  MEASUREMENT OF ALTITUDES BY DIFFERENCES OF ATMOSPHERIC PRESSURE—HISTORICAL NOTE—MERCURIAL BAROMETER—CONSTRUCTION—OPERATION—ANEROID BAROMETER—CONSTRUCTION—VARIOUS IMPROVEMENTS—HYPSOMETER. 808.—Historical Note.—The observation that the atmosphere decreases in density with increase of height is due to Alhazen the Saracen, about a.d. 1000. By this he explains that a ray of light entering the atmosphere obliquely follows a curvilinear path, bending towards the denser strata, that is concave towards the earth. He showed that a body will receive difference of pressure in a rare and a dense atmosphere, and calculated that the height of the atmosphere to its final attenuation would be from his data nearly 58½ miles. The practical instruments that have been devised for measuring altitudes, by the differences of pressure due to the weight of superincumbent atmosphere are the barometer, the aneroid, and the hypsometer. The barometer was invented by Torricelli about the year 1640. Its principle was demonstrated and first applied to altitude measurement by Pascal in 1647. The aneroid barometer was suggested by Conti in 1798, and said to be devised as a practical instrument by Vidie in 1808. The hypsometer or boiling-point thermometer, which depends for its boiling temperature upon the pressure of the atmosphere above the liquid which surrounds it, was suggested by Fahrenheit in 1724, experimented with by de Luc 809.—The Mercurial Barometer.—The principle of the barometer is generally understood. If a glass tube, closed at one end, 33 inches long, say of ¼ inch or over in bore, be filled brimful of mercury and the point of the forefinger be firmly pressed on the surface of the mercury, the tube may be inverted without the admission of air. If the covered end of the tube be now plunged into a basin of mercury and the finger slowly withdrawn from under the tube beneath the surface of the mercury, the latter will sink in the tube to about 30 inches above the surface of that in the basin—that is, if the experiment be performed at about the sea level. The empty space in what now becomes the top of the tube is termed a Torricellian vacuum. 810.—In removing the pressure of the atmosphere from its surface in the tube, which in the above experiment produces the barometer, the pressure of the atmosphere then falls only upon the exposed surface of the mercury in the 811.—The mean height of the barometrical column in Great Britain, at sea level at the temperature of 32° Fahr., is about 29·95 ins. A cubic inch of mercury at this temperature weighs 0·48967 lbs. Therefore 29·95 × 0·48967 = 14·66 lbs. gives the mean pressure of the atmosphere on each square inch of surface of the earth in this latitude. Nearer the tropics the pressure is greater, near the poles less. It can be shown that as the heights ascended by the barometer increase in arithmetical progression, the pressure upon the mercury diminishes in geometrical progression. 812.—Mountain Barometer.—The barometer used for measuring altitudes, to which the above term has been applied, is now made only upon Fortin's plan, in which the bottom of the cistern wherein the glass tube is plunged is made of fine, close-grained leather, the best for the purpose being a stout kid. The pores of the leather must be sufficiently fine not to admit of the escape of the mercury, and yet at the same time sufficiently soft and pliable to transmit the exterior pressure of the air. Fortin's construction permits the cistern to be closed entirely secure from leakage of the mercury, 813.—The Glass Tube is made of mild flint glass thoroughly annealed and sufficiently stout to resist all the strain and percussion that may occur with fair usage. One end of the tube is slowly sealed by the blow-pipe, so that the closed end may be as strong as the other parts. 814.—Mercury—Filling the Barometer Tube.—The mercury of commerce is generally impure, and it contains occluded air. For standard and mountain barometers the mercury should be distilled in an iron apparatus, at just its boiling heat, leaving about one-sixth of the mercury in the still. The tube, which should be perfectly clean, is left about 12 inches too long for the barometer. It is charged with clean mercury for about 36 inches in height. It is then boiled in a special circular charcoal stove, in the centre of which there is a vertical iron tube of 2 inches diameter. The barometer tube is introduced from the bottom of the stove, to heat about 4 inches of the top of the mercury only. The tube remains in this position till the mercury boils. It is then elevated for another 4 inches and again brought to boiling point, and so on until the end of the tube is reached. Under this process the air and some impurities rise to the surface of the mercury, and the tube is considered to be properly boiled. The end of the tube is then cut off to its proper length and inserted in the cistern, 815.