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this by 10,000,

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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

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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.
range above it, we obtain a mean rate of expansion
for that range.

Dec. of
Temp.
Log. dift.

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
2.10
2.11
2.II

42

,482 1489

32

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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
20

Dengity Expanfion
18.2
172

1762
18.8

Barom. of Ait of 100o ptsExpansion
192
1974

by ro.

examined by 212°. 132

1380

19'4

20'0
118'0
20.8

29'95 31952 483.89 2*2825
93
2106

30'07 30'77. 482010 2'2741
72

29:48 29990 480*74 2°2676
52
216

29'90 30'13 485.86 2.2918
32

31'4.
20'0

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

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212

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1996

132 II2 92

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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
Temp. Bulk. Di Expaut.
'

72
for 1.

1043,788

25'943 Io29 52 1017,845

17845 089

32 1000,000
13489

375, 1807
192 13474
387

Mean expanfion
1993
13087.

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
72
10942

of compression is altered; for in this spec
238
62
10704

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
209 20.9
9574

experiments of Gen. Roy,
243
9.331

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 $

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1'944

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212

1897

2006

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72 62

238

23.8

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22'6

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10
P N É U MÁTICS

. 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.
Temp. Builk

for 10
the standard temperature 32°; for in its
form, it thews the expansibility of air originally of
the

141,504 temperature c. This will be done with for:

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
1093,864
14.228

0711

1079,636
Table f.

14'9.37
92
1064,699

20*911
Expant.

1'045 Temp. 'Bulk. Differ

72 1043,788
for 1.

25.943 I'297
52
10!7,845
17845

0892

1000,000
13489

375,
192
13474

09786

Mean expanfion
387

19'3
172 13087
132
12685

1996
392

From this very extensive and judicious ran
413
12272

experiments, it is evident, that the expaoli
426
11846
21:3

of air by heat, is greateit when the air is abo
443

22'1
:92
11403

ordinary denfity, and that in small densities
226 2206
82
I1177

greatly diminished. It appears also, that the
235 23.5
10942

of compression is altered; for in this specim
10704

the rare air, half of the whole expansion hap
2493
10461

about the temperature 99', but in air of ordi
10:26
235
- 23'5

density at so's. The experiments of AMONT
226
32

related in the Mem. of the Acad. at Paris 1
217

2107
9783

&c. are confiftent with these more perspici
209 20.9
9574

experiments of Gen. Roy.
2002
9.3.31

After this account of the expansion of air,
This will give for the mean expansion of 1000

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
mon density, we may insert the experiments made

if- - be the expanfion of one degree, we r
by Gen. Roy on fuch airs. They are expressed
in the following table; where column first con-
tains the densities measured by the inches of mer

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 :
1000 parts of nach air, by being heated from o to
212 ; and column third is the mean expansion for of the barometrical heights, upon the suppofit

ever be the elevation indicated by the differe

that the air is of the temperature 32°, we n
TABLE G.

multiply this by o'c0229 for every degree that
Density. for 2120 for so.
Expansion Expaní.

air is waraler, or colder than 33. The prod
must be added to the elevation in the first c.

and subtracted in the latter.
451'54
2'130

Sir GEORGE SHUCKBURGH deduces O'oc
62'3 423-23
1996

from his experiments, as the mean expansion
412'09

air in the ordinary cases: and this is proba!
545
439087
2'075

nearer the truth; because Gen. Ray's experime
497 443*24

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

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