. 10000000 this by 10,000, 1001 1000 1000 a tions of the axis of the atmospherical logarithmic. both suffer the same change of temperature; and Therefore, if we'multiply our common logarithms as the air may be warmed or cooled when the by 10,000, they will express the fathoms of the mercury is not, or may change its temperature axis of the atmospherical logarithmic; nothing is independent of it, still greater variations of specific more eagly done." Our logarithms contain what gravity may occur. The general effect of an is called the index or characteristic, which is an augmentation of the specific gravity of the mercury integer and a number of decimal places. Let us must be to increase the fubtangent of the atmosphejuft remove the integer-place four figures to the rical logarithmic; in which case the logarithms of right hand: thus the logarithm of 60 is 1.7781513, the densities, as measured by inches of mercury, which is one integer and 7781513 will express measures that are greater than fathoms Multiply in the same proportion that the subtangent is in creased; or, when the air is more expanded than $13 and we obtain 17781,513, the mercury, it will require a greater heigbt of homogeneous atmosphere to balance 30 inches of or 19731 513. mercury, and a given fall of mercury will then correspond to a thicker ftratum of air. The practical application of all this reasoning is To perfe&t this method, therefore, we must learn obvious and easy; observe the heights of the by experiment how much mercury expands by an mercury in the barometer at the upper and lower increase of temperature; we must also learn how stations in inches and decimals; take the logarithms much the air expands by the fame, or any change of these, and subtract the one from the other; the of temperature, and how much its elasticity is difference between them (accounting the four first affected by it. Both these circumstances must be decimal figures as integers) is the difference of confidered in the case of air ; for it might happen elevation of fathoms. that the elasticity of the air is not so much affected EXAMPLL. by heat as its bulk is. It will, therefore, be proper Merc. Height at the lower station 29,8 1°4742163 to state the experiments which have been made for upper station 29,1 104638930 ascertaining these two expansions. The most accurate, and the best adapted expeDiff. of Log. X 10000 oʻ0103233 riments for ascertaining the expansion of mercury, 233 or 103 fathoms and of a fathom, which is are those of General Roy, published in the Philof. Trans. vol. 67. He exposed 30 inches of mercury, 619,392 feet, or 619 feet 44 inches; differing from actually supported by the atmosphere in a barothe approximated' value formerly found about £ meter, in a nice apparatus, by which it could be an inch. made of one uniform temperature through its Such is the general nature of the barometric whole length; and he noted the expansion of it in measurement of heights first suggested by Dr decimals of an inch. These are contained in the HALLEY; and it has been verified by numberless following table; where the first column expresses comparisons of the heights calculated in this way the temperature by Fahrenheit's thermometer, the with the fame height measured geometrically. It second the bulk of the mercury, and the third the was thus that the precise specific gravity of air and expansion of an inch of mercury for an increase of mercury was most accurately determined; namely, one degree in the adjoining temperatures. by observing, that when the temperature of air and TABLE A. mercury was 32, the difference of the logarithms of the mercurial heights were precisely the fathoms Temp. Bulk of 8., Expan. for 1o. of elevation. But it requires many corrections to adjust this method to the circumstances of the 30,5 117 0,0000763 case; and it was not till very lately that it has 0,0000787 been so far adjusted to them as to become useful. 192 30,4652 0,0000810 We are chiefly indebted to Mr De Luc for the 182 30,4409 0,0000833 improvements. The great elevations in Switzer. 172 3094199 0,0000857 land enabled him to make an immense number 162 30,3902 0,0000880 of observations, in almost every variety of circum 192 30,3638 0,0000903 frances. Sir GEORGE SHUCKBOURGH also made 142 30,3367 0,0000933 a great number with most accurate instruments in 132 30,3090 0,0000943 much greater elevations, in the same country; and 30,2807 0,0000963 be made many chamber experiments for deter 30,2518 0,0000983 mining the laws of variation in the fubordinate 30,2223 0,0001003 circumftances. General Roy also made many to 30,1922 0,0001023 the same purpose. And to these two gentlemen 82 30,1615 0,0001043 we are chiefly obliged for the corrections which 72 30,1302 0,0001063 are now generally adopted. 