—The lower part of the barometer tube, after it is filled, is attached to a thin boxwood socket of about an inch in depth by means of hot thin glue. The socket piece is afterwards bound over with sewing silk, which is again covered with glue, and is finally varnished so as to form an elastic, secure fitting upon the glass. The socket-piece is secured to a wide boxwood collar, Fig. 390, D. Upon the under side of the collar an ivory gauge peg X is inserted, which forms the index point for reading the surface of the mercury in the cistern upon the Fortin principle. 816.—The Cistern.—The glass sighting tube, Fig. 390 H, of the cistern, through which the mercury and gauge point X are visible, is made about 1½ inches long and from 1 inch to 1½ inches internal diameter, the glass being 1/8 inch to 1/5 inch in thickness, ground square at its ends. The upper end of the glass fits upon the boxwood collar D, with the interval of an indiarubber band to make the fitting air-tight. The lower end of the glass tube fits upon the boxwood collar I, with an interval of a turned leather collar. The boxwood collar prolonged forms the lower part of the cistern. This has a second boxwood collar screwed upon it, to which the leather bag E is attached by silk and glue. A stout leather capping plug is glued upon the lower end of the bag, upon which the boxwood cap of the adjusting screw F presses for adjustment of the mercury, or to close the tube. Fig. 389.—Mountain barometer erected for use. Fig. 390.—Section through the cistern. Fig. 391.—Vernier reading, showing gauge point S. Fig. 392.—Sling case for carrying. Larger image 817.—The Cistern Casing, which is of brass, consists of upper and lower collar pieces, Fig. 390 AA' and BB', and their attachments. The upper collar is fixed to the casing tube of the barometer. In the inside of this collar a leather washer is placed, which comes above the boxwood collar on the glass tube D and makes soft contact between these parts. The lower collar has been partly described with the cistern. This has a brass tube E screwed upon it, covering the 818.—The Stem, or Barometer Casing Tube, is made of brass, about ¾ inch diameter. This has a slot, of about ¼ inch in width, down two concentrically opposite sides, from near the top of the tube downwards for about 20 inches. The tube is graduated along one open edge next the slot in inches and tenths, these being again subdivided to twentieths, and figured to read from 13 inches to 32 inches of mercury, as shown in detail for the upper part in Fig. 391. The same space is divided into centimetres and millimetres if metrical measure be used. Within the outer tube an inner tube of about 12 inches in length fits telescopically to move with a soft smooth motion. This inner tube carries one vernier at top and one at bottom, Fig. 389, rr'. The top vernier, shown Fig. 391, is placed above a slot in this tube which corresponds with the outer tube, so that the level of the mercury can be seen below the top vernier-piece at S. The verniers are divided into 50, so that, reading into the 20, they give reading 50 × 20, or 1000 to the inch. The inner tube carries a rack about 11 inches long, which moves by a pinion fixed upon a cock-piece, Fig. 389 m, on the outer tube in the same manner as before described for telescope racking, art. 96. Two stay-pieces placed over the outer tube hold the slots firmly at an equal opening. A ring is placed at the head of the barometer to suspend it in a room, to be used, if required, as an ordinary meteorological barometer, as shown at the top of Fig. 391. 819.—Mounting of the Barometer.—The barometer is mounted upon a tripod formed of three light tubes with steel points, as shown Fig. 389. These screw into a collar which is packed in the cap of the leather case. The collar has two opposite screws that screw into a second collar, which is also held by two opposite points at right angles to the first. The points of the screws form axes in the manner of a Hook's joint, permitting the barometer to take a vertical position by the superior gravity of its cistern and lower parts. 820.—The Thermometer, shown at Fig. 389 t, has its bulb brought as nearly as possible into contact with the glass tube enclosed in the casing tube. It is commonly divided with both centigrade and Fahrenheit scales. Correct observation of the thermometer is necessary to be made with every observation of the barometer, as the specific gravity of the mercury, and consequently the height of the column, depend partly upon this for its correct determination. 821.—The Packing Case, Fig. 392, is made of solid leather lined with thick felt to fit the barometer. The legs are placed in packings outside the case. In packing for carriage the screw of the cistern is turned nearly home, leaving only sufficient space for any probable expansion of the mercury from increase of temperature. The barometer should always be carried in an inverted position, as this precludes the possibility of air getting into it, and even tends to exclude, by the jarring motion of carrying, any air that may have accidentally become occluded. A strap is attached to the case for holding it over the shoulder. 822.—Reading the Barometer.—It will be observed that the mercury against the sides of the tube presents an upward curved appearance, due to the resistance of the glass to perfect contact, and the cohesion of the mercury in what is termed capillary action. This beading, as it is termed, varies according to whether the mercury is rising or falling. It
