THE ANEROID BAROMETER, ITS THEORY AND 
 ITS USE, WITH SPECIAL REFERENCE TO THE 
 DETERMINATION OF ALTITUDES. 
 
 BY 
 
 
 E. A. GIESELER, C. E. 
 
 (Reprinted from the Journal of the Franklin Institute, November, 1889,; 
 
 PHILADELPHIA ; 
 

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 ) 
 
CM 
 
 
 ivio i , .., 
 
 at 
 
 Oak Btre^ 
 
 The aneroid BAROMETER, its VARIOUS FORMS, 
 ITS THEORY AND ITS USE, with SPECIAL 
 REFERENCE to the DETERMINA¬ 
 TION OF ALTITUDES. 
 
 By E. a. Gieseler, C.E. 
 
 I. GENERAL DISCUSSION. 
 
 The motor of all aneroids consists in an hermetically 
 sealed box, the air of which has been exhausted as com¬ 
 pletely as practicable, and the flexible sides of which will 
 consequently perform certain motions, when the pressure of 
 the atmosphere changes. These motions are, however, too 
 small to be perceived by the unaided eye, and they are, 
 therefore, transmitted to a suitable mechanism, by means of 
 which they are magnified to such an extent that they can 
 be discerned and measured. 
 
 The invention of the aneroid dates back to the beginning 
 of this century, one of the oldest forms being the one con- 
 
 44098 
 
2 
 
 structed by Bourdon, in which the box has the shape of a 
 tube sealed at both ends, and bent into the shape of a circle. 
 A small open space remains between the two ends, and dia¬ 
 metrically opposite this gap the tube is fastened to a sup¬ 
 porting plate. The cross-section of this tube is either rec¬ 
 tangular or oval, and the direction of its greatest height or 
 diameter stands at right angles to the plane of the circle 
 into which the tube has been bent, which is parallel to the 
 supporting plate. 
 
 When compressed air or steam is admitted into such a 
 tube, the inner pressureThus created will have the tendency 
 to straighten it, on account of the excess of pressure exer¬ 
 cised on the greater area of the outer circular side as com¬ 
 pared with the smaller area of the inner circular side. Any 
 increawSe^'of the inner pressure will result in a further flatten¬ 
 ing of th^,'circle into which the tube has been bent, while a 
 decrease of it will cause such curve to be sharpened. 
 
 Precisely the reverse will take place, when the tube has 
 been exhausted, because then the acting force, instead of 
 being an inside pressure, will be the outside pressure of the 
 atmosphere. The tube being held as described before at 
 one point only, which is situated diametrically opposite the 
 opening between the two ends, it is evident that the 
 changes of form of the curve must result in movements of 
 these ends; under the influence of high- atmospheric pres¬ 
 sure they will approach each other, while a decrease of pres¬ 
 sure will widen the gap between them. The movements of 
 the ends are transmitted by a simple arrangement to a hand 
 pointing on a graduated dial. They are magnified either 
 by levers acting on the short arm of the hand or pointer, or, 
 when the latter is mounted centrally, by means of a toothed 
 wheel and pinion. 
 
 This form of the aneroid has nowadays been entirely 
 superseded by others, in which the vacuum box has the 
 shape of a flat cylinder, into the upper and lower circular 
 ends of which concentric grooves are pressed in order to 
 equalize the motions performed by them under the influence 
 of the varying atmospheric pressure. To the side of the 
 vacuum box is soldered a small tin pipe, through which the 
 
3 
 
 air is exhausted. After this has been done the pipe is sealed 
 and the upper and lower ends of the box are now deflected 
 towards its interior by the pressure of the atmosphere, the 
 amount of such deflections for a given pressure being 
 dependent on the strength of the plates. This must be 
 sufficient to prevent too great a departure from the horizon¬ 
 tal positions, in order not to strain the plates beyond their 
 limit of elasticity. The movements are, therefore, neces¬ 
 sarily small; a fall of of an inch in the mercurial barom¬ 
 eter corresponding to an approach of about of an inch 
 
 of the plates of the vacuum chamber. 
 
 II. THE NAUDET ANEROID. 
 
 To measure such exceedingly small quantities, one class 
 of modern aneroids is provided with an ingenious mechan¬ 
 ism invented by Vidi and later improved by Naudet, the 
 main parts of which are shown in Fig. /. 
 