62 30,0984 0,0001077 This method, however cannot apply to every 52 30,0661 0,0001093 case; it depends on the specific gravity of air and 42 30,0333 0,0001110 mercury, combined with the supposition that this 32 30,0000 0,0001127 is affected only by a change of pressure. But since 29,9662 0,0001143 all bodies are expanded by heat, and perhaps not 29,9319 0,0001160 equally, a change of temperature will change the 29,8971 0,0000177 reiative gravity of mercury and air, even although 29,8901 The 2120 202 30,4888 1 22 II2 102 92 12 The scale of the thermometer is constructed on products will be the corrections of the respedive the supposition that the successive degrees of beat logarithms. are measured by equal increments of bulk in the There is still an easier way of applying the logamercury of the column; but that the corresponding rithmic correction. If both the mercurial temperaexpansions of this column do continually diminish, tures are the same, the differences of their logarithms General Roy attributes to the gradual detachment will be the same, although each may be a good deal of elastic matter from the mercury by heat, which above or below the standard temperature, if the expresses on the top of the column, and therefore pansion he very nearly equable. The correction will shortens it. He applied a boiling heat tothe vacuum be necessary only when the temperatures at the two a-top, without producing any farther depression; stations are different, and 'will be proportional to a proof that the barometer had been carefully this difference. Therefore, if the difference of the filled. It had indeed been boiled through its mercurial temperature's be multiplied by o'0000444, whole length. He had attempted to measure the the product will be the correction to be made on mercurial expansion in the usual way, by filling the difference of the logarithms of the mercurial 30 inches of the tube with boiled mercury, and heights. But farther, since the differences of the loexpofing it to the heat with the open end upper- garithms of the mercurial heights are also the difmoft. But here it is evident that the expansion of ferences of elevation in English fathoms, it follows the tube and its solid contents must be taken into that the correction is also a difference of elevation in the account. The expansion of the tube was English fathoms, or that the correction for one de. found so exceedingly irregular, and so incapable gree of difference of mercurial temperature is 444 of being determined with precision for the tubes of a fathom, or 32 inches, or 2 feet 8 inches. which were to be employed, that he was obliged to This correction of 2.8 for every degree of differhave recourse to the method with the real baro-ence of temperature must be subtračted from the meter. In this no regard was necessary to any cir- elevation found by the general rate, when the mercumstance but the perpendicular height. There cury at the upper station is colder than that at the was, befides, a propriety in examining the mercury lower. For when this is the case, the mercurial in the very condition in which it was used for column at the upper ftation will appear too fort, measuring the preflure of the atmosphere; be- the pressure of the atmosphere too small, and there. cause, whatever complication there was in the fore the elevation in the atmosphere will appear results, it was the same in the barometer in actual greater than it really is. Therefore the rule for this use. correction will be to multiply oʻ0000444 by the de. The most obvious manner of applying these grees of difference between the mercurial tempera. experinients on the expansion of mercury to our tures at the two stations, and to add or fubtract the purpose, is to reduce the observed height of the product from the elevation found by the general mercury to what it would have been if it were rule, according as the mercury at the upper ftation of the temperature 32. Thus, fuppofe that the is hotter or colder than that at the lower. observed mercurial height is 29*2, and that the If the experiments of Gen. Roy on the expansion temperature of the mercury is 720 make 30*1302: of the mercury in a real barometer be thought 30=29*2 : 29'0738. This will be the true mealure most deserving of attention, and the expanfion be of the density of the air of the standard temperature. considered as variable, the logarithmic difference That we may obtain the exact temperature of the corresponding to this expantion for the mean mercury, it is proper that the observation be made temperature of the two barometers may be taken. by a thermometer attached to the barometer frame, These logarithmic differences are contained in the so as to warm and cool along with it. Or, this following table, which