For altitude the upper and lower stations are taken, and the difference subtracted for difference of barometrical scale. 823.—Difference in Altitude in feet taken from Barometrical Inches.—Complete barometrical tables for this comparison will be found in Molesworth's and other pocket-books in use by all engineers. It is therefore unnecessary to occupy our space with them. A very approximate rule may be given, which was proposed by Mr. R. Strachan in the Meteorological Magazine, as follows:— "Read the barometer to the nearest hundredth of an inch; subtract the upper reading from the lower, leaving out the decimal point; and then multiply the difference by 9, which gives the elevation in feet. Thus:—
824.—Capillarity.—For meteorological observations a quantity must be added to the reading equal to the resistance of the tube in capillary action to the rise of the mercury. This is greater in an unboiled tube than in one in which the mercury is boiled. For altitude measurements with a single barometer, or by two barometers with equal tubes, it may be neglected, as it will be equal in all parts of the tube. Where two barometers of different bores are used, the following table gives the correction:—
825.—Temperature Correction.—As the mercury increases in temperature it becomes specifically lighter, therefore rises higher in the tube under equal atmospheric pressure. The temperature is indicated by the thermometer, shown at Fig. 389 t. The expansion of mercury for 1° Fahr. is 0·000101; but the brass tube also expands 0·0000104, and it is the difference between the two expansions that we require, the mercury expanding about 7·15 more than the brass. If we subtract from the reading ·00014 of the observed altitude for every degree of Fahrenheit above 32°, the correction will be practically very near. Thus for a single reading—thermometer, 52° Fahr.; barometer, 30 inches -(52 - 32) × 30 × ·00014 = ·084, making the true reading 30 - ·084 = 29·916 inches at 32° Fahr. Tables for correction without any calculation will be found in Molesworth's and other pocket-books. 826.—Gravity Correction.—The force of gravity decreases as we ascend to a higher level in proportion to the square of Time.—Humboldt discovered that the barometer varied within the tropics at different hours of the day. This has also been found to be general to some extent in all countries, depending upon many conditions. It is only important for consideration of altitude measurements, that it is advisable if possible to take the upper and lower stations simultaneously by a pair of barometers for exact determination of altitude. 827.—Aneroid Barometer.—The first introduction of this instrument into England was by Pierre Armand, le Comte de Fontainmareau. Fig. 393.—Stanley's civil engineer's aneroid. Larger image The aneroid practically in its present form was devised by Lucien Vidie from 1848 to 1862. Fig. 394.—Perspective view of the interior of an aneroid. Larger image 828.—The construction of this aneroid is shown in Fig. 394, which is of a 4½-inch instrument, aneroids made for surveying being of two sizes, 3 inches and 4½ inches. A is a solid plate of metal 1/8 inch in thickness, termed the base plate; B the vacuum chamber, circularly corrugated on both sides, made of thin, hard-rolled German silver containing a large percentage of nickel. 829.—An axis is projected from the lower side of the chamber, of about 1/5 inch diameter. This is tapped with a screw and screwed firmly down into the base plate with a counternut. On the upper side of the vacuum chamber the axis is projected upwards to receive the tension of a strong, very flexible spring D above it, to be described. A bridge-piece EE of steel of strong section strides over the vacuum chamber. This piece has a stout arm-piece projecting from it towards A, which is secured to the base plate by a screw that is left open to a hole indicated near A through the outer case of the instrument, by means of which the bridge-piece can be rocked so as to produce more or less 830.—Compensation for Temperature.—This is a somewhat difficult matter, which is generally brought about by several modifications of parts. Some ordinary aneroids will move upwards about 1/10 inch of mercury by a rise of temperature of 8° centigrade only. This is caused principally by the increase of temperature softening the spring to render it less rigid, and the softening of the vacuum chamber to render it more flexible or sensitive to atmospheric pressure. Some little difference is also caused by the unequal relative expansion of the lever, arms, spring, and chain, these parts being of steel and brass. Compensation can be made in the lever arm G by making this curved and of two unequally expansive metals, as zinc and steel, so that the curvature increases with increase of temperature and the lever shortens. Compensation can also be partially made by making the base plate in two metals—iron and brass—so as to press the standards fixed through the two metals nearer or further apart with temperature changes. But the whole subject is too technical to be entered upon in our limited space, as it depends so much upon the construction of the instrument, which is modified in various ways by different makers in order to effect this correction. 