1858.] On Hypsoinetrical Measurements. 347 



The numbers in columns (5) and (7) of this table at once shew 

 that whilst the hypothesis of Professor Forbes is not rigorously 

 true, n decreasing with the temperature, it is still a very good proxi- 

 mation when the heights are under 10,000 feet, or the boiling-point 

 above 193° Faht. ; and as 112 is about the mean value of n, we have 

 by substitution in equation (2), and using 60369 feet as the value 

 of L,— 



A = 539.01 (T — TO, (3) 



as the expression for the height uncorrected for the temperature of 

 the air. Professor Forbes, in the paper above referred to, gives 

 549.5 as the value of the co-efficient, and in a later paper on the 

 same subject he proposes 543.2 feet as best representing observa- 

 tions when the boiling-point is above 190° Faht. or when the 

 heights are under 12,000 feet; but when the boiling-. point is above 

 192° F., he states in a note that the co-efficient should be only 535 

 feet, in order to express the heights as derived from Eegnault's 

 table of tensions. 



3. After making due allowance for errors of observation, it is evi- 

 dent that the values of n in column (5) of the preceding table, decrease 

 with the temperature. Hence, in order to derive a formula which 

 shall accurately represent heights in terms of the boiling-point of 

 water, it is only necessary to determine the value of n at the stand- 

 ard boiling-point, and the mean rate of its variation for tempera- 

 tures near that point. For this purpose Eegnault's tension series, 

 from the method by which he obtained his experimental values, 

 may be taken as representing the pressures under which water 

 boils at different temperatures.* For temperatures near 100° Cent, 

 however, Moritz has shewn that the values in Eegnault's table are 

 slightly in error on account of the constants not having been calcu- 

 lated with sufficient accuracy. Moritz has corrected and published 

 the values of the tensions where they differ from Eegnault's. f In 

 what follows, I have used these corrected values. 



Now, from equation (1) we at once derive, — 



* Ann. cle Chim. ct dc Phys. July 18 44. Forbes, Eclin. Phil. Trans, vol. xxi 

 part II. p. 238. 



t Bullet, de la classe Physico-math. cle 1' Acad, dc St. Petersbourg, xiii. -11. 



