Attraction of Mass, and some New Gas Equations. 69 



attraction. Hence the pressure p from the exterior is 

 supported by p l9 but the pressure II from the interior 

 towards the surface is opposed by the same force. The 

 condition of equilibrium is satisfied when 



n-pi =p+pi 



P +2 Pl = n, 



and it is immaterial whether the pressure II exists between 

 the surface and the interior conforming to the principle of 

 the equality of action and reaction, or in the interior. In the 

 former case only, II would be identical with the " Intrinsic 

 Pressure " of Laplace in the case of liquids, and the pressure p 

 in the interior would be transmitted undiminished towards the 

 exterior and be equal to the pressure p from the exterior on 

 the gas, no matter how great the intermediate " Intrinsic 

 Pressure " II. 



Making the total pressure II of an actual gas equal 

 to II of a perfect gas at the same volume (absolute) and 

 temperature, we then find 



^(^j*-— > ( A ) 



in which a is the constant of attraction if the density of 

 the actual gas were proportional to the pressure II, and 



j—-p-^==p 1 . In whatever way the volume v is measured, 



the density of the gas is , when it exerts a pressure 

 R . T 



V 



At the critical state the three points of the curve of 

 equation (A) denoting the three values of v ^satisfying 

 the equation coincide with the two points for which the first 

 and second derivatives are equal to 0. 



We obtain 



4a E . T c 



dp 



dv 



= 0, 



d 2 p_ 

 dv 2 



= 0, 



12a 2R.T, 



• • • (i.) 



{v e +by- „.« > • • • ("•) 



whence v = 2b (10) 



Hence (v. equations (1) and (2)), 

 N, =|N, 1 



/S = §J, \ ; (11) 



v = I) » 