831.—Dial and Hand.—From the delicacy of the structure 832.—The ordinary method of reading the aneroid is to let the index point read over the divisions. The author devised a plan, which he has used for many years, of fixing a small plate of aluminium upon the point of the hand, level with the scale, which is raised on a step to read it upon its inside edge, to a fine line on the aluminium. By this means error of parallax in reading is entirely avoided. The author also places an adjustable magnifier to move over the index for reading. This last improvement is now followed by other makers. A pointer also revolves with the outer rim to show the last reading before ascent or descent. Instruments made with care in the points just indicated must necessarily become expensive. Where the aneroid is to 833.—The Altitude Scale is generally placed near the periphery of the dial; it is the all-important part to the surveyor. This scale is usually set out from a mean of atmospheric pressure at sea level, taken from Sir George B. Airy's tables, which give the extreme pressure of 31 inches barometric pressure for zero at sea level. With this pressure altitudes are taken at intervals according to the indices tested under the air-pump, and the intermediate divisions are graduated to scale. These index points are shown in the table below for a few points:—
It may be generally observed that the more open the scale the less altitude can be obtained by a single revolution of the 834.—Movable Altitude Scale.—In this the altitude scale revolves so as to be able to set it at zero for ascending from any point. As the barometrical scale diminishes, it is necessarily inaccurate, and cannot therefore be used upon a surveying aneroid; but the plan is pleasant for approximate measurements for amusement in making ascents. It is only mentioned here for the reason that the inaccuracy of the movable scale is not always recognised. 835.—Adjustment of the Aneroid.—There is a screw at the back of every aneroid somewhere under the point A, Fig. 394, by means of which an aneroid may be brought to the reading of a mercurial barometer at the position the mercury may be read. Where a good instrument has been set by the maker to a standard barometer, it is not wise to alter it frequently if it keeps in good working order for altitude measurements without being again set by a standard. On the other hand, however well the aneroid may have been made it works gradually to a slight change, caused by the smooth wearing of parts in action. It is well to have an aneroid, after one or two years' wear, cleaned and adjusted by the maker. It will then, if a good instrument, work well for many years. 836.—Directions for Measuring Altitudes.—Turn the outer rim of the instrument until the index carried thereby reads to the same point as the index hand. Raise the magnifier until the reading comes into sharp focus. Hold the instrument as nearly horizontal as possible, and tap the case lightly with the thumb-nail two or three times, so as to overcome any slight friction of its mechanism. This places the action of the works in equilibrium. Write down the observation as it now reads in the pocket-book, taking thousands 837.—Various Improvements in the Aneroid.—It is uncertain whether any great internal improvements have been made in this instrument, except by Vidie, at various times. Many attempts have been made to increase the length of scale to obtain more open reading. These attempts have all been in the direction of increasing the difference of space between the fulcra of the levers or by additional gearwork, producing thereby a greater multiplication of the small unit of displacement of the axis of the vacuum chamber beyond the normal × 500, which is already great. The multiplication has been Fig. 395.—Watkin's extended scale surveying aneroid. Larger image 838.—Watkin's Extended Scale Aneroid.—This instrument is shown at Fig. 395, and has a very extended reading, consisting of three complete circles, in place of the usual single scale, with a hand or pointer sufficiently long to extend Fig. 396.—Face. Fig. 397.—Back. Larger image 839.—Watkin's New Patent Mountain Aneroid Barometer.—This instrument, of which both a front and back view is shown above at Figs. 396 and 397, is the invention of Colonel H. S. Watkin. The special feature is that it can be put in or out of action as required, and when out of action is impervious to the influence of variations in atmospheric pressure. This relieves the strain on It has an aluminium case for lightness, is made in two sizes (3 inch and 4½ inch), and has a sling leather case. These plans are again on their trial. It is the author's opinion on the subject, knowing the delicacy and skill shown in Vidie's work, that little improvement is likely to be obtained by magnification of the small motion of the vacuum chamber by mechanical means, which must necessarily be by a process both delicate and highly frictional. Attempts, he thinks, may otherwise be successfully made in the magnification of the small motion of the hand in a frictionless manner by optical means to obtain clearer definition. 