14 Dr. Arnott mi the Measurements of Heiyhts. 



110"1223 Log. j^ -If 4932 for the actual temperature : but it appears he 

 obtained this from Saussure's thermometer by equal corrections to all the 

 boiling points observed, which I do not consider strictly correct. 



For such a thermometer, and by means of the formula I liavc suggested, 

 we may discover the boiling point con'esponding to any other pressure, say 

 20 inches, and thence derive the co-efficient by which the difi'erence of the 

 boiling points require to be multiplied, so as to give the approximate 

 height. At the mean temperature of freezing, this is 990 for the Centigrade 

 thermometer, by using the logarithmic tables, or 992J nearly, if it be 

 thought necessary to employ Galbraith's : the one gives 1000 for the 

 constant multiplier, when the mean temperature of the air is 2^" Cent. ; 

 the other, when the mean temperature is 1°'8 ; and adapting these to 

 Fahrenheit's thermometer, the multiplier becomes 560, at the mean tem- 

 perature of 32°, using the logarithmic tables, or at the temperature of 

 about 32-G, by using Galbraith's tables. Such give tlie approximate 

 heights almost the same as by Pi'ofessor Forbes' method, who takes the 

 co-efficient 549|- also at a mean temperature of 32°, which corresponds to 

 5.50, at a mean temperature of 32°-5, and to a multiplier of 1000, when 

 the centesimal scale is adopted, the mean temperature then being 2"8, or 

 21° nearly, as formerly noticed by me. 



The diiference between these may, if thought necessary, be corrected 

 whilst correcting the approximate height, by considering the same constant 

 multiplier as having been fixed to correspond to different mean tempera- 

 tures : twice the mean temperature adopted having to be deducted from 

 the sum of the detached thermometers. 



In the elevated mountains of India and South America, it is difficult 

 to have a simultaneous series of observations carried on at the level of the 

 sea, and hence, I believe, the barometer is generally assumed to stand 

 there steadily at 30 inches : and if the thermometer be adjusted to boil 

 at 212° Fahr., or 100" Cent, under that pressure, the difficulty of finding 

 the approximate height by the boiling point is removed : but we have no 

 precise method of correcting the approximate height for the variable 

 temperature of the external air, without actual observation. At the same 

 time, it appears to me that we may approximate to this also. 



It has been long ago observed by Playfair, Leslie, and other elementary 

 writers, (I know not who discovered that the decrease was uniform, it 

 was confirmed by Lagrange in 1772,) that for heights in this country the 

 mean temperature decreases 1" Fahr. for about every 90 yards, or 270 

 feet of ascent : and although the difference of temperature of the atmos- 

 phere between two places is by no means constant, still, in favourable 

 circumstances, I have found that 1° Cent, for every 500 feet of ascent, is 

 not very far from the truth. This law seems also to be applicable to 

 Switzerland ; but if I may draw conclusions from some isolated observa- 

 tions made by Humboldt in South America, it would appear that in the 

 tropics it requires about 700 and sometimes 1000 feet to correspond to 

 1° of the same scale. More observations require to be made on this 



