BAR 



to thermometers of particular fcales, for the convenience of 

 c-alciilation ; but the Icalcs will be dilTercnt from ihofe of 

 M. Dc Luc. The thermometer, attached to the barometer, 

 will belt be divided with the interval between freezing and 

 boiling water, confiiling of 81.4 degrees ( = i8oX.452); 

 the freezing point may be marked o, and the point of boil- 

 ing water will be 81.4 ; for then, if the difference of height 

 of this thermometer, at the two ftations, be called d, we 

 fiinll have d =0.452 x D, for d : D :: 81.4: 180:: 

 0.452 : 1. and the number of degrees exprefTtd by (/will 

 (liew immediately the correc'tion for the difference of heat 

 of the two barometers. If the thermometer, dcfigned to 

 fhew the temperature of the air, be divided with the inter- 

 val between freezing and boiling water =: 200, and the 

 freezing point be marked — 9, and the boiling point +19I1 

 and the heights of this thermometer, at the two ilations, 



be called G and I, wc fhall have —=z = 



449 Z X 500 I OOQ 



For F — 40 = F— 32 — 8 is the height of Fahrenheit's 

 thermometer, reckoned from 8 degrees above freezing, and 



F-32-8 

 44.0 : fco :; 180 : 200 : : 8:9, and the fraclion . 



449 



increafing both the numerator and denominator in the 

 ratio of 449 to 500, will become 



500 



500 



= F— 32 X 



500 

 449 



G + I , , G + I , ^ 



^ .becaulc -1-9 



2x500 — locc 2 



Hence, if the thermometer of the baro- 

 meter has the freezing point marked o, and the point of 

 boihng water 81.4, and the difference of its height, at the 

 two ilations, be called d; and the thermometer for mcafur- 

 ing the temperature of the air be divided with the interval 

 of 200 between the freezing point and that of boiling 

 water, and the firft be marked — 9, and the latter -\- 191, 

 and the degrees, ftevvn by this, at the the two ftations, be 

 called G and I ; the formula, that will give the height of 

 the upper ftation above the lower one, in Englifh fathoms, 



, r^ I T 



will be log. 13— log. i + ^ X l -\ J1-, which multiplied 



1000 

 by 6, will give 'the height in Englifli feet. It is to be ob- 

 ferved, that + </, or — d, is to be ufcd, as the thermometer, 

 attached to the barometer, is higheft at the lower or upper 

 ftation ; and if G and I fhould happen to fall below o of 

 the fcale, or to be fubtradlive, they muft be applied accord- 

 ingly in the calculation. 



The rules, cxprelfcd in the aboTe formula, will he in com- 

 mon language as follow : 



I. The rule adapted to Fahrenheit's thermometer is this. 



Take the difference of the tabular logarithms of the ob- 

 ferved heights of the barometer at the two ftations, confider- 

 ing the four firft figures, cxclufively of the index, as whole 

 number?, and the three remaining figures to the right as 

 decimals, and fubtrad or add y-e^^^th part of the diff'erence of 

 the altitude of the Fahrenheit's thermometer, attached to 

 the barometer at the two ftatio'is, according as it was higheft 

 at the lower or upper ftation: thus you will have the 

 height of the upper ftation above the' lower in Englifti 

 • fathoms nearly. This is to be corrected in the following 

 maimer : fay, as 449 is to the difference of the mean alti- 

 tude of Fahrenheit's thermometer, expofed to the air at the 

 two ftations, from 40°, fo is the height of the upper ftation 

 found nearly to the correftion of the fame : which, added 



BAR 



or fubtrafted, according as the mean altitude of Fahren- 

 heit's thermometer was higher or lower than 40", wil! give 

 the true height of the upper ftation above the lower, in 

 Englifti fathom?, and multiplied by 6 in Englidi feet. 



II. The rule adapted to two thermometers of particular 

 fcales is as follows. Take the difference of the tabular lo- 

 garithms of the obferved hcigl'.ts of the barometer, at the 

 two ftations, confidering the four firft figures, cxclufively of 

 the index, as whole numbers, and the three remaining figures 

 to the right as decimals ; and fubtraiit or add the difference- 

 of the thermometer, of a particular fcale, attached to the 

 barometer, at the two ftations, according as it was highefl 

 at the lower or upper ftation, and you v/ill have the height 

 of the upper ftation above the lower one, in Englilh fathoms 

 nearly^ fubjeift to the following eorreftion : fay, as looo 

 is to the fum of the altitudes of the thermometer of a parti- 

 cular fcale, expofed to the air at both ftations, fo is the 

 height of the upper ftation above the lower, found nearly, 

 to the corredlion of the fame ; which, added or fubtradled, 

 according as the fum of the altitudes of the thermometers, 

 expofed to the air, is pofitive or negative, will give the 

 true height of the upper ftation above the lower in Enghlh 

 fiithoms, and multiplied by 6, in Englilli ftet. Dr. Horf- 

 ley, the prefent bilhop of St. Afapli, has given a co-npa- 

 rifon of M. De Luc's rules with theory, reduced them to. 

 Englifli meafures of length, and adapted them to Fa'nren- 

 heit's fcale of the thermometer, and added tables and pre- 

 cepts for expediting the praftieal application of them in 

 the Phil. Tranf. vol. Ixiv. p. 214. See Atmofpherical Lo- 

 garithmic, and Fixed Poiitls of Thermome rtRs. 



The fcene of M. De Luc's firft obfervatioiis was mount 

 Saleve, near Geneva. Here he felcCled i j ft itions at dif- 

 ferent elevations ; and the following table abftradlcd and 

 abridged from his minute details ( Rccheiches, &c. vol. ii. 

 p. 213, &c.) ihews the refult of his operations : 



The lateft and moft accurate experiments" and obferva- 

 tions relating to this fubjedl, are thofe of fir* George Shuck- 

 burgh, and general Roy. In order to render the method of 

 meafuring altitudes by the barometer more ptrfed, it is 

 necefl^ii-y toafcertainbyappropriateexperimentsthe expanfion 

 of mercury by any increafe of temperature, and alfo the 

 expanfion of air by the fame, or by any chancre of tempe- 

 rature ; and alfo the variations to which its elafticity is fubjeft. 



It has been already ftated, that M. De Luc eftimates the 

 expanfion of quickfilver, between the temperatures of melt- 

 ing ice and boiling water, to be exaftly 6 French lines, or 

 .532875 decimal parts of an Enghlh inch. But he fuppofed 

 the barometer to ftand at 27 Fr. inches, or 28.77525 Eng. 

 jjkchea ; whereas, if it had flood at 30 inches, it would have 



beea 



