BAR 



B A K 



Sir George Shuckburgh, in his barometrical obfervatJons, 

 reckoned the equation for the expanfion of mercury =: 

 .00323 of an inch for every degree of Fahrenheit's thermo- 

 meter in a col'jmn of 30 inches, inftead of .00312 ufed by 

 M. De Luc : but this difference, he fays, will not occahon 

 an alteration in the refult of any one of his obfervations of 

 more than 5 inches ; and he confidcrs it as of no account. 

 In another part of the fame paper (Phil. Tranf. vol. Lsvii. 

 p. 567.), he eftimates this equation, allowing .00042 for the 

 eftett of the expanlion of gtais for i"' upon a column of 30 

 inches, at .00304 of an inch for each degree, when the 

 barometer ftands at 30 inches. He adds, that there is 

 ground for the fufpicioa, that the expanfion of mercury is 

 not direftly as the heat (liewn by the barometer, but in a 

 ratio fomewhat different ; owing, as he conceives, to fome of 

 the mercury bein^ converted into an elallic vapour in the 

 vacuum that takes place at the top of the Torricellian tube, 

 which prefTes upon the column of mercury and thus counter. 

 atts in a fmall degree the expanfion from heat. It docs not, 

 however, appear to be a confiderable quantity, not amount- 

 ing to above -j^^th of the whole expanfion in a range of 40° 

 of temperature. General Roy was incommoded in liis experi- 

 ments by the alternate expanfion and condenfation of the 

 elalHc vapour contained in the upper part of his tube. 

 Lord Charles Cavendifh found the difference between the 

 expanfion of mercury and glafj, from 180° of lieat, to be 

 .469. And taking into the account Mr. Smeaton's dila- 

 tation of glafs, the total expanfion of 30 inches of mercuiy, 

 fays general Roy, will be .544, vvhich gives a rate of ex- 

 panfion of only .003022 for each degree. Phil. Tranf. 

 vol. Ixvii. p. 671. 673. 678. 



After all, there will be a difference in the fpecific gravity 

 of the mercury that is ufed, which will occalion iiregulari- 

 ties that arenoteafily obviated. Mercury Has been thought 

 fufficiently pure for a barometer, when it is fo far cleared 

 of all calcinable matter as not to drag or iuUy the tube. 

 Neverthcleis in this ftate it may contain a confiderable por- 

 tion of other metals, particularly of filver, bifmulh, and tin, 

 which will diminilh its fpecific gravity. It has been ob- 

 tained by revivification from cinnabar of the fpecific gravity 

 of 14.229, and it is thought veiy fine if it be 13.65. The 

 fpecific gravity of the mercury in the barometers ufed by 

 fir George Shuckburgh was 13.61 with 68° of heat ; but 

 it is fcldom found fo heavy. Thefe variations muil affcft 

 the ultimate reiults ; and in order to obtain precifion, it 

 is abfolutely neceCfary to know the denfity of the mercury 

 that is employed. The fubtangent of the atmofpherical 

 logarilhmic, or the height of tl;e homogeneous atmofphere, 

 will increafe in the fame proportion with the denfity of 

 the mercui-y ; and the elevation correfponding to t'^^th of an 

 inch of barometric height will vai-y in the fame propor- 

 tion. 



Another circumflance which demands attention in this 

 bufinefs is the temperature of the air ; as the change that 

 is produced by heat in its denfity is of much greater moment 

 than that of the mercury. The relative gravity of the two, 

 on which the fubtangent of the logarithmic curve depends, 

 and confequently the unit of our fcale of elevation, is 

 much more affeCted by the heat of the air than by the heat 

 of the mercury. M. De Luc v/as led from his obfervations 

 to conclude, that at a certain temperature, marked +i6| in 

 his fcale, and nearly 69°^ of Fahrenheit's, the difference of 

 the logarithms of the heights of tlie mercury in the baro- 

 meter, at the upper and the lower li-itions, gave the height 

 of the former of thofe ftations above the latter in locoths 

 of a French toife ; but that at eveiy other temperature 

 above or below 69°^, a correAion of .00223 of the whole 



was to be added or fubtrafted for every degree of tht 

 thennometer. Ey obfervationB ftill more accurate, it has 

 been found, that the temperature at which the difference of 



the logarithms gives the height in Englifh fathoms is 32°, 

 and that the correftion at other temperatures is .00243 of 

 that difference for every degree of the thermometer. The 

 manner of ellimating the temperature of the air, adopted 

 in all thefe obfervations, was the fame ; an arithmetical m;an 

 was taken between the heights of the thennometer, at tlic 

 upper and lower ftations, and was fuppofed to be uniformly 

 diffufi-il through the column of air intercepted between them. 

 M. De Luc, however, was apprized of the inaccuracy of 

 this fuppofition ; and general Roy, too, has obferved, that 

 one of the cliief caufes of error in barometrical computa- 

 tion proceeds from the mode of ellimating the temperature 

 of the column of air from that of its extremities, which 

 muil be faulty in proportion as the height and difference of 

 temperature are great. Indeed it fcldom or never happens, 

 that any particular ftratum of air is uniformly of the lame 

 temperature. It is commonly much colder above ; and it 

 is alio of different conilitutions. Below it is warm, loaded 

 with vapour, and very expanfible ; above it is cold, much 

 drier, and lefs expanfible both by its drynefs and its rarity. 

 Currents of wind, alfo, are often difpofed in ftrata, which 

 retain their places for a confiderable time ; and as they 

 come from different regions, are of different temperatures 

 and conilitutions. It is neither certain that the whole 

 intennediate llratum expands ahke, nor that the expanfion 

 is equal in the different intermediate temperatures. Rare 

 air expands lefs than that which is denfer ; and there is a 

 particular elevation at which the general expanfion, inflead 

 of diminidiiag the denfity of the air, increafes it by the 

 fuperior expanfion of that which is below. But no general 

 rule has been eflablillied by which we can obtain a more 

 accurate corredlion than by taking the expanfion for the 

 mean temperature. 



Sir George Shuckburgh has exhibited the refult of 

 feveral experiments on the expanfion of air by a change of 

 temperature in the following table ; where is feen the in- 

 creafe in bulk of lOQo parts of air of the temperature of 

 freezing and preffure of 30? inches, by an addition of I 

 degree of heat in Fahrenheit's thermometer. 



Table IV. 



Obfervations. 



With the 

 firll mano- 

 meter, 



With ano. 

 thcr ma- 

 nometer, 



1 - 



Number ot'de- 

 gites ilic air 

 was healed. 



14.6 

 32.2 



40-3 

 46.6 



49-7 

 51. 1 



23-7 

 13-1 

 22.0 

 28.0 

 21.5 

 30.1 

 22.6 



Expanlicn for 

 J*-" in loooihs 

 oi' the whole. 



2.30 



2-43 

 2.48 

 2.45 

 2.48 

 2.51 

 2.36 

 2.24 

 2.38 

 2.50 



2-34 

 2.44 



2-44 



The mean of thelc two forts 

 different inilrumeuts, is 2.43, v 

 freezing become by expanfion fr 

 parts or 1002.385 parts withths 



I Mean from 

 J> the firll niano. 

 I meter 2.44. 



J 



Mean from 

 > thefecondraa- 

 I nometer 2.42 

 J 



of obfervations, made with 



z. 1000 parti of die air at 



rom 1° of heat equal 1002.43 



I'tandard temperature 39°. 7. 



Whereas 



