THE COLLOIDAL STATE 85 



Certain difficulties in the atomic theory of Dalton, when applied to the volumes 

 of gases taking part in reactions, were removed by accepting the law proposed by 

 Avogadro in 1813, namely, "equal volumes of gases at the same pressure contain 

 equal numbers of molecules." Now, if molecules have an actual existence, it 

 follows that, in a definite volume of any gas, say one cubic millimetre, there is 

 a certain definite number of molecules. This number which, of course, varies with 

 temperature and pressure, is known as " Avogadro's constant," when standard tem- 

 perature and pressure are taken, and is usually designated by the letter N. It 

 has been determined by several independent methods, and the fact that the values 

 obtained lie very near together is, in itself, powerful evidence of the truth of the 

 assumption on which they were calculated. A short account of these methods will 

 be found in Perrin's monograph (1910, pp. 75-93). 



Further, according to the kinetic theory of gases, these molecules although 

 very minute have a finite size, and the space occupied by the molecule, or rather 

 by its sphere of action, is very small compared with the space unoccupied. At 

 all temperatures above absolute zero the molecules are in ceaseless movement. 

 Any one molecule will travel in a certain direction until it meets another one. 

 After collision and interchange of kinetic energy, the two molecules will rebound 

 and travel again, but with a velocity changed in direction and in magnitude, until 

 further collisions occur. It will be seen that the kinetic energy of any individual 

 molecule will vary from moment to moment, but will oscillate about a mean value. 

 Similarly, the distance travelled between collisions will vary about a certain value, 

 called the " mean free path." 



It is interesting to remember that, although the first actual publication of the kinetic 

 theory was made, independently, by Kroenig in 1856 and by Clausius in 1857, a complete 

 development of the theory had been sent to the Royal Society in 1845 by J. J. Waterston. 

 This paper, unfortunately, was not printed until 1892, in the Philosophical Transactions, 

 having been found by Lord Rayleigh in the archives. 



Similar statements apply to liquids, with the exception that the molecules are 

 in such close relation that the cohesive force of attraction, the quantity a of Van 

 der Waals' equation, about which we shall have more to say later, comes into 

 play much more powerfully, as does also the other quantity b, representing the 

 volume of the molecules themselves. In the case of solids, this molecular move- 

 ment, due to heat, must be supposed to be confined to oscillation about a mean 

 position. The molecules of solids do not continually change their places, as is the 

 case with gases and liquids. 



Let us now fix our attention on a particular molecule in the interior of a 

 liquid. It will be di'iven hither and thither by the impact of other molecules, 

 upwards, downwards, and so on, occasionally taking a comparatively long journey 

 before collision with another molecule. 



It can be easily shown (Perrin, 1910, p. 11) that the mean molecular kinetic 

 energy is the same in all gases, and van't Hoff has shown that the same state- 

 ment holds for dilute solutions ; so that a molecule of alcohol in solution in water 

 has the same kinetic energy as each molecule of the water. __ Again, the molecules 

 of sugar in solution have the same mean energy as those of the water, as also have 

 those of any other molecule, light or heavy, in true solution. Why, then, should 

 we not extend the conception to aggregates of molecules, in other words, to- 

 colloidal particles 1 This is the starting point of Perrin's important work. 



Consider first what will happen to a particle very large in comparison with 

 the molecules of the liquid in which it is immersed. It will be bombarded on 

 all sides by a large number of molecules, moving in all possible directions, 

 whose resultant will be zero or very nearly so, and no movement will be 

 perceptible. As the particles are imagined to become smaller and smaller, 

 they will be hit by fewer and fewer molecules simultaneously, so that the 

 forces acting on them will cease to be balanced, and the particles will be 

 driven hither and thither just as the molecules of the liquid itself. There is 

 thus every reason to suppose that their mean kinetic energy will also be 

 identical with that of the molecules of the liquid or of any other molecule 

 in solution. 