840.—An improvement was made in the aneroid in one direction by the late Thomas Cooke 841.—Bourdon's Aneroid, invented by C. Bourdon in 1849. 842.—Hypsometer, or Boiling-point Thermometer.—That water or any other liquid boils at a certain temperature, according to the amount of atmospheric pressure surrounding it, is easily observed by placing a cup of boiling hot water under the receiver of an air-pump. At first the surface will remain still, but as the pressure of the air is pumped off it may be made to boil time after time until it arrives at a low temperature. The temperature at which the water boils as the air is rarified may be easily followed by observation of a thermometer immersed in the cup of water; and at the same time, if a barometer be placed in connection with the receiver it will indicate the pressure, from which the scale of differences may be practically made. For the civil engineer this instrument, accompanied by the aneroid, is in every way superior to the mountain barometer, which must necessarily have a three-feet tube, as the hypsometer is much lighter, more portable, and less liable to injury, and perhaps, from the uncertainty of keeping a pure vacuum in the barometer, safer as a means of observation. Fig. 398.—Hypsometer, or boiling point thermometer. Fig. 399.—Case for hypsometer. Larger image 843.—The modern form of instrument is shown in Fig. 398. The boiler shown immediately over the lamp is filled about half full of rain water by lifting off its covering tube C. The covering tube has a smaller tube, about 3 inches long and ½ inch diameter leading upwards from it, through which the thermometer bulb is passed into the boiler. This tube is covered by the jacket J, formed of four telescopic tubes that are extended, as shown in the figure, for use, but which close up quite compactly when the instrument is put in its case. The upper drawer of the jacket tube is about 844.—The Thermometer, upon which the action of the instrument depends, has a stout stem about 6 inches long and ¼ inch diameter, with a very fine, flat, oval bore about ·01 inch wide and not much over ·005 inch in thickness. The stem is divided very openly for about 25° below 100° centigrade, each degree being subdivided into 10, below 212° if Fahrenheit scale be used, with each degree divided into 5. The divisions are filled in with lamp-black, and the stem is backed with white enamel to give clear reading. The thermometer T when in use is surrounded by a vulcanized indiarubber collar I which slips over its stem to adjust it to position in the boiler tube as shown. In placing the thermometer in its jacket, it is important to hold it erect to be sure it passes into the leading tube from the boiler, as there is generally just room for it to catch by the side of this tube, where if it were pressed down it would break the bulb. When the thermometer is out of use the rubber collar is removed, and the thermometer is placed in a tubular metal case which is lined with indiarubber tubing, so that no jar can injure it. The whole apparatus when closed is carried in a solid leather case, which contains divisions for the separate parts of the apparatus, and a strap for passing over the shoulder for carrying it. Fig. 399 shows the general form of case. 845.—Use of the Hypsometer.—Saussure calculated, from data of his ascents of Swiss mountains, that the temperature of boiling water decreased 1° centigrade for every 978·5 feet of ascent, where the mean temperature of the atmosphere was estimated at 0° centigrade, or freezing point. If the temperature of the surrounding atmosphere be taken as 5·5° centigrade, the ascent per degree of that scale is 1000 feet. This becomes, therefore, the most convenient data to calculate from, allowing 3·9 feet per 1000 per degree centigrade for Sometimes the thermometer is divided to Fahrenheit degrees, subdivided into 5 to read by interspace and line to ·1° F. This may be changed to centigrade for use of the above formula by taking 32° F. lower than the reading and multiplying by 5/9. Thus— 60° Fahr. = 5/9 (60 - 32) = 15·55° centigrade. The calculation proposed by Lefroy is, however, simpler for Fahrenheit scale. To allow for diminution of boiling temperature, with height from 212°, with barometer at 30 inches, take 511 feet of altitude for the first degree and add 2 feet for each succeeding degree. Thus, taking height of first station = h corrected for 212° Fahr., 30 inches barometer, remembering decrease of barometrical pressure acts the same as increase of height. Then— | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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