It was shown in chap. V that the determination of gave us at once a knowledge of the exact number of molecules in a cubic centimeter of a gas. Before this was known we had fairly satisfactory information as to the relative diameters of different molecules, for we have known for a hundred years that different gases when at the same temperature and pressure possess the same number of molecules per cubic centimeter (Avogadro’s rule). From this it is at once evident that, as the molecules of gases eternally dart hither and thither and ricochet against one another and the walls of the containing vessel, the average distance through which one of them will go between collisions with its neighbors will depend upon how big it is. The larger the diameter the less will be the mean distance between collisions—a quantity which is technically called “the mean free path.” Indeed, it is not difficult to see that in different gases the mean free path is an inverse measure of the molecular cross-section. The exact relation is easily deduced (see Appendix E). It is [Pg 184] in which is the molecular diameter and is the number of molecules per cubic centimeter of the gas. Now, we have long had methods of measuring , for it is upon this that the coefficient of viscosity of the gas largely depends. When, therefore, we have measured the viscosities of different gases we can compute the corresponding ’s, and then from equation (31) the relative diameters , since is the same for all gases at the same temperature and pressure. But the absolute value of can be found only after the absolute value of is known. If we insert in equation (31) the value of found from by the method presented in chap. V, it is found that the average diameter of the atom of the monatomic gas helium is , that of the diatomic hydrogen molecule is a trifle more, while the diameters of the molecules of the diatomic gases, oxygen and nitrogen, are 50 per cent larger.[135] This would make the diameter of a single atom of hydrogen a trifle smaller, and that of a single atom of oxygen or nitrogen a trifle larger than that of helium. By the average molecular diameter we mean the average distance to which the centers of two molecules approach one another in such impacts as are continually occurring in connection with the motions of thermal agitation of gas molecules—this and nothing more.