1858.] On Hypsometrical Measurements. 349 



100 — T 



h m = 94082 x 



228.626 + T K 9 ) 



and log 7/ m = 4.973506 + log (100 — T) — log (228.626 + tf), 



when expressed in metres above the point where water boils at 

 100° cent. 



4. Now if the boiling-point on Fahrenheit's scale coincided exactly 

 with that on the centigrade, that is if 212° F. represented the tem- 

 perature of boiling water under a pressure of 29.9218 inches of 

 mercury,* this formula, and the logarithms of the pressures in the 

 table of Moritz might at once be modified to suit the English scales. 

 But if the thermometer be so constructed that the boiling-point is 

 at 212° F. under 30 inches of pressure, the centigrade ought, in the 

 same circumstances, to shew 100°. 0729 ; and. as the freezing point 

 may be considered invariable, 176° F. will coincide with 80°.0583 

 C. To make the necessary correction for this difference, which is 

 often overlooked, I have, after interpolation among Moritz's pressures, 

 derived the following formula of essentially the same form as that 

 first used by Biot,f and which accurately represents the results 

 derived from Moritz's table, — 



Log B T = log 30 — 0.008641566 (212° — T) ) 



[ (10) 

 —0.0000143365 (212° — T) 2 — 0.00000003161 (212° — T) s .) 



This formula, which is adapted to Fahrenheit's scale, will give the same 

 results as the more complicated one of Eegnault when T lies be. 

 tween 172° and 216° Faht. The values of the logarithms of the 

 pressures in the table of Moritz may, in like manner, be represented 

 between 78° and 102° C. by the formula,— 



" J' adoptcrai les temperatures, au therrnoinetre a mercure, divise en cent 

 degres, depuis la temperature de la glace fondante, jusqu'a celle de l'eau bouil- 

 lante sous unft prcssion equivalente au poids d'une colonne de mercure, de soix- 

 ante et seize centimetres de hauteur." Laplace, Exposition du Si/stcme du Monde 

 — avert issement. 



t Biot,Traite de Physique (1816) torn. I. p. 278 j also Ency. Metropol. (1845) 



vol. iv. p. 2JU. 



9 (/. 



