BAR 



been .f5Jj5'^» becaufe the expanfion is proportional to the 

 length of the ccliimn. It has alfo been fliewn, that M. De 

 Luc's boihng point is 2.2" lower than that of Englifli 

 thermometers, reducing it to 209.8 of Fahrenheit and 

 making the interval between freezing and boiling only 

 177.8 degrees. Hence the expanfion .555556 mud be 

 augmented in the proportion of 177.8 to 180, which gives 

 for the total .5624297 or .56243, on a difference of tem- 

 perature of 180°. Thus the expanfion for each degree, 

 fuppofing it to be arithmetical, or unifonnly the fame in all 

 parts of thefcii.^-, will be .OC312461. But from information 

 communicated by M. De Luc to general Roy, it appears 

 that the difference of temperature in his experiments am.ount- 

 ed to about 31^ of Reaumur, or 72° of P'ahrenhcit, above 

 freezing; and therefore, .00312461 x 72 = .225 nearly 

 will denote the rate of expanfion, from which he deduced 

 that for i8o°. 



The experiments of general Roy for afcertaining the ex- 

 panfion of mercury are minutely detailed in the Phil. Tranf. 

 vol. Ixvii. p. 659 — 682. He expofed 30 inches of mercury, 

 fuftained in a barometer by the atmol'phere, in a nice ap- 

 paratus, by whicli it could be made of on; uniform tempe- 

 rature, through its whole length ; and he noted the expan- 

 fions of it in dccira.ils of an inch. The refuk appears in the 

 following table ; of which the firll column exprefl'es the tem- 

 perature by Fahrenheit's thermometer, the fecond column 

 expr^lTes t\\< bulk of the mercury in confequence of its ex- 

 paniion, and the third column (hews the expanfion of one inch 

 of mercury for an increafe of one degree in the adjoining 

 temperatures. 



T.\ELE L 



By this table the obferved height of tiie mercury may 

 be reduced to what it would have been if it were of the 

 temperature 32. Suppofe that the mercurial height is ob- 

 ferved to be 29.2, and that the temperi\.ure of the mercury 

 is 72°; fay 30.1302 : 30 ;: 29.2 ; 29.0738, which would 



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be the true meafure of the denfity of the air of the ftandard 

 temperature. In order to obtain the exact temoerature of the 

 mercury, the obfervation lliould be made by a thermometer 

 attached to the frame of the barometer, that it may warm 

 and cool along with it. This, however, may be done, with 

 fufficient accuracy, without a table ; ^s the expanfion of an 

 inch of mercury for one degree decreafts very nearly -;-|^th 

 part in each fucceeding degree. If therefore we take from 

 the expanfion at 32° its thoufandth part for each degree 

 of any range above it, we obtain a mean rate of expanfion 

 for that range. When the obferved temperature of the 

 mercury is below 32^, this correftion mull be added, in 

 order to obtaii. the mean expanfion. This rule will be 

 m.ore exzdl if we fuppofe the expanfion at 32^ to be 

 0.C001127, as in the table. Then, by ir.ulciplying the 

 mercurial height by this expanfion, we obtain the correction 

 to be fublracfed or added as the temperature of the mercury 

 vias above or below 32°. Thub, in the former example of 

 72°, take 40, the excefs of 72° above 32°, from o.oooi 127, 

 and we have 0.0001087. Multiply this by 40, and we 

 have the whole expanfion of one inch of mercury = 

 O.CO4348. Multiply the inches of mercurial height, viz. 

 29.2 by this expanfion, and we have for the correftion 

 0.12696; which, fubtracled from the obferved height, 

 leaves 29.07304, differing from the exatt quantity lefs than 

 the thoufandth part of an inch. This correftion may be 

 made by another procefs, ftill more fimple ; or by multiply- 

 ing the obferved height of the mercury by the difference 

 of its temperature from 32°, and cutting off four cyphers 

 before the decimals of the mercurial height r and this me- 

 thod will feldom err one hundredth of an inch. Having 

 thus correfted the obferved mercurial heights by reducing 

 them to what they would have been if the mercury had 

 been of the ftandard temperature, the logarithms of the 

 correfted heights are taken ; and their difference, multiplied 

 by iccoo, uill give the difference of elevations, in Englilh 

 fathoms. Another method of applyiiig this correftion, 

 more expeditious and not lefs accurate, is as follows. As 

 the difference of the logarithms of the mercurial heights is 

 the meafure of the ratio of thofe heights, fo likewife the ' 

 difference of the logarithms of the obferved and correfted 

 heights at any ftation is the meafure of the ratio of thofe 

 heights ; and, therefore, this laft difference of the logarithms 

 is the meafure of the correftion of this ratio. But the ob- 

 ferved height is to the correfted height as i to i. 000102 ; 

 and the logarithm of this ratio, or the difference of the loga- 

 rithms of I and 1.000102, is 0.0000444. This is the cor- 

 reftion for each degree by which the temperature of the 

 mercury differs from 32. Therefore multiply o.ccoo444by 

 the difference of the mercurial temperatures from 32, and 

 the produfts will be the correftions of the refpeftive loga- 

 rithms. The following method of applying the logarithmic 

 correftion is more eafy than the former. The correftion 

 will only be neceffary, whin the temperatures at the two 

 ftations are different, and it will be proportional to this dif- 

 ference. Therefore, if the difference of the mercurial 

 temperatures be multiplied by 0.0C00444, the produft 

 will be the correftion required on tiie difference of the loga- 

 rithms of the mercurial heights. Moreover, fince the dif- 

 ferences of the logarithms of the mercurial heights are alfo 

 the differences of elevation in Englilli fathoms, it follows, 

 that the correftion is alfo a difference of elevation ii»Eng- • 

 lilh fathoms ; or that the correftion for one degree of 

 difference of mercurial temperature is -5%^ of a fathom 

 = 32 inches =; 2 feet 8 inches. This coiTeCtion of 2.8 for 

 every degree of difference of temperature muft be fub- 

 7 traded 



