VOL. LXIV.] PHILOSOPHICAL TRANSACTIONS. 523 



in round numbers to 210 degrees, which is distant only 178 from 32, the point 

 of freezing. Hence an extent of 80° of M. De Luc's thermometer, answers to 

 an extent of 178 of our Fahrenheit's thermometer; and putting p for the 

 degrees of this thermometer, corresponding to c of M. De Luc's, we shall have 

 c : F — 32 :: 80 : 178, and c = (f — 32) X -fify-i which substituted in M. De 



Luc's formula gives (log. b — log. b) X {I -\ 575 ) = i^°S- ^ ~ 'og- ^) X 



(1 + ^J^'ll^Jhz2l^ = (log. B - log. i) X (1 + ~^). Where the 

 answer will still come out in French toises, though adapted to Fahrenheit's ther- 

 mometer. To bring it out in English fathoms, or measure of 6 feet, multiply 

 the above expression by 1.06575, and we shall have in round numbers (log. b 



— log. b) X {i -\ -rpr) > which will express the height between the 2 stations 



in English fathoms. 



' In the foregoing expressions, b and b, as before said, signify heights of the 

 barometer, at the lower and higher stations, both corrected according to M. 

 de Luc's directions, for the difference of heat between a fixed temperature, 

 (namely -i- of the interval between freezing and boiling water), and the present 

 heat, indicated by the thermometer attached to the barometer at each station ; 

 but it is not necessary to correct both barometers for the efFect of heat, but only 

 one for the difference of heat of the two; which will be more convenient also on 

 another account, because the difference of heat, at the two stations, will be ge- 

 nerally small, and the correction to reduce one barometer to the heat of the 

 other will consequently be small also; whereas the difference of the present heat, 

 and the fixed temperature, and consequently the correction of both barometers, 

 may be frequently very considerable: this is evident: because if the heat of the 

 barometers, at both stations, was the same, however different from the fixed 

 temperature chosen by M. de Luc, no correction would be necessary; the 

 mercury in the barometer in both stations being expanded in the same propor- 

 tion, and consequently the difference of the logarithms of its height, at both 

 stations, being the same, as if the heat of both barometers had agreed with that 

 of the fixed temperature. I shall now therefore suppose the upper barometer is 

 to be corrected, to reduce it to the temperature of the lower one, and that b 

 signifies the height of this barometer, as observed, and not yet corrected; the 

 correction, from wliat has been said above, calling d the difference of height of 

 the thermometer attached to the barometer at the two stations, will be + — , 



— 54k 



according as the thermometer stands highest at the lower or upper station ; and 

 the upper barometer corrected, instead of b, will heb + — , which substituted 



in the formula, gives [log. b — log. (b + ;rr-)] X (l H — IIo")' Butthecor- 



3x2 



