408 Count Paul de Saint-Robert on the Measurement 



A glance at Table III. will enable one to see that the law of 

 uniform decrease is a pretty near approximation to the true law 

 of decrease. We perceive indeed that the diminution of density- 

 is slower the higher we ascend, but the law of uniform decrease 

 holds very nearly the whole way from the level of the sea up to 

 30,000 feet ; while BessePs assumption deviates much more from 

 the results of actual observations. I think that, without looking 

 for a more complicated law, we may well adopt this for calcula- 

 ting by the barometer heights that never reach that limit, and 

 for determining atmospheric refraction, which, as we shall see 

 further on, is for the most part dependent on the first envelope 

 of air not extending very far from the earth's surface. 



This identical hypothesis was adopted by Laplace for the de- 

 termination of terrestrial refraction*. 



I proceed to examine the results of adopting this law in refer- 

 ence to the pressure and temperature of atmospheric strata. 



Introducing the law of density, 



— = 1 — ax, 

 Po 

 in the equation of equilibrium of the atmosphere, 



W h Po 



we get, after integration, 



£.«i_._L["i_(JLfL 



p 2ah L \p / J 



At the upper limit of the atmosphere we must have the pressure 

 p — 0; so that the density of the upper layer of air is given by 

 equation 



— =V / l-2flA. 

 Po 



In order that the density may be a real quantity, as is required 

 by the equilibrium of the upper strata of the atmosphere, it is 

 necessary that 2ah should be inferior to unity, or 



Since 



a\ Po J 



it follows that the height of the atmosphere would be in that 

 case less than 2h ; that is to say, less than ten or eleven miles, 



* Laplace, Mecanique Celeste, vol. iv. p. 277- 



