406 Count Paul de Saint-Robert on the Measurement 



be respectively / = 526°*2,jo =30 inches. The third column was 

 obtained by help of Regaault's Table of the elastic force of 

 vapour. The fourth was calculated by equation (2), and the 

 fifth by equation (3). The sixth gives the value of r— r , or of 

 the altitude, taking into consideration the variation of gravity. 



The height of a homogeneous atmosphere, at the temperature 

 of melting ice and 30 inches pressure, was taken equal to 26,254 

 feet ; so that the height at the absolute temperature t , at the- 

 pressure p , and with the mixture of vapour at the pressure <xr, 

 will be 



h = 26254 Aa<i Jf° e- 



493*2 (;? —mw ) 



When the sky was partially clear, 



/ =526°-2, i? = 30 in -> ^ = 0*39 in. ; 

 therefore 



£=28,148 feet. 



When the sky was cloudy, 



/ =526°*2, j» =30in., *r =0*48 in. ; 

 therefore 



A=28,180feet. 



With these values of h, the heights x contained in the fifth 

 column were calculated. 



The comparison of Table II. with Table I. shows that the alti- 

 tudes calculated by Laplace's formula fall short of the real ones, 

 and consequently that it requires a negative correction, which 

 result I had already advanced in my former paper. As far as the 

 height is moderate, the difference is small; but it becomes of 

 consequence for great elevations. The difference at 13,000 feet 

 (which is a little more than the height of Monviso) is already 

 73 feet; and at 16,000 feet (not much more than the height of 

 Mont Blanc) it becomes 109 feet. 



On inspection of Table II., it will be seen that the density of 

 the air decreases at first more rapidly than the increase of height 

 up to about 5000 feet, and after that point it decreases less 

 rapidly than the increase of altitude, but that on the whole the 

 decrease of density is nearly proportional to the increase of ele- 

 vation. 



Many laws of density have been assumed by mathematicians 

 for the purpose of calculating atmospheric refraction. The 

 principal ones are that of Thomas Simpson, assuming the den- 

 sity to decrease uniformly as the height increases ; that of Bessel, 

 supposing the density to decrease in a geometrical progression; 

 that of Laplace, partaking both of the arithmetical and geome- 

 trical progression of variation of density ; that of Ivory, suppo- 



