174 Mr. Herapath on the Velocity of Sound and 



2d. The total altitude of the air is equal to 



rh{F-\- 448) . 



80 ' il.)l.|:n 



or, at a medium, better than 30 miles ; andaftt^'bUier times 

 varies directly as the Fahr. temp. + 448. i0iJ«n9fvi*ii 'iii\ 



3d. Since r and h are estimated at a common temperature, 

 when air is constant, the other must be constant too in the 

 same air; and therefore the quantity of air has nothing to do 

 with its total altitude. This would be the same whether there 

 was a half, a third, or a 100 times the quantity. 



4th. Other things being alike, the altitude of an atmosphere 

 is reciprocally proportional to the attraction of the body it sur- 

 rounds at its surface, and the specific gravity of the air under 

 a given pressure and temperature conjointly. If, therefore, 

 our globe was surrounded with hydrogen, its altitude would be 

 about Hf times higher than our atmosphere is. 



Hence a means of determining the altitude of the atmos- 

 pheres of any of the celestial bodies ; and reciprocally, having 

 the altitudes and the nature of the airs, their attractive forces. 

 And hence, too, a proof of the small attractive forces of 

 comets, which have been found by other methods, with a 

 means of computing them, at least approximatively. 



5th. By (1) reduced to (4), it appears that the velocity of 

 sound at the surface is independent of the pressure of the 

 atmosphere; and by (2), that the pressure in the higher 

 regions is dependent on this very velocity^ and varies with it, 

 being greater or less as this is greater or less. This apparent 

 paradox is easily explained : for at the surface the pressure 

 results from the total quantity of air, but at a given altitude 

 from the total quantity minus that below, which depends on 

 the temperature at the surface, and thence on the velocity of 

 sound. 



6th. Our barometric formula (2) requires no aid from the 

 temperatures of the external air. It includes all that is needful 

 within itself, and merely requires that the barometers be of one 

 or reduced to one temperature. Even this it might do without. 

 But as I have elsewhere remarked, Laplace's formula in this 

 respect is singularly helpless ; it not merely affords no means 

 of finding the difference of temperatures, but cannot do with- 

 out it. 



