PROPERTIES OP MATTER IN THE GASEOUS STATE. 
793 
rfG Sr ell Sr 
^ dr 2 ^^dr 2 ’ 
8/ 5 
for the inequality has reference to the uniform gas at a point distant — from the point 
at which I represents the inequalities, and therefore the change in G + I must be added 
to or subtracted from the inequality, as the case may be. 
79. The following assumptions may all be deduced from first principles, but the 
necessary reasoning is long, and it is thought that the assumptions are sufficiently 
obvious. 
Assumptions. 
I. That the condition,of the gas, as already defined (Art. 78), at any instant within 
an element of volume depends entirely on the numbers and, component velocities of the 
molecules which, in a unit of time, enter at each part of the surface of the element; 
and hence if the molecules enter one element in exactly the same manner as the molecules 
enter a geometrically similar element, the condition of the gas ivithin the elements must 
be similar. 
II. That the number and component velocities of the molecules which leave each 
elementary portion of the surface of an element, depend only on the condition of the 
gas ivithin the element and the manner in which the molecules enter; and therefore by 
(I.) depend only on the manner in which molecules enter. Also since the gas imme¬ 
diately outside the element consists of the molecules entering and leaving, its condition 
depends only on the molecules entering. So that if molecules enter corresponding 
portions of the surfaces of two geometrically similar elements in exactly the same 
manner the gas about the elements must be exactly similar. 
III. That whatever be the nature of the action between the molecules, the effect of 
encounters within an element must cdways tend to produce or maintain the same relative 
motion amongst the molecules, which relative motion is that of a uniform gas; and 
hence the encounters must render the manner in which the molecules leave the 
element, as compared with that in which they enter, more nearly similar to the 
manner of a uniform gas. 
That is to say, if A, B, C, D, &c., be a series of geometrically similar spherical 
elements, and the gas about B is such that the molecules enter B in exactly the same 
manner as they leave the opposite sides of A, and the gas about C such that the 
molecules enter as they leave the opposite side of B and so on, the gas about each 
element being such that the molecules enter the element exactly as they leave the 
opposite side of the preceding element, then according to the assumption the gas about 
each element will be more nearly uniform than that about the preceding element, so that 
eventually about the n th element the gas would be uniform, n being indefinitely great. 
This may be expressed algebraically. Putting li for the number of encounters 
5 i 2 