 To the base or foundation plate B B are firmly attached 
 a laminated spring's and the vacuum chamber V. The latter 
 carries upon its centre an upright pillar P, which passes 
 through an opening in,the spring and presses on its upper 
 side by means of the knife edge'A. An elastic system is in 
 this way formed by vacuum chamber and spring and the 
 pulsations of the former will be imparted to the latter. The 
 horizontal arm A is firmly attached to the spring and will 
 therefore follow its movements. These will appear in a 
 magnified scale at the end L and are transmitted by the two 
 links L and L' to the rocker shaft which turns in bearings 
 attached to the base plate, but not shown in the diagram. 
 The turning motions of R are further magnified by the arm 
 A’ and thence transmitted by a small chain Cto the central 
 shaft /, which carries the index pointer. The required ten- 
 vsion on the chain is produced by a spiral spring acting on 
 
4 
 
 the central shaft. This spring and the bearings for the cen¬ 
 tral shaft are not shown in the diagram. 
 
 The graduation of the dial on which moves the index 
 pointer, like the hand on a watch dial, is made to correspond 
 as nearly as possible with the reading of the mercurial 
 barometer, and, like the latter, is expressed in millimetres 
 or in inches. Perfect accuracy in this respect cannot be 
 attained; there will always be required a certain correction 
 for graduation. This and the corrections for temperature 
 are the most important ones for practical work and will be 
 discussed further below. 
 
 As apparent from the above, the use of the Naudet ane¬ 
 roid is very simple; in fact, the handling and reading of no 
 instrument could be simpler. But this advantage is obtained 
 by means which, in themselves, constitute the source of 
 undoubted defects. The magnification and the measuring 
 of the small movements of the vacuum chamber are per¬ 
 formed by means of an exceedingly delicate mechanism, 
 which is liable to get out of order unless great care is exer¬ 
 cised in handling and transporting the instrument. Such 
 constant and unremitting care, however, cannot be exercised 
 under all circumstances, especially not in our country where 
 the aneroid, in the hands of the railroad engineer for 
 instance, is frequently subjected to swift transportation on 
 horseback over many miles of rough country, the jolting and 
 jarring of which are almost certain to prove injurious to the 
 instrument. Even ordinary transportation in good packing 
 frequently puts a Naudet out of working order, and no dealer 
 in these instruments can warrant their safe arrival at the 
 end of a long railroad journey. 
 
 Hence the frequent complaints of engineers, who have 
 bought instruments in New York or some other great centre 
 and to their dismay find them giving out completely when 
 needed, a calamity which will be all the more annoying, 
 when it happens, as it naturally often does, at a place far 
 removed from any facilities for repairing. 
 
 Aside from such heavy shocks, which may at once render 
 a Naudet perfectly useless, an instrument actually used in 
 the field is necessarily exposed to small shocks, which even 
 
5 
 
 the most careful and experienced observer cannot entirely 
 avoid, and the continuance of which tends to produce a- 
 slackening of the mechanism. The gradual deteriorating 
 from this cause of Naudet aneroids, during their use in the 
 field, is a well-established fact, even when they are in the 
 hands of the best observers (Report of Mr. J. Campbell, 
 R. N., published in U. S. Monthly Weather Review, September 
 1879). 
 
 Finally a very important defect .should be mentioned 
 here, which may not inadequately be termed the “ elastic 
 reaction ” of the instrument and which asserts itself in the 
 tardiness with which the mechanism accommodates itself 
 to changes in atmospheric pressure. 
 
 C. Kroeber, in his experiments with Naudet aneroids 
 {Zeitschrift fiir Verniessiingswesen, Heft. 8, 1881), has found that 
 it took the instrument about two days to accommodate itself 
 to a change of pressure corresponding to five inches of the 
 mercurial column, the readings taken immediately after the 
 pressure had been changed differing nearly two-tenths of 
 an inch from the final ones. If not considered in the case 
 of a measurement of altitudes this difference would have 
 constituted an error of about 200 feet in about 5,000 feet. 
 
 It is true that the quality of “ elastic reaction ” in a 
 measure is common to all aneroids, but it is especially pro¬ 
 nounced in the Naudet, on account of its peculiar and com 
 plicated mechanism. As apparent from the above, the latter 
 circumstance constitutes the origin of several serious 
 defects, the only remedy for which, evidently consists in a' 
 simplification of the mechanism. 
 
 But it is as evident that such a simplification could not 
 be attained, without at the same time sacrificing in a meas¬ 
 ure the ease and simplicity of handling and reading the 
 instrument. Some of the work, which in the Naudet aner¬ 
 oid is performed by the complicated mechanism itself, in an 
 instrument of simpler construction necessarily had to 
 devolve on the observer. The difficulty then, con.sisted in 
 harmonizing, in the most advantageous manner possible, 
 requirements, the fulfilment of one of which impaired the 
 fulfilment of the other. 
 
