of Heights by the Barometer. 409 



which height is no doubt too small, it having been estimated by- 

 means of the duration of the twilight to be between forty and 

 fifty miles. 



The value we have adopted for a, 



a = 000002266, 

 being greater than 



^=0-00001776, 



renders imaginary the value of — correspondent to 



Po 

 p-0. 



In this case the density becomes nothing at the height 



x = - =44,131 feet, 

 a 



which corresponds to a pressure 



-=1- A =0-2161; 



p Q 2ati 



so that the density is reduced to nothing before the pressure, 

 which is physically impossible. It follows that with this value 

 of a the equilibrium of the upper strata could not exist. But 

 we must bear in mind that for our purpose of determining alti- 

 tudes and refractions, it is quite sufficient that the law adopted 

 represents the constitution of the atmosphere in the first envelope 

 of air near the earth's surface, and that it is useless to consider 

 the higher strata, which do not materially affect the inquiries we 

 are about. 



Coming now to the temperature, if we neglect the aqueous 

 vapour, or even if we suppose its tension to bear a constant ratio 

 to the tension of dry air, we shall have 



P _ Pt . 



Po Po'o' 

 therefore 



l-Po_ l (Po P\ 

 t p 2ah\ p p /' 



By substituting the value of p in x, we shall obtain 



t _ 2h-2x + ax' 2 

 t ~ U(\-ax) ' 

 hence 



2A/ 2ah-l 



t t n \ + 2—2ah-axJ' 



