424- Mr. Ivory on the Astronomical Refractions. 



given mass of air placed at any height, will always retain the 

 same quantity of heat, either in a state affecting the ther- 

 mometer, or combined with it in a latent form. Thus, if a 

 cubic foot of air taken at the earth's surface were carried up 

 in the atmosphere, none of its heat would be dissipated ; the 

 portion that disappears with respect to the thermometer, be- 

 ing wholly absorbed as the air dilates, and being necessary to 

 maintain the expansion caused by the diminution of pressure. 

 As I write hastily, I cannot enter upon the pi-oofs of this 

 law, which I adopt for the purpose of bringing down to the 

 earth's surface the equations that have been shown to take 

 place in the atmosphere. Suppose a portion of air at the 

 earth's surface to be contained in a close vessel ; the pressure, 

 density, and temperature, being p', 1, t', both within the 

 vessel and in the open air. Extract a part of the air from the 

 vessel; what remains will dilate itself, will become colder, 

 and then will resume the general temperature. Let 1 — x de- 

 note the density of the expanded air, and the heat that 

 combines with it in a latent form. The pressure within the 

 vessel, after the air has resumed the general temperature, will 

 evidently be^?' x (1 — x). Put p for the pressure that prevails 

 within the vessel, the instant the air is extracted ; before any 

 extraneous heat has been communicated to the dilated air 

 from the surrounding objects; and consequently, when its 

 temperature is equal to t'— : then the equations (A) which 

 take place in the atmosphere, being brought down to the 

 earth's surface by Dal ton's law, will be as follows, viz. 



n 4 



y = (i-*)* 



He i# 



i-I+^O-*). 3 



It is remarkable that these equations are the same with those 

 given by M. Poisson, at p. 264< of the Connaissance de Terns 

 for 1826, published six months after my paper was read be- 

 fore the R. S. There is a very small difference in the index 

 of the power of the density ; which instead of f is found to 

 be equal to 1'3492 by the experiments of MM. Clement and 



* The densities 1 — a and 1 — x are connected by this equation, viz. 



(1-a)* =(l-.r) i 



If a mass of air elevated in the atmosphere, and haying the density 

 1 — a, be carried down to the earth's surface while its temperature re- 

 mains unchanged ; the pressure and density increasing in the same propor- 

 tion, when the first is equal to p' X (1 — w),the other will be equal to (1 — <j)| ; 

 and then the pressure, density, and temperature, will be the same as in the 

 close vessel, the instant the air is extracted, and before the accession of 

 any extraneous heat. 



Desormes, 