is carried as far as 112°, may be done without the help of a table, and with beyond which it is not probable that any observasufficient accuracy, from the circumstance, that tions will be made. The number for each tem. the expansion of an inch of mercury for one degree perature is the difference between the logarithms diminishes very nearly both part in each fucceed. of 30 inches, of the temperature 32, and of 30 ing degree. If therefore we take from the expan- inches expanded by that temperature. fion at 32° its thousand part for each degree of any TABLE B. Dec. of Ft. In. There is another way of applying this correction, Fath. fully more expeditious and equally accurate. The difference of the logarithms of the mercurial heights 112° 0.0000427 »427 2.7 is the measure of the ratio of those heights. In like 0.0000436 9436 manner the difference of the logarithms of the ob 0.0000444 9444 served and corrected heights at any station is the 82 0.0000453 453 2.9 measure of the ratio of those heights. Therefore 72 0.0000460 2460 2.9 this last difference of the logarithms is the measure 62 0.0000468 of the correction of this ratio. Now, the observed 52 0.0000475 7475 height is to the corrected height nearly as i to 0.0000482 1'000.102. The logarithm of this ratio, or the 0.0000489 difference of the logarithms of 1 and 1'000102 is 0.0000497 9497 3.0 O‘0000444. This is the correction for each degree 0.0000504 9504 3.0 that the temperature of the mercury differs from 32. Therefore multiply o‘0000444 by the difference It is also neceffary to attend to the temperature of the mercurial temperatures from 32, and the of the air; and the change produced by heat in IO2 2.7 92 28 9468 2.IO 42 ,482 1489 32 22 12 212 20 20 112 20 20 20 97'2 75*6 53'0 22:6 20 20 I2 its density is of much greater consequence than he wished to examine the expanfion of air twice that of the mercury. The relative gravity of the or thrice as dense, he used a column of 30 or 60 iwo, on which the subtangent of the logarithmic inches long; and to examine the expansion of all curve depends, and consequently the unit of our that is rarer than the external air, he placed the scale of elevations, is much more affected by the tube, with the ball, uppermoft, the open end comheat of the air, than by the heat of the mercıxy. ing through a hole in the bottom of the vessel This adjustment is of incomparably greater diffi. containing the mixtures or water. By this policulty than the former, and we can hardly hope tion the column of mercury was hanging in the to make it perfect. We shall relate the chief ex- tube, supported by the pressure of the atmofperiments which have been made on the expan- phere; and the elasticity of the included air was Son of air, and notice the circumstances which measured by the difference between the fufpendleave the matter still imperfecl. ed column and the common barometer. Gen. Roy compared a mercurial and an air The following table contains the expansion of thermometer, each of which was graduated arith. 1000 parts of air, nearly of the common density, metically, that is, the units of the scales were equal by heating it from o to 212. The first column bulks of mercury, and equal bulks (perhaps dif- contains the height of the barometer ; the ad conferent from the former) of air. He found their tains this height augmented by the small column progress as in the following table: of mercury in the tube of the manometer, and TABLE C. therefore expreffes the density of the air examin ed; the 3d contains the total expansion of 1000 Merc. Diff, Air. Diff. parts: and the 4th contains the expanfion for ro, supposing it uniform throughout. 20 TABLE DE 212'0 1786 192 1944 Dengity Expanfion 1762 Barom. of Ait of 100o ptsExpansion by ro. examined by 212°. 132 1380 19'4 20'0 29'95 31952 483.89 2*2825 30'07 30'77. 482010 2'2741 29:48 29990 480*74 2°2676 29'90 30'13 485.86 2.2918 31'4. 29'96 489-45 30'92 2*3087 II'4 29.90 30°55 476°04 2'2455 It has been eftablished by many experiments 29'95 487 55 2'2998 30'07 482.80 that equal increments of heat produce equal in 2'2774 trements in the bulk of mercury. The differences 29:48 48947 23087 of temperature are therefore expreffed by the ad Mean colomn, and may be confidered as equal; and 30'62 484'21 2'2840 the numbers of the 3d column must be allowed to Hence the mean expansion of 1000 parts of air Expre's the same temperatures with those of the of the density 30*62 by one degree of Fahrenheit's Sth. They dire&ly expreis the bulks of the air, thermometer is 2'284, or that of 1000 becomes and the numbers of the 4th column express the 1000*284. If this expansion be supposed to foilow differences of these bulks. These are evidently the same rate that was observed in the comparianequal, and shew that