Properties of a Molecule in a Substance. 105 



a point b on a nlane abc (fig. .1), and draw a sphere of 

 radius r around it, and let the angle a line through b makes 



Fijr. 1. 



with the plane be denoted by 6. Suppose s molecules impinge 

 per cm. 2 per second at right angles on the surface of the 

 sphere. The number impinging on a circular belt of breadth 

 r . d6 and radius rcosB is therefore 2iir 2 scos0.d0. The 

 pressure exerted by a molecule on impinging on the plane abc 

 at an angle 6 is proportional to its component velocity at right 



angles to the plane, and thus equal to A or A sin 9. 



Hence the molecules in the solid angle it impinging on the 

 point b exert the pressure 



J 



7T 



. 27rr 2 sA sin 6 . cos 6 . cW = irr 2 sA, 



If u denote the number of molecules impinging on the 

 point b we have 



U = 27T7 ,2 5, 



and the pressure exerted by the molecules may be written 



u 



^A. Hence if n denote the total number of molecules 



passing through 1 cm. 2 per second, the pressure they 

 exert is 



U -K = nl-27 x 10" 20 VTm. 



The pressure under consideration is balanced by the sum 

 of the external pressure and the negative pressure due to 

 the attraction of the molecules upon one another, called the 

 intrinsic pressure. Hence, if these two quantities are denoted 



