CONTRIBUTIONS TO SCIENCE. 563 



the error : diminishing very rapidly as the error increases, 

 according to the ordinary hypothesis respecting " errors of 

 observation " developed by Laplace. If on such a diagram a 

 series of concentric circles be drawn, say an inch apart, about 

 the centre of the target, and the number of shots between 

 each consecutive pair of circles counted, the number will be 

 found to be greatest for a particular pair, but there is nothing 

 to prevent some shots from hitting the target at any distance 

 from the centre. If the length of the line joining the centre 

 of the target with any bullet mark be taken to represent the 

 velocity of a molecule, the diagram will represent the law 

 of distribution of velocities among the molecules of a gas 

 when they have acted on one another for an indefinite time. 

 They will congregate about a particular value, but there is 

 nothing to prevent some individuals possessing a velocity as 

 great or as small as we please. 



The momentum of a particle depends on the product of 

 its mass and its velocity ; its kinetic energy on the product 

 of its mass and the square of its velocity. One of the first 

 and most important properties of gases which Maxwell 

 showed to be a consequence of the kinetic theory was, that 

 when two groups of molecules are in equilibrium, being 

 separated only by a diaphragm which can transmit the 

 impacts of the particles, the average kinetic energy of the 

 molecules must be the same in each group. Identifying the 

 kinetic energy of the molecules with the heat of the gas, 

 since we know that for equilibrium the gases must be at the 

 same temperature, it follows that the specific heat varies 

 inversely as the mass of a molecule, which is the dynamical 

 expression of the law of Dulong and Petit, a law which 

 states that the products of the specific heat and combining 

 weight is the same for each element. The pressure of a 

 gas is proportional to the kinetic energy of unit volume of 

 a gas, and, since the average kinetic energy of the molecules 

 is the same for each gas at the same temperature, it follows 

 that equal volumes of two gases at the same pressure and 

 temperature contain the same number of molecules, and hence 

 the density of a gas at standard temperature and pressure is 