common air expands most son of the mercurial and air thermometer, the exof a'i when of the temperature 62 nearly. pansion of a thousand parts of air for one degree The next point was to determine what was the of heat at the different intermediate temperature, actual increase of bulk by some known increase of will be as in the following table. beat. For this purpose he took a tube, having a TABLE E. farrow bore, and a ball at one end. He meafur. Total Expantion ed the capacity of both the ball and the tube, and for' 19. divided the cube into equal spaces, which bore a determined proportion to the capacity of the ball. 484,210 192 This apparatus was set in a long cylinder filled 2'0099 444,011 2'0080 with frigorific mixtures, or with water, which 402,452 2'1475 could be uniformly heated up to the boiling tem 152 359,503 2'2155 perature, and was accompanied by a nice ther 132 315,193 2.2840 Dometer. The expansion of the air was measur ,269,513 2'3754 ed by a column of mercury which rose or sunk in 92 222,006 2'4211 the tube. The tube being of a small bore, the 87 mercury did not drop out of it ; and the bore be. 72 197,795 2'3 124 172,671 25581 faz chosen as equal as posible, this column re. 147,090 2'6037 mained of an uniform length, whatever part of 52 T21,033 the tube it chanced to occupy. By this contri. 2'5124 vance he was able to examine the expanlibility of 95,929 2'4211 32 77,718 2'3297 1.1 of various denfities. When the column of 48,421 2*2383 tercary contained only a single drop or two, the 26,038 2'1698 W13 nearly the density of the external air, if Pul.XVIII. Part I. ar 30*60 30-60 30.00 Temp. Expansion. 212 172 112 22 12 2 1 2 112 1*04 212 192 12685 | 392 1996 132 II2 92 426 235 23.8 If we would have a mean expanfion for any ty, being greatelt about the temperatu particular range, as berween 12° and 92°; whích - fo that its expanfibility by heat dimin is the most ikely to comprehend all the geodæti. 'its denfity; but he could not determ cal observations, we need only take the difference of gradation. When reduced to abou of the bulks 26'038 and 222.000=195*968, and density of common air, its expansion divide this by the interval of temperature 80", lows: and we obtain 2*4496, or 2'45 for the mean expansion for ro. It would perhaps be better to TABLE II. adapt the table to a mass of 1000 parts of air of Differ. Expo the Standard temperature :2°; for in its present Temp., Bull. for i form, it shews the expansibility of air originally of the temperature c. This will be done with fat. 1141,504 7075 ficient ceu-acy, by saying (for 212°) r071718: 191.1234,429 12-264 06 1484,219=1000; 1:849, and fo of the reft. Thus 1122,165 we shall contruct the tollowing table of the ex 1108,015 14'150.1007 14'151 0*70 panfion of 10,000 parts of air. 132 1093,864 14228 0*71 Table F. 1079,636 149.37 074 92 1064,699 20'91T 72 1043,788 25'943 Io29 52 1017,845 17845 089 32 1000,000 375, 1807 Mean expanfion 0*781 132 From this very extensive and judicious 413 2006 12272 experiments, it is evident, that the expa 11846 21'3 of air by heat, is greatest when the air is a 443 22*1 11403 ordinary denfity, and that in small denfit 22'6 82. 11177 greatly dimmithed. It appears also, that 2395 of compression is altered; for in this spec the rare air, half of the whole expansion 1 243 10461 52 2493 about the temperature 99', but in air of d 10:26 235 - 235 density at 105. The experiments of AMO 226 22'6 32 related in the Mem. of the Acad. at Pari 217 217 9783 &c. are confiftent with these more perf experiments of Gen. Roy, After this account of the expansion of This will give for the mean expanfion of 1000 fee that the height through which we mun parts of air between 12° and 92=229. Although produce a given fall of the mercury in th it cannot bappen, that in measuring the differences meter, or the thickness of the stratum of a of elevation near the earth's surface, we shall have ponderant with a tenth of an inch of m occahon to employ air greatly exceeding the com muft increase with the expansion of air, al mon denfity, we may insert the experiments made it be the expanfion of one degree, w 2:29 by Gen. Roy on fuch airs. They are expressed in the following table; where column firft con DOOO. tains the densities meaiured by the inches of mer. multipy the excess of the temperature of cury that they will fupport when of the tempera: above 32° by 0:00229, and multiply the p ture 33o; column second is the expanfion of by 87 to obtain the thickness of the il 1000 parts of fuch air, by being heated from o to where the barometer stands at 30 inches: or 212 ; and column third is the mean expansion for ever be the elevation indicated by the dif r. of the barometrical heights, upon the supp TABLE G. that the air is of the temperature 32°, we multiply this by oʻ00229 for every degree th Density. Expansion Expaní. bir is warmier or colder than 32. The pr for 1120. for 1°. must be added to the elevation in the first and subtracted in the latter. 