6 
 
 III. THE GOLDSCHMID ANEROID. 
 
 This problem was solved after years of experiments by 
 J. Goldschmid, of Zurich, about i860, through an entirely 
 novel construction, in which the movements of the vacuum 
 chamber are measured by a micrometer screw acting on a 
 peculiar lever arrangement, combined with optical magnifi¬ 
 cation. In the following diagram, the left-hand side of 
 which represents ' a section through the instrument, the 
 exceedingly simple arrangement of the working parts is 
 clearly shown. 
 
 To the centre of the top of the vacuum chamber A A is 
 soldered a crank-shaped piece, which ends at one extremity 
 in an upward turned knife edge ; the latter supports the 
 main lever e e'\ which in its turn swings freely around the 
 fulcrum e". The movements of the vacuum chamber are 
 
 Fig. 2 
 
 transmitted by the supporting knife edge to the main lever, 
 the end e of which carries a small hammer-shaped piece. 
 On the face of this is marked a horizontal index line, which 
 will move vertically up and down, according to the varying 
 pressure of the atmosphere. These movements take place 
 alongside of a vertical ivory scale, which serves to measure 
 them and which bears a graduation corresponding to the 
 full inches of the mercurial column (see the right-hand side 
 of Fig. a, which shows the hammer and scale in front view). 
 
 While from the ivory scale the full inches only of the 
 aneroid reading can be taken, the following arrangement 
 serves for measuring the tenths and hundredths of inches. 
 A fine and light spring e' e” is soldered to the main lever 
 near the end e "; at the other end e' it carries a small ham¬ 
 mer, similar to the one described before; when no pressure 
 is exercised on the spring this hammer is held by the elas- 
 
7 
 
 ticity of the same a little above the top of the hammer 
 standing at the same time sideways of it. 
 
 To the cover T T, of the brass case enclosing the entire 
 apparatus, is attached the micrometer screw M, which can 
 therefore be screwed up or down by turning such cover. 
 The lower pointed end of the micrometer acts on the spring 
 £' e", and when a reading is to be taken it is screwed down 
 until the spring has been depressed so much that the index 
 line of e' coincides with the index line of e. 
 
 It is at once clear that this position of the two hammers, 
 which is shown in the diagram, corresponds to a certain dis¬ 
 tance between the point of the micrometer screw and the 
 main lever, a distance which remains the same for all the 
 various positions into which the main lever may be raised 
 or lowered by the movements of the vacuum box. The 
 point up to which the micrometer screw has to be screwed 
 down, in order to make the two index lines coincide, is thus 
 made a measure of the position in altitude of the main 
 lever. This measure is read by means of a graduation 
 ■engraved on the circumference of the cover and dividing 
 the same into loo equal parts, each of which corresponds to 
 one hundredth of an inch of mercurial barometer height. 
 The graduation is so wide that thousandths can easily be 
 estimated. 
 
 The modus operandi then, in using the Goldschmid 
 aneroid, is as follows: 
 
 The outer morocco case of the instrument is opened, and 
 holding the latter in a horizontal position the cover is 
 screwed down, whiie at the same time the two little ham¬ 
 mers, protruding from the brass case through a window-like 
 opening, are observed by means of the attached microscope. 
 When the upper hammer is seen to commence moving 
 downward, then the micrometer screw should be turned 
 carefully and slowly, and when the two index lines coincide 
 it is stopped entirely. Before such coincidence is obtained 
 the instrument should be tapped lightly on the top, in order 
 to eliminate any inertia of the mechanism. It is very 
 important that this tapping should always be done in the 
 same position of the hammers, because if, for instance, it is 
 
8 
 
 
 done sometimes before coincidence and at other times at 
 coincidence, then differences in the readings will be the con¬ 
 sequence, that may amount to as much as yj-g- of an inch. 
 In order to insure uniformity in this respect it is advisable 
 to make it a standing rule, to tap ivheii the lower edge of the 
 upper hammer arrives at coincidenee with the index line; thence 
 forward the screw should be turned very carefully, avoiding 
 all further shocks. 
 
 IV. DISCUSSION OF THE CORRECTIONS. 
 
 In order to find, from the reading obtained by a Naudet 
 or a Goldschmid aneroid, the height of the mercurial column 
 of 32° Fahrenheit temperature, corresponding to the same 
 pressure, three corrections are required, viz : for tempera¬ 
 ture, for graduation and for position, the latter not being 
 required when the instrument is used for measuring alti¬ 
 tudes only. 
 
