.48629

65

.48643

66

.48657

67

.48671

68

.48686

69

.48700

70

.48714

71

.48728

72

.48742

73

.48756

74

.48770

75

.48785

76

.48799

77

.48813

78

.48827

79

.48841

80

.48855

81

.48869

82

.48883

83

.48897

84

.48911

85

.48926

86

.48940

87

.48954

88

.48968

89

.48982

90

.48996

91

.49010

92

.49024

93

.49038

94

.49052

95

.49066

96

.49080

97

.49094

98

.49108

99

.49122

3100

.49136

TABLE III.

BAROMETRIC READINGS IN MILLIMETERS.—

ALTITUDES IN METERS.

This is from Radau’s table. The formula for calculation of difference of altitude of two stations is

in which D is the difference of height in meters, h and h' are barometer readings in millimeters and t and t' are the temperatures in centigrade degrees.

Mill.

Meters.

500

3365.4

501

3349.4

502

3333.5

503

3317.6

504

3301.7

505

3285.9

506

3270.1

507

3254.3

508

3238.5

509

3222.8

510

3207.1

511

3191.5

512

3175.9

513

3160.3

514

3144.7

515

3129.2

516

3113.7

517

3098.2

518

3082.8

519

3067.4

520

3052.0

521

3036.6

522

3021.3

523

3006.0

524

2990.7

525

2975.5

526

2960.3

527

2945.1

528

2930.0

529

2914.9

530

2899.8

531

2884.7

532

2869.7

533

2854.7

534

2839.7

535

2824.7

536

2809.8

537

2794.9

538

2780.0

539

2765.2

540

2750.4

541

2735.6

542

2720.9

543

2706.1

544

2691.4

545

2676.8

546

2662.1

547

2647.5

548

2632.9

549

2618.3

550

2603.8

551

2589.3

552

2574.8

553

2560.3

554

2545.9

555

2531.5

556

2517.1

557

2502.7

558

2488.4

559

2474.1

560

2459.8

561

2445.6

562

2431.4

563

2417.2

564

2403.0

565

2388.8

566

2374.7

567

2360.6

568

2346.5

569

2332.5

570

2318.4

571

2304.4

572

2290.4

573

2276.5

574

2262.6

575

2248.7

576

2234.8

577

2220.9

578

2207.1

579

2193.3

580

2179.5

581

2165.7

582

2152.0

583

2138.3

584

2124.6

585

2110.9

586

2097.3

587

2083.7

588

2070.1

589

2056.5

590

2042.9

591

2029.4

592

2015.9

593

2002.4

594

1989.0

595

1975.5

596

1962.1

597

1948.7

598

1935.4

599

1922.0

600

1908.7

601

1895.4

602

1882.1

603

1868.8

604

1855.6

605

1842.4

606

1829.2

607

1816.0

608

1802.9

609

1789.8

610

1776.7

611

1763.6

612

1750.5

613

1737.5

614

1724.4

615

1711.4

616

1698.5

617

1685.5

618

1672.6

619

1659.7

620

1646.8

621

1633.9

622

1621.0

623

1608.2

624

1595.4

625

1582.6

626

1569.8

627

1557.1

628

1544.4

629

1531.7

630

1519.0

631

1506.3

632

1493.7

633

1481.0

634

1468.4

635

1455.8

636

1443.3

637

1430.7

638

1418.2

639

1405.7

640

1393.2

641

1380.7

642

1368.3

643

1355.8

644

1343.4

645

1331.0

646

1318.7

647

1306.3

648

1294.0

649

1281.7

650

1269.4

651

1257.1

652

1244.8

653

1232.6

654

1220.4

655

1208.2

656

1196.0

657

1183.8

658

1171.7

659

1159.5

660

1147.4

661

1135.3

662

1123.3

663

1111.3

664

1099.2

665

1087.2

666

1075.2

667

1063.2

668

1051.2

669

1039.3

670

1027.3

671

1015.4

672

1003.5

673

991.7

674

979.8

675

968.0

676

956.1

677

944.3

678

932.6

679

920.8

680

909.0

681

897.3

682

885.6

683

873.9

684

862.2

685

850.5

686

838.9

687

827.3

688

815.6

689

804.0

690

792.5

691

780.9

692

769.3

693

757.8

694

746.3

695

734.8

696

723.3

697

711.9

698

700.4

699

689.0

700

677.6

701

666.2

702

654.8

703

643.4

704

632.1

705

620.7

706

609.4

707

598.1

708

586.8

709

575.6

710

564.3

711

553.1

712

541 8

713

530.6

714

519.5

715

508.3

716

497.1

717

486.0

718

474.8

719

463.7

720

452.6

721

441.6

722

430.5

723

419.4

724

408.4

725

397.4

726

386.4

727

375.4

728

364.4

729

353.5

730

342.5