1or7 451'54 2130 Sir GEORGE SHUCKBURGH deduces c 423-23 1996 from his experiments, as the mean expanfi 41209 air in the ordinary cases: and this is pro 34°5 439087 2075 nearer the truth; because Gen. Roy's exper:: 497 44324 2o91 were made on air which was freer from than the ordinary air in the fields; and a 2'047 minute quantity of damp increases its expan There is much more frequent occafion to ope. ty by heat in a prodigious degree. The rate in uir that is rarer than the ordinary ftate of difficulty is how to apply this correction ; 9 the fuperficial-atmosphere. Gen. Róy accor. ther, how to determine the temperature of th ) dingly inade many experiments on such airs. He in those extensive and deep strata in which th found in general, that their expansibility by heat vations are measured. It seldom or never fràs analogous to that of air in its ordinary'denfi- pens, that the stratum of tbe same temper $ throug! I2 6293 8965 1'944 Mean 75*2 2 1 2 0*354 we 112 Ó*747 32 212 1897 2006 132 112 72 62 238 23.8 243 52 42 22'6 10 . SECT. If we would have a mean expanfion for any ty, being greatelt about the temperature 6 particular range, as between 12° and 92°, which to that its expanfibility by heat diminithe is the most likely y to comprehend all the geodæti. its denfity ; but he could not determine t cal obfervations, we need only take the difference of gradation. When reduced to abönt of the bulks 26*038 and 222.000=195*968 , and density of common air; its expansion was divide e this by the interval of temperature 80°, lows: and we obtain 2-4496, or 2-45 for the mean es TABLE. II. pansion for 1°. It would perhaps be better 'to Expanı. adapt the table to a mala of 1000 parts of Differ. for 10 141,504 temperature c. This will be done with for: 7°075 2891.... 11.34,429 12.264 ficient accuracy, by Taying (for 212°) 7071718: 6°673 1484,210=1000: 1:849, and fo of the reft? Thuis 3122,165 14150 **0*708 shall contruct the following table of the ex 1921108,015 14'151 00708 pandop of 10,000 parts of air. 132 0711 1079,636 14'9.37 20*911 1'045 Temp. 'Bulk. Differ 72 1043,788 25.943 I'297 0892 1000,000 375, 09786 Mean expanfion 19'3 1996 From this very extensive and judicious ran experiments, it is evident, that the expaoli of air by heat, is greateit when the air is abo 22'1 ordinary denfity, and that in small densities greatly diminished. It appears also, that the of compression is altered; for in this specim the rare air, half of the whole expansion hap about the temperature 99', but in air of ordi density at so's. The experiments of AMONT related in the Mem. of the Acad. at Paris 1 2107 &c. are confiftent with these more perspici experiments of Gen. Roy. After this account of the expansion of air, see that the height through which we must ri parts of air betweeu 12° and 9232 29. Although produce a given fall of the mercury in the b it cannot happen, that in meaturing the differences meter, or the thickness of the stratum of air e of elevation near the earth's surface, we shall have ponderant with a tenth of an inch of merc occalion to employ air greatly exceeding the com- must increase with the expansion of air, and 2'29 if- - be the expanfion of one degree, we r multipy the excefs of the temperature of the above 32° by 0:00229, and multiply the proc cury that they will support when of the tempera: by 87 to obtain the thickness of the strat ture 339; column second is the expansion of where the barometer stands at 30 inches : ever be the elevation indicated by the differe that the air is of the temperature 32°, we n multiply this by o'c0229 for every degree that air is waraler, or colder than 33. The prod and subtracted in the latter. Sir GEORGE SHUCKBURGH deduces O'oc from his experiments, as the mean expansion air in the ordinary cases: and this is proba! nearer the truth; because Gen. Ray's experime were made on air which was sreer from dar and a va than the ordinary air in the fields ; Mean 252 minute quantity of damp increases its expansib There is much mbre frequent occafion to ope. ty by heat in a prodigious degree. The gre rate in dir that is rarer than the ordinary state of difficulty is how to apply this correction; or the fuperficial- atmosphere. Gen. Roy accor. ther, how to determine the temperature of the : dingly irade many experiments on such airs. He in those cxtensive and deep Strata in which the el found in general, that their expanfibility by heat rations are measured. It seldom or never ha was analogous to that of air in its ordinary denfis pens, that the stratum is of the fame temperatu 5 |