BAR 



rrery column of air, Tvhetherlonijr orthort, wlllconfequenfly 

 be greater than the uppcrmoft fcftion of it. For the iicat, 

 by diflblviiig the moillure, produces a vapour lighter tlum 

 air, which, mixing with its particles, removes them farther 

 from each other, increnfes the elaiUcity of the general mafs, 

 and diminiflits its fpecilic gravity comparatively more than 

 it doth that of the feftion immediately above it, where there 

 is lefs heat and left 'moillure. Hence general Roy infers, 

 that the equation for the air, in any affigncd veitical, will 

 gradually decreale as tlie elevation of the place above the 

 fca increafes, and That it will vanifh at the top of the atmo- 

 fphere. Between the tropics there ii a great degree of Ini- 

 midity in the air ; and, on the contrary, the polar atmo- 

 fphcres are very dry. The heat and moillure being grcateft 

 at the equator, there the claftieity or equation will likewife 

 be tlie greatcft at the level of the fca ; and the zero of the 

 fcale will neceifurily defceud to a lower point of the thermo- 

 meter, than that to which it correfponds in middle latitudes. 

 As the elallicity of the air at the level of the fca, or equal 

 heights above it, with the fame degree of heat, will always 

 be proportionable to the quantity of moillure difiblved in it, 

 it will therefore gradually decreafe from the equator towards 

 the poles ; that is, the zero of the fcale will afcer.d in the 

 thermometer, coincide with the 3 2d degree in the middle lati- 

 tudes, and in its motion upwards, will give the equation to 

 be applied wiih the contrary fign, in high latitudes. At 

 Spitsbergen, it would feem that the fpccific gravity of air 

 to mercury is about i to 10224, and in Peru about i to 

 13100. 'this difTerence is with great probability afcribed 

 to the greater drynefs of the circumpolar air; fo that the 

 denfity of the^ir was greater than could have been inferred 

 merely from its comprtfrion and its temperature. 



From the above account of the expanfion of air, it is 

 plain that the height through which we muH rife in order 

 to produce a given fall of the mercury in the barometer, or 

 tlie thiekiiefs'^of the llratum of air equiponderant with a 

 tenth of an inch of mercury, mull increale with the expan- 

 llon of air ; and hence, if .00229 be the expanfion for one 

 degree, we mull multiply the exccfs of the temperature of 

 the air above 32° by D.C0229, and the produifl b\* 87, in or- 

 der to obtain the thickntfs of the ftratum where the baro- 

 meter (lands at 30 inches : or whatever be the elevation in- 

 dicated by the difference of the barometrical heights, upon 

 the fuppofition that the air is of the temperature of 32% 

 we mull multiply this by .00229 for every degree that the air 

 is warmer or colder than 32. The produA mull be added 

 to the elevation in the firil cafe, and fubtrafted in the latter. 

 Sir George Shuckburgh deduces .0024 from his experiments 

 as the mean expanfion of air in the ordinary cafes : and this 

 is probably near the truth ; bccaufe general Roy's experi- 

 ments were made on air wliich was more free from damp 

 than the ordinary air in the fields ; and it fuffieiently appears 

 from his experiments, as already dated, that a very fraall 

 quantity of damp increafes its expanfibility by heat in a 

 prodigious degree. We (hall now refer for a more particu- 

 lar accouut of the fubjeft of this article to the papers of 

 the allronomer royal and of Dr. Flordcy, Pliilof. Tranf. vol. 

 Ixiv. p. 15S, &c. Id. p. 214, &c. and for the papers of 

 fir George Shuckburgh and general Roy to the Phil. Tranf. 

 vol. Ixvii. p. 5 1 3, &c. and p. 653, &c. and alio to profeffor 

 Playfair's paper on the caufes which affecl the accuracy of 

 barometrical meafurem.ents in the Edinb. Tranf. vol. i. p. 87, 

 &c. : and fubjoin in one view a fummary of the moll ap- 

 proved and eafy rules for the pradlice of this mode of mea- 

 fsreraent l-Uuftratcd by examples. 



The tirll is M. Dt Li c's method, already given in anether 

 form. 



BAR 



1. Subtraa the logarithm of the barometrical height at 

 the upper ilation from the logaritlim of that at the lower, 

 and count the index and four tirll decimal hgures ol the re- 

 mainder as fathoms, tlie reft as a decimal fradion. Call this 



the elevation. 



2. Note the different temperatures of the mercury at the 

 two'llations, and the mean temperature. Multiply the lo- 

 garithmic expanfion rorrefponding to this mean temperature 

 (in Table II.) bv the difference of the two temperatures, 

 and fubtrad the produft from the elevation, if the barome- 

 ter has been coldell at the upper (lation ; otherwife, add it. 

 Call the difference, or tlie fum, the appriximat.-d elevntion. 



3. Note the difTcrence of the temperatures of the air at the 

 two nations by a detached thermometer, and alfo the m.ean 

 temperature and its difTereuee from 32°. Multiply this dif- 

 ference by the expanfion of air for the mean temperature, 

 and multiply the approximated elevation by I ±_^this pro- 

 duft according as the air is above or below 32°. Ttve pro. 

 duft is the corrcfl eleviUiou in fathoms and decimals. 



Example. 



Suppofe that the mercury in the barometer at the lower 

 flation was at 29.4 inches, that its temperature was 50°, and 

 the temperature of the air 45° ; and let the height of the 

 mercnrv at the upper Ilation be 25.19 inches, its tempera- 

 ture 46, and the temperature ot the air 39. Here we have 



Merc, heights Temp. mere. Mean Temp. air. Mean 



2'>'r "" 50 ,8 -^5 



25.19 4^ 39 



1. Log. of 29.4 

 Log. of 25.19 



42 



1.4012282 



Elevation in fathoms - - • 



2. Expatilion for.48° . - • .473 



Multiply by 4 - - - 4 



Approximated elevation - - 



3. Expanfion of air at 42 - 0.0023S 



Mult, by 42 X 32 = 10° 10 



0.0238 



Multiply .... 



I3y .... 



Produft ;= the correft elevation 



671.191 



i.Sgz- 



669.299 



669.299 

 1.023S 



685.328- 



II. Sir George Shuckburgh's method. 



1. Reduce the barometric heights to what they would' 

 be if they were of the temperature of 32°. 



2. The difference of the logarithms of the reduced baro- 

 metrical heights will give the approximate elevation. 



3. Correft the approximate elevation as before. 



Exrimple, the fame as before. 

 I. Mean expanfion for 1° from Table I. . ccooiil 

 18'' X o.oooiii X 29.4 =r 0.059 



Kubtraft this from . 29.4 



Rednccd barometric height 

 Expanfion from Tab. I. is 

 14" X o 0001 II X 25.19 



Subtraft from 



29-3-'rI 



0.039 

 25.J90 



o.cooi II 



Reduced barometric height 25.151 

 2. Log. 29.341 - - 1.4674749 



Log. 25.151 



1-4005553 



Approximated elevation 669.196 



3. This muitipiied by 1.0238 gives 685.125- 



Sir 