731

331.6

732

320.7

733

309.8

734

298.9

735

288.0

736

277.2

737

266.3

738

255.5

739

244.7

740

233.9

741

223.1

742

212.3

743

201.6

744

190.8

745

180.1

746

169.4

747

158.7

748

148.0

749

137.4

750

126.7

751

116.1

752

105.5

753

94.9

754

84.3

755

73.7

756

63.1

757

52.6

758

42.0

759

31.5

760

21.0

761

10.5

762

0.0

763

-10.5

764

-20.9

765

-31.4

766

-41.8

767

-52.2

768

-62.6

769

-73.0

770

-83.4

771

-93.7

772

-104.1

773

-114.4

774

-124.7

775

-135.0

776

-145.3

777

-155.6

778

-165.9

779

-176.1

780

-186.4

In comparing the Aneroid with a Mercurial Barometer, correct the latter by the following table, subtracting the corrections.

TABLE IV.

REDUCTION OF MERCURIAL

COLUMN TO 32° FAHR.

Brass scale to barometer correct at 62° Fahr.

Temp.

°F.

30”

25”

20”

32

.009

.008

.006

35

.017

.015

.012

40

.031

.026

.021

45

.044

.037

.030

50

.058

.048

.038

55

.071

.059

.047

60

.084

.070

.056

65

.098

.082

.065

70

.111

.093

.074

75

.125

.104

.083

80

.138

.115

.092

85

.151

.126

.101

90

.164

.137

.110

95

.178

.148

.118

100

.191

.159

.127

TABLE V.

BAROMETRIC PRESSURES CORRESPONDING

TO BOILING WATER TEMPERATURES.

Whole Deg.

Tenths of each Degree.

.0

.2

.4

.6

.8

in.

in.

in.

in.

in.

183

16.317

16.389

16.461

16.533

16.605

184

16.618

16.752

16.826

16.900

16.974

185

17.048

17.122

17.197

17.272

17.348

186

17.423

17.499

17.575

17.652

17.729

187

17.806

17.883

17.961

18.039

18.117

188

18.195

18.274

18.353

18.432

18.512

189

18.592

18.672

18.753

18.833

18.914

190

18.996

19.077

19.159

19.241

19.324

191

19.407

19.490

19.573

19.657

19.741

192

19.825

19.910

19.995

20.080

20.166

193

20.251

20.338

20.424

20.511

20.598

194

20.685

20.773

20.861

20.949

21.038

195

21.126

21.216

21.305

21.395

21.485

196

21.576

21.666

21.758

21.849

21.941

197

22.033

22.125

22.218

22.311

22.404

198

22.498

22.592

22.686

22.781

22.876

199

22.971

23.067

23.163

23.259

23.356

200

23.453

23.550

23.648

23.746

23.845

201

23.943

24.042

24.142

24.241

24.341

202

24.442

24.542

24.644

24.745

24.847

203

24.949

25.051

25.154

25.257

25.361

204

25.465

25.569

25.674

25.779

25.884

205

25.990

26.096

26.202

26.309

26.416

206

26.523

26.631

26.740

26.848

26.957

207

27.066

27.176

27.286

27.397

27.507

208

27.618

27.730

27.842

27.954

28.067

209

28.180

28.293

28.407

28.521

28.636

210

28.751

28.866

28.982

29.098

29.215

211

29.331

29.449

29.566

29.684

29.803

212

29.922

30.041

30.161

30.281

30.401

Transcriber’s Notes:

The cover image was created by the transcriber, and is in the public domain.

The illustrations have been moved so that they do not break up paragraphs and so that they are next to the text they illustrate.

Typographical and punctuation errors have been silently corrected.

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Table of Contents

THE ANEROID BAROMETER: ITS Construction and Use.

CONTENTS.

PREFACE TO SECOND EDITION.

CHAPTER I. THE ATMOSPHERE.

CHAPTER II. BAROMETRIC MEASUREMENTS OF ALTITUDES.

CHAPTER III. ANEROID BAROMETERS: THEIR CONSTRUCTION.

CHAPTER IV. THE USE OF ANEROID BAROMETERS.

CHAPTER V. SUGGESTIONS IN REGARD TO THE SELECTION AND SYSTEMATIC USE OF AN ANEROID.

TABLE I. FOR ESTIMATING HEIGHTS BY THE ANEROID.

TABLE II.

TABLE III. BAROMETRIC READINGS IN MILLIMETERS.— ALTITUDES IN METERS.

TABLE IV. REDUCTION OF MERCURIAL COLUMN TO 32° FAHR.

TABLE V. BAROMETRIC PRESSURES CORRESPONDING TO BOILING WATER TEMPERATURES.

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