 Let ^ represent the reading of the aneroid, F the tem¬ 
 perature of the instrument in degrees Fahrenheit, and 
 the reading that would have been obtained if the tempera¬ 
 ture had been 32° Fahrenheit, then we have, concerning the 
 correction for temperature: 
 
 A,=AfaF{f) (I) 
 
 wherein a is the coefficient for temperature, the structure of 
 the function t for the present remaining undecided. 
 
 Regarding the correction for graduation, aneroids are 
 generally set so, that at a reading of thirty inches there is 
 coincidence between them and the mifercurial barometer, 
 after the correction for temperature has been made on both. 
 The coefficient of graduation is the difference between one 
 inch of the mercurial column and one inch of the aneroid 
 graduation: this—multiplied by the difference, thirty—read¬ 
 ing, clearly renders the correction for graduation. Hence 
 we have 
 
 (.30-A,) 
 
 wherein the height of the mercurial column reduced to- 
 the freezing point and ^9 the coefficient for graduation. 
 
9 
 
 The above described coincidence between the aneroid 
 and the mercurial at thirty inches, even if completely 
 attained, rarely lasts long, and in order to compensate for 
 this a constant must be added to the right-hand side of the 
 above equation. This constant is the correction for position 
 and is generally designated by the letter C; we therefore 
 have finally 
 
 ^0—(30 (^) 
 
 Proceeding now to discuss the structure of the above 
 function of /, equation (i), it should be remembered that 
 each change in temperature causes two different forces to 
 act on the mechanism. In the first place, the corrugated 
 surface of the vacuum chamber having a greater area than 
 corresponds to its circumference, is expanded too much by 
 a rise in temperature, and this excess of expansion causes a 
 depression of the surface. The reason why the latter is not 
 raised instead of being depressed is to be found in the circum¬ 
 stance, that in all good instruments it is bent slightly 
 towards the interior, so that, even under a minimum of 
 atmospherical pressure, it will only rise about to the horizon¬ 
 tal, but never bulge outward beyond this. 
 
 The second force is created by the small quantity of air, 
 present in all so-called vacuum chambers, being expanded by 
 the additional heat imparted to it, thus exercising an inside 
 pressure, that tends to counteract the first described force. 
 
 In the Naudet aneroid the chamber is exhausted as much 
 as possible, and the inside pressure caused by a rise of tem¬ 
 perature under all ordinary circumstances is therefore miich 
 smaller than the force caused by surface expansion of the 
 box and pressing such surface towards the interior. These 
 instruments will therefore be affected by a rise of tempera¬ 
 ture in the same way as by an increase of atmospherical 
 pressure, that is, the reading of the instrument will become 
 higher. Hence the correction for temperature in Naudet 
 aneroids is subtractive for all temperatures above the freez¬ 
 ing point and additive for all temperatures below. 
 
 \ 
 
 From what has been said, it is clear that the second or 
 inside force ean be increased by admitting additional air 
 
lO 
 
 into the vacuum chamber, and it was suggested by Professor 
 Kohlrausch, that in this way the two forces might be made 
 to counterbalance each other entirely, thus reducing the 
 correction for temperature to nothing. The impossibility of 
 this was demonstrated bv Professor Weilenmann, whose 
 extensive theoretical and experimental researches on this 
 subject rendered the following results : 
 
 (1) When the temperatures are plotted as ordinates and 
 the corrections pertaining to them as abscisses, then a para¬ 
 bola is obtained. 
 
 (2) The apex of this parabola can be shifted to lower or 
 higher temperatures, by respectively increasing or diminish¬ 
 ing the amount of air contained in the chamber. 
 
 Although these principles differ theoretically from Bauern- 
 feind’s opinion, that the correction for temperature increases 
 in direct proportion to the temperature, yet for Naudet 
 aneroids, with highly exhausted chambers, there is no great 
 practical difference between both assertions. This will be 
 seen clearly from the following diagram, in the left-hand 
 part of which a correction curve for temperature is shown, 
 that was obtained bv Professor Weilenmann from actual 
 tests with an aneroid, the chamber of which was exhausted 
 as completely as possible. For all such temperatures as are 
 likely to occur in practical work, this curve does not depart 
 materiallv from a straight line, which latter would be the 
 expression of Bauernfeind’s law in the diagram. 
 
 TEMPERATURE IN IdEGREES CELSIUS. 
 
