242 PHILOSOPHICAL TRANSACTIONS. [aNNO J 777. 



the rule for measuring heights with the barometer. When tlie mean tempera- 

 ture of the column of air to be measured is at 32° of Fahrenheit, the difference 

 of the common logarithms of the equated heights of quicksilver in the inferior 

 and superior barometers, expressed in 1000th parts of an inch, gives the real 

 height in fathoms and 1000th parts, the 3 figures towards the right hand being 

 decimals, and the rest integers; which, being multiplied by 6, gives the result 

 in feet. 



Let us next consider, in a general way, how far this will correspond with 

 Mr. De Luc's observations in extreme temperatures. It has already been 

 remarked, that when the temperature of the air was at 69°.32, as indicated by 

 thermometers exposed to the sun's rays, Mr. De Luc found that the differences 

 of the common logarithms of the heights of the barometers at the two stations, 

 gave the altitude between them, in French toises and 1000th parts: in which 

 case the specific gravity of quicksilver to air was as 11232 to 1. When his 

 formula is adapted to English measures, the zero of the scale necessarily 

 descends to 39.74, where the English fathom bears the same proportion to the 

 modulus of the common logarithms, as, in the former case, the French toise 

 did to that modulus, the equation for the intermediate temperature being now 

 applied with the contrary sign. As it has been shown, that the British observa- 

 tions differ in their circumstances from those on Saleve, and require a greater 

 equation, it is unnecessary to enter into any minute comparison of the two sets : 

 yet, that some idea may be formed of the cause, of part at least, of the differ- 

 ence that takes place between them, I have collected into one view, the com- 

 putations of such as were made in extreme temperatures; namely, the coldest 

 of those at sun-rising; the coldest and hottest of the ordinary observations; 

 also those on the Dole, at Genoa, and at Turin, by which the heights of the 

 lake of Geneva and of Turin, above the sea at Genoa, were obtained. 



From the table it appears, that when the temperature of the air is at 29°.5, 

 the logarithmic excess is-pJ^-j^; and at 75°.5 reduced temperature, the defect is 

 ,ggo, The sum of the two equations .'o^o being divided by the difference of 

 temperature 46", we have, as in the British observations, nearly 2.3 for each 

 degree, which is greater than that applied by Mr. De Luc's rule, in the propor- 

 tion of 23 to 21. That too small an equation has been used in these hottest 

 observations, supposing the original zero and temperature to remain, is suffi- 

 ciently evident: for -r^-o being divided by 42" the difference of temperature, we 

 have, as before, 2.3 very nearly for the equation answering to each degree. 

 Also, if we consider the ratio of the weight of quicksilver to air, actually 

 resulting from the observations themselves, the same kind of error still exists. 

 Now if from the aggregate of these observations, the same method be adopted, 

 as was used in the British, for finding the zero of the scale, we shall hav<> it as 

 follows : 



