5'2'2 I-HILOSOPHICAL TRANSACTIONS. [aNNO 1774. 



his subsequent calculations. Calling these two altitudes of the barometer b and 

 b, putting log. B and log. b, for the logarithms of b and b, taking only the first 

 4 places of figures, after the characteristic, or considering the remaining figures 

 as decimals, and putting c for the mean height of a thermometer, exposed to 

 the air at top and bottom of the hill, the freezing point being 0, and the pint 

 of boiling water at 80, he finds, by his experiments, that the height of the hill 

 will be given in French toises, when c is l6|-, by simply taking the difference 

 of the logarithms of the heights of the barometer, or will be equal to log. b 

 — log. b; and in any other degree of heat, will be greater or less, in proportion 

 as the rarity of the air is greater or less, than in the fixed temperature; or 

 greater or less by -y-fx part of the whole, for every degree of the thermometer 

 reckoned from the fixed temperature \Q\; and consequently the height of the 

 place will be expressed generally in French toises, by this formula, log, a — 



log. b + (log. B - log. b) X '-^ = (log B - log. i) X (1 + -^). 



To reduce i\\\% formula to English measure, and to the scale of Fahrenheit's 



thermometer, we should first premise some particulars. The French foot is to 



the English foot, as 1.06575 to 1, as was found by a very accurate experiment: 



see Phil. Trans., vol 58, for 1768, p. 926; and it is well known, that the point 



of freezing, on Fahrenheit's thermometer, is at 32, and that of boiling water 



at 212, or the interval between them 180 degrees. But M. De Luc's point of 



boiling water 80, was marked when the barometer was at 27 French inches; 



and it is the custom of our principal English workmen to mark the point of 



boiling water, 212, on Fahrenheit's thermometer, when the barometer stands 



at 30 inches, which is equal to 28 inches 1.8 lines French measure; or 13.8 



lines higher than M. De Luc's barometer, when he set off the point of boiling 



water on his thermometers ; and it is well known, that the heat of boiling water 



varies with the weight of the atmosphere: M. De Luc finds, by his experiments, 



this rule, that an increase of 1 line in the height of the barometer, raises the 



quicksilver of the thermometer, placed in boiling water, by -j-rW part of the 



interval between the freezing point and that of boiling water: he afterwards 



indeed found, that this rule would not answer for such large variations of the 



barometer, as take place in ascending to very great heights above the earth's 



surface; but it is accurate enough for any small variation of the barometer, on 



one side or other of its mean height in these lowest regions of the atmosphere. 



The change therefore of the boiling point on Fahrenheit's scale, for a change of 



1 line in the barometer, will be tVVt = 0-16; therefore 13.8 lines will cause 



0.16 X 13.8 =2.2 degrees of Fahrenheit's scale; and a thermometer, whose 



point of boiling water was marked 212, when the barometer stood at 30 English 



inches = 28 inches 1.8 lines French measure, will, when the barometer 



descends to 27 French inches, sink 2.2 degrees in boiling water, or to 209.8, or 



