240 ' PHILOSOPHICAL TRANSACTIONS. [anNO 1777- 



to Entrlisli measures, has fixed it. This first step towards a correction of the 

 rule, naturally pointed out the 'id thing to be aimed at, namely, the obtaining 

 of a sufficient number of cold observations, near the zero, and as far as possible 

 below it, that the equation might disajjpear entirely, and even come to be applied 

 with the contrary sign. Of this kind the winter seasons of 1774 and 1775 af- 

 forded a few on the small heights in and near the metropolis; but the best that 

 have been furnished, are those which Dr. Lind, assisted by Mr. Hoy, made on 

 Arthur's Seat near Edinburgh; and those which Capt. Calderwood made on the 

 Cairn-hills, being a part of the Pentland range to the ?outh-west of that city. 



By comparing these sets of observations togetlier, it appeared from all of them, 

 that when the air was at or near the freezing temperature, the logarithmic dif- 

 ferences gave the real height, in English fathoms and thousandth parts, without 

 any equation ; and when considerably below that point, the equation was to be 

 subtracted, or applied with the sign — instead of -|-. It was further perceived, 

 that the same general conclusion might be dravyn from the coldest, not only of 

 the sun-rising, but even on the ordinary observations on Saleve, some reduction 

 of the temperature being in certain cases made, on account of the exposure of 

 the thermometer to the sun's rays: hence I was led to suppose, that the morn- 

 ing observations, instead of being made exceptions from the rule, were those 

 which it might be presumed would form the best basis for deducing the equation 

 depending on the heat of the air; because the mean temperature of the column 

 was then found to differ least from that of its extremities; whereas in the hottest 

 time of the day, that difference was generally the greatest. Having been enabled, 

 by means of the cold observations, to form some judgment whereabout the zero 

 of the scale would fall, below which the equation was negative, and above it 

 affirmative; it followed of course, that the next principal thing to be sought for, 

 was the maximum of equation, or that corresponding to the highest temperatures 

 the climate of our island would afford. 



By comparing the tables of barometrical results, it will be found, that the 

 observations for extreme temperatures belong to the Edinburgh class of observa- 

 tions (N° 4) it being thought best in this case to omit the few liot ones obtained 

 on the inconsiderable heights near London: the mean of the coldest, answering 

 to the temperature of 21°. 73, make the logarithmic excess -r|-rir; and the mean 

 of the hottest, corresponding to the temperature of 6y°.6, give a defect of 

 -pSJ-j-. Now the sum of the two equations -pULSg-^ being divided by the difference 

 of temperature 47°.S5, we have nearly 2.3 for the mean rate of the equation on 

 each degree, which is less than that resulting from the operations of the mano- 

 meter. Again, from the mean of the very best observations, as being made on the 

 greatest heights, when tlie temperature of the air is 52°, it appears, that the 

 defect is from ''-^^tr°> "r '^-5 for each degree nearly, which agrees perfectly well 