 Professor Weilenmaim’s above named principles have 
 been utilized in the construction of the Goldschmid aneroid 
 for the purpose of reducing as much as possible the correc¬ 
 tion for temperature. An amount of air corresponding to a 
 few inches of the mercurial column is admitted into the 
 vaccuum chamber, thereby shifting the apex of the parabola 
 to near the freezing point and consequently reducing to 
 practically nothing the corrections in that vicinity. An 
 example of this is given in the right-hand part of Fi^. j, 
 where a correction curve is shown for a vacuum box, which 
 contained an amount of air corresponding to six inches 
 
of the mercurial column. The characteristic differences 
 between this curve and the high vacuum curve in the left- 
 hand part of the same diagram, are at once apparent and 
 strikingly to the advantage of the former. Under the 
 influence of high temperatures the inner pressure now 
 exceeds the force, bending the surface towards the in¬ 
 terior, in other words, such influence will act on the Gold- 
 schmid aneroid like a decrease of atmospheric pressure. 
 
 Summing up, we find that the correction for temperature 
 for the Goldschmid instruments in the vicinity of the freez¬ 
 ing point is practically nothing, again, that as a general rule 
 it is everywhere considerably less than for the Naudet 
 aneroid or for the mercurial barometer, and, finally, that what 
 little there is of it, is additive. 
 
 While the Goldschmid aneroid is not claimed to be 
 entirely compensated for temperature, the corrections for 
 the latter are doubtless in it reduced to very small quanti¬ 
 ties, a table of which, resulting from careful tests made by 
 the manufacturer, accompanies every instrument. 
 
 For some of the Naudets in the market, entire compen¬ 
 sation is claimed, but if the practical test is made, probably 
 one out of ten will be actually found so, while the correc¬ 
 tions of most of the rest will exceed those of the Gold¬ 
 schmid, without the purchaser being furnished with a table 
 for them. 
 
 A simple and very effective method of ascertaining the 
 correction for temperature consists in the use of warm, tepid 
 and cold water baths, and finally the ice bath. By their 
 means the inner temperature of an instrument can be varied 
 from the freezing point upward, to say ioo° or more. The 
 observations must of course be made together with obser¬ 
 vations on a mercurial, and both are recorded in about the 
 following way: 
 
12 
 
 Mercurial 
 
 Thermometer. 
 
 Aneroid. 
 
 -^0 
 
 A 
 
 / 
 
 A' 
 
 29094 — A' 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 29149 
 
 29-073 
 
 670 
 
 29-016 
 
 0-078 
 
 29 ' i 48 
 
 29*070 
 
 66-2 
 
 29*014 
 
 0-080 
 
 29-143 
 
 29-073 
 
 750 
 
 29-022 
 
 0*072 
 
 29-132 
 
 29-074 
 
 74’4 
 
 29*035 
 
 0*059 
 
 etc. 
 
 etc. 
 
 etc. 
 
 etc. 
 
 etc. 
 
 In this table the letters at the heads of the various 
 columns have the following meaning : 
 
 (1) reading of the mercurial barometer in inches 
 and decimals, as reduced to the freezing point. 
 
 (2) A is the reading of the aneroid under the same pres¬ 
 sure. 
 
 (3) t is the inner temperature of the aneroid in degrees 
 Fahrenheit and decimals. 
 
 (4) A' is what the aneroid would have read, if the pres¬ 
 sure during the entire series of observations had constantly 
 remained at B\ == 29^094 (this being the average of all the 
 
 of the entire series). 
 
 The value of A'is found in the following manner: In 
 the case of the actual example cited here a preliminary 
 determination had been made, showing that rooo inch of 
 the aneroid corresponded to 0*970 inch of the mercurial 
 column. If, therefore, in the case of the first observation 
 for instance, the mercurial barometer had read 29*094 (instead 
 of 29*149), that is 0*055 l®ss than it actually did read, then 
 the aneroid would clearly have read X 0*055 = 0*057 less 
 than it actually did read, that is to say 29*073—0*057 = 
 29*016. The difference between the value 29*094— A' as 
 found for the freezing point and as found for any other 
 temperature renders the correction for such temperature. 
 These differences should be found for the various tempera¬ 
 tures from the freezing point upward to say 100° F., and 
 then plotted, as shown in Fig.j; from the curve thus obtained 
 a table of corrections is easily deduced. 
 
13 
 
 The correction for graduation has been assumed in equa¬ 
 tion (2) to stand in direct proportion to the difference 30.— 
 Reading, an assumption, which although not strictly correct 
 is sufficiently so for most practical purposes. 
 
 Each Goldschmid aneroid being furnished with a table 
 of corrections for graduations, as well as for temperature, 
 the owner of one of these instruments is saved the trouble 
 of investigations in this respect. 
 
