28 SCIENCE PROGRESS 



As we assume that any actual gas can be ultimately brought 

 into the solid state through all the others, we may discuss the 

 relations of quantities in the gaseous state as the least compli- 

 cated, without any loss of generality. The kinetic theory 

 assumes that all pure gases consist of a vast number of particles 

 which are exactly similar in volume (5), shape, and mass (m) to 

 one another, and that they are all striving to move in straight 

 lines with velocities which are continually varying about a 

 certain mean value («)• These particles or molecules are 

 known to be exceedingly small ; so, where the gas is in a com- 

 paratively rarefied condition and the size of the molecules is very 

 small compared with the average distance between them, it is 

 possible, as a first approximation, to neglect the size of the 

 molecules and to treat them as if they were only mathematical 

 points without any action on one another, and merely endowed 

 with mass and velocity, that is, with kinetic energy. The 

 molecules are continually striking against the walls of the 

 containing vessel with blows the force of which depends upon 

 their kinetic energy, and hence on their velocity. If we call the 

 combined effect of these blows the pressure, and measure it as 

 a distributed force applied to every square centimetre of the wall, 

 it is easily found that 



( 1 ) p = § . n . \ mu* = \du- 



where («) is the number of molecules per cubic centimetre, 

 (u) has the value given above, and d is the density = ijv, 

 where v is the volume of the gas. Hence we have pv = %u 2 . 

 Comparatively rough experiments with air or similar gases 

 under moderately small pressures made by the early experi- 

 menters, or more accurate experiments made more recently 

 at really small pressures, have shown that as a first approxima- 

 tion the relation 



(2) pv= R/„(i+a/) = RT 



holds for gases, where R and a are constants, and / is the 

 temperature centigrade. The value of T is then clearly 

 determined when the value of a is known. 



This relation is known as the Boyle-GayLussac-Avogadro 

 law, and is the most simple equation of state. By comparing 

 the two values for pv, it will be seen that %u 2 = RT, and hence 

 that the temperature and the mean velocity are very closely 

 related. Also that, where T = / (i -f at) = 0, u would be zero, and 