 For Naudet aneroids these tables have to be obtained by 
 the purchaser, through direct comparison of the aneroid 
 with the mercurial barometer, the readings of both being 
 reduced to the freezing point by means of the previously 
 
 hjghly Exhaust. / 50 ^^'of A/r 
 
 determined correction for temperature. The observations 
 are recorded in tabulated form as follows: 
 
 ^0 
 
 A 
 
 \ 
 
 t 
 
 •^0 
 
 0 
 
 1 
 
 0 ^ 
 
 29 ‘ 97 o 
 
 29'960 
 
 72 
 
 30*000 
 
 0-030 
 
 29‘420 
 
 29‘450 
 
 76 
 
 29-500 
 
 0-080 
 
 28'87o 
 
 28'940 
 
 78 
 
 29*000 
 
 0-130 
 
 wherein the various letters have the same meaning as in 
 equations (i) and (2). From the table it is seen that in this 
 case the constant correction for position was 
 
 0-03 
 
 and that 1*000 inch of the aneroid correspond to rioo inch 
 
14 
 
 of the mercurial; the coefficient of graduation therefore 
 was 
 
 y9 = —0-100 
 
 and by means of these figures a table of corrections for 
 graduation can easily be worked out according to equa¬ 
 tion (2). 
 
 But if it is desired to use the aneroid at great altitudes, 
 then it would not be safe to assume the coefficient /9 to 
 remain constantly the same, and the investigation should 
 in this case be extended to lower pressures, either, by * 
 making comparisons between the mercurial barometer and 
 the aneroid at various altitudes, or by making them by 
 means of the air-pump. If the'latter method, however, is 
 selected, then a certain correction of the results will have 
 to be made, the nature of which is explained by Dr. C. 
 Koppe as follows: 
 
 Suppose an aneroid and a mercurial barometer to be at the 
 same locality and subjected to the same atmospheric pres¬ 
 sure, and again suppose a sudden decrease of the force of 
 gravity to take place there. What influence would such an 
 event have on the reading of the two instruments ? 
 
 Manifestly the reading of the mercurial barometer would 
 not be affected in the least, the weight of the column of air 
 being diminished in the same ratio as that of the mercurial 
 column. 
 
 It would be quite different, however, with the aneroid. 
 While the weight of the column of air has diminished, the 
 elastic force of the vacuum chamber has remained the same; 
 the instrument will therefore record a lower pressure. 
 
 Consequently, if a journey is undertaken with an aneroid 
 and a mercurial barometer, which read precisely alike, then 
 the coincidence between both will only last as long as the 
 force of gravity remains unchanged. But this force is 
 different in different latitudes, and at different altitudes, and 
 from the latter circumstance results the necessity of a cor¬ 
 rection of such tables for graduation, that were obtained 
 by means of the air-pump. 
 
 It is clear from the above that a reading of twenty-four 
 inches of the mercurial barometer, taken at the level of the 
 
15 
 
 sea under an air-pump, indicates a greater actual pressure of 
 air than the same reading taken at an altitude of 7,000 feet 
 above the level of the sea. Hence, a correction has to be 
 added to the reading of the aneroid at 7,000 feet altitude, in 
 order to obtain coincidence of such reading with the mercu¬ 
 rial barometer. The amount of this correction has been 
 computed by Professor Weilenmann as follows: 
 
 Reading (inches),. 31*5 28*0 24*0 20‘o i6'o 
 
 Correction, . . . o +0-105 +0*189 +0-270 +0-312 
 
 The arithmetical sums of these figures and the corre¬ 
 sponding corrections found by means of the air-pump are 
 the final corrections for graduation. 
 
 The difficulty caused by “ elastic reaction,” which was 
 mentioned in the beginning of this article is, of course, 
 present also in the Goldschmid aneroid, and the above 
 investigations, as well as all measurements of altitudes, 
 should be carried on with due regard to it. The instru¬ 
 ment must be given time in order to fully accommodate 
 itself to any sudden changes of pressure. 
 
 But while Kroeber found that the Naudet required days 
 for this, he found the Goldschmid practically accommodated 
 after one or two hours. Again, he found the extreme dif¬ 
 ferences resulting from elastic reaction in the latter instru¬ 
 ment only about one-fourth of those in the former. Both 
 these advantages of the Goldschmid, as compared with the 
 Naudet, are doubtless due to the extreme simplicity of the 
 former’s mechanism, and in view of them it may be safely 
 asserted that the gradual changes of pressure, taking place 
 during ordinary explorations of mountainous country, will 
 not produce any appreciable errors of elastic reaction in the 
 Goldschmid aneroid. 
 
 V. THE DETERMINATION OF DIFFERENCES OF ALTITUDE BY 
 MEANS OF THE ANEROID BAROMETER. 
 
 The measuring of altitudes by means of the barometer, 
 is mainly based on two suppositions, viz : Firstly, that the 
 atmospheric strata of equal pressure are horizontal, and 
 secondly, that the temperature of a vertical column of air is 
 
i6 
 
 N 
 
 % 
 
 equal to the arithmetical mean of the temperature observed 
 at its top and at its bottom. 
 
 These two conditions are probably never fulfilled com¬ 
 pletely in nature, but they are always fulfilled more or less 
 approximately. On the g-reater or smaller deviation from 
 them of the actually existing conditions, depends the exacti¬ 
 tude of the result in each case, leaving out the considera¬ 
 tion, of course, of avoidable errors of observations. 
 
 In accordance with the two principles mentioned, the 
 process of barometric measurement may be described thus: 
 By means of the barometer, be it a mercurial or be it an 
 aneroid, the weight of a column of air is determined, and 
 from the observed temperature of such column its length is 
 found. 
 
 During observations for altitude, therefore, the tempera¬ 
 ture of the air as well as that of the instrument must be 
 observed; the first one for the purpose named just now, the 
 last one for the purpose of taking into proper account the 
 x:orrections for temperature, by reducing both observations 
 to uniform temperature. Besides this, the observations 
 made at the upper and at the lower stations must of course 
 be corrected to graduation, so that thus their difference is 
 made equal as nearly as possible to the difference that would 
 have been obtained by using a mercurial barometer. 
 
 It is clear at once that the observations at the upper and 
 lower stations should be made simultaneously in order to 
 obtain both as nearly as possible under the same atmos¬ 
 pheric conditions. Observations made by one observer, in 
 passing from point to point with his instrument, are quite 
 unreliable, unless he returns to the previous point after each 
 observation in order to take a second reading there, and 
 thus to find the changes that have taken place in pressure 
 and temperature. Only by means of this tedious and time¬ 
 robbing procedure, can anything like fair results be obtained 
 by one observer. 
 
 For serious work then, two observers, and at least two 
 instruments are required, and the readings of the latter, as 
 well as the outer and inner temperature, should be recorded 
 with great exactitude, so as to be enabled to subsequently 
 
17 
 
 introduce the proper corrections, without which the results 
 are worthless. Great care also should be taken not to expose 
 •the aneroid to the direct rays of the sun when taking an 
 observation, but to let it assume as nearly as possible the 
 temperature of the .surrounding air in the shadow. 
 
 The modus operandi in determining differences of altitude 
 may be described about as follows; 
 
 A stationary instrument, with an observer, is placed at some 
 point of known altitude that has been selected as the basis 
 of operations. This instrument is observed regularly every , 
 fifteen or thirty minutes, and a careful record kept of such 
 readings, as well as of the time and temperature correspond¬ 
 ing to each. 
 
 Meanwhile, the engineer travels through the district he 
 intends to survey, taking observations wherever he sees fit, 
 and keeping a careful record of their location, time, temper¬ 
 ature, etc. When he is through with his work, an observa¬ 
 tion at the point of known altitude is computed for each of 
 his observations, from the record kept by the assistant; this 
 having been done, the difference of altitude between each 
 point of observation and the point of known altitude is 
 obtained in a simple way, by means of the subjoined table 
 No. I, which has been taken from Meteorological and Physical 
 Tables of the Smithsonian Institution. [Other convenient tables 
 are given in The Aneroid Barometer, Van Nostrand, New 
 York, 1888, and in the above mentioned publication of the 
 Smithsonian Institution.] 
 
 For instance, suppose 29*5 to have been the reading at 
 the point of known altitude, and 26*5 the reading taken by 
 the engineer, both corrected to graduation, etc., and reduced 
 to 32"^ F., and again, suppose 70° and 60° to have been the 
 respective temperatures of the surrounding air, then we 
 obtain from the table; 
 
 For 29*5 inches and 70° F. 96'5 
 
 For 26'5 inches and 60° F,,. 
 
 Mean, .ioo’9 
 
 This mean, multiplied by the difference of the two read- 
 
 2* 
 
i8 
 
 ing-s expressed in tenths of an inch, renders the difference 
 in altitude: 
 
 30 X 100*9 3,027 ft. 
 
 The use of this table gives results of sufficient accuracy 
 for all practical purposes, so that recourse to the compli¬ 
 cated barometrical formula is not required. 
 
 Readings should always be taken in the same position of 
 instrument, preferably the horizontal one. 
 
 Table No. i. 
 
 HEIGHT IN FEET OF A COLUMN OF AIR CORRESPONDING TO ONfe-TENTH OF AN INCH IN THE 
 
 BAROMETER. 
 
 Barometer 
 Reading in 
 Inches. 
 
 
 Temperature of Air in Degrees Fahrenheit. 
 
 
 0 
 
 0 
 
 50“ 
 
 60° 
 
 70° 
 
 00 
 
 c 
 
 P 
 
 1 
 
 90° 
 
 23-0 
 
 Ii6'2 
 
 ii8-8 
 
 121-3 
 
 1238 
 
 1 . 126-4 
 
 129-9 
 
 23 5 
 
 i^ 3’7 
 
 1i6'2 
 
 118-7 
 
 121*2 
 
 123-7 
 
 126 I 
 
 24*0 
 
 111-3 
 
 113-8 
 
 I i6-2 
 
 118'6 
 
 121 *1 
 
 123-5 
 
 24-5 
 
 log - 1 
 
 Ill's 
 
 113 8 
 
 h6-2 
 
 118-6 
 
 121-0 
 
 25-0 
 
 io6'9 
 
 109-3 
 
 111'6 
 
 113-9 
 
 116-3 
 
 118 6 
 
 25*5 
 
 104‘8 
 
 107*1 
 
 109-3 
 
 111-6 
 
 113 9 
 
 116-2 
 
 260 
 
 102’7 
 
 1050 
 
 107-2 
 
 109-5 
 
 111*7 
 
 114*0 
 
 26-5 
 
 ioo'g 
 
 103-1 
 
 105-3 
 
 107-5 
 
 109-7 
 
 111-8 
 
 27*0 
 
 gyo 
 
 101*2 
 
 103-3 
 
 105-5 
 
 107-6 
 
 109-8 
 
 27*5 
 
 97 2 
 
 993 
 
 101*4 
 
 103-5 
 
 105-6 
 
 107 8 
 
 28’0 
 
 95'4 
 
 97'5 
 
 99 6 
 
 ioi'7 
 
 103-8 
 
 105-9 
 
 28-5 
 
 93-8 
 
 95-8 
 
 97-9 
 
 99-9 
 
 loi '9 
 
 103-9 
 
 29*0 
 
 92*1 
 
 94 ’I 
 
 96-2 
 
 98-2 
 
 IOO'2 
 
 102*2 
 
 295 
 
 906 
 
 r 92-5 
 
 94-5 
 
 96-5 
 
 98-5 
 
 100*4 
 
 30 0 
 
 89-1 
 
 91*0 
 
 92-9 
 
 94-9 
 
 96-8 
 
 q8-8 
 
 30 5 
 
 876 
 
 89-5 
 
 91-4 
 
 93-3 
 
 95-2 
 
 97 2 
 
 Table No. 2. 
 
 REDUCTION OF MERCURIAL COLUMN TO 32° F., BRASS SCALE TO BAROMETERS CORRECT AT 62° F. 
 
 
 Reading of Barometer. 
 
 Tempera- 
 
 
 
 
 ture. 
 
 
 
 
 
 30 inches. 
 
 25 inches. 
 
 20 inches. 
 
 32° 
 
 -009 
 
 •co8 
 
 -006 
 
 35 ° 
 
 ■017 
 
 -015 
 
 ‘012 
 
 40° 
 
 -031 
 
 -026 
 
 *021 
 
 45 ° 
 
 -044 
 
 . -037 
 
 *030 
 
 50 ° 
 
 -058 
 
 -048 
 
 -038 
 
 55 ° 
 
 *071 
 
 -059 
 
 -047 
 
 60O 
 
 -084 
 
 070 
 
 -056 
 
 (^ 5 ° 
 
 -098 
 
 -082 
 
 -065 
 
 ^ 70 ° 
 
 * 1 II 
 
 -093 
 
 -074 
 
 v ^.0 
 
 -125 
 
 *104 
 
 -083 
 
 80O 
 
 ■138 
 
 -115 
 
 ’092 
 
 85O 
 
 ■151 
 
 -126 
 
 'lOI 
 
 90^’ 
 
 -164 
 
 -137 
 
 -no 
 
 95 ° 
 
 -178 
 
 -148 
 
 -118 
 
 100° 
 
 -191 
 
 • 
 
 -159 
 
 -127 
 
 The corrections contained in this table have to be sub¬ 
 tracted from the reading- of the mercurial barometer, in order 
 to reduce the same to a temperature of 32^ F. 
 
Wl. I?.