MOLECULES. 365 



The further development of the theory is generally supposed to have 

 begun with a paper by Kro'nig, which does not, however, so far as I can see, 

 contain any improvement on what had gone before. It seems, however, to have 

 drawn the attention of Professor Clausius to the subject, and to him we owe 

 a very large part of what has been since accomplished. 



We all know that air or any other gas placed in a vessel presses against 

 the sides of the vessel, and against the surface of any body placed within it. 

 On the kinetic theory this pressure is entirely due to the molecules striking 

 against these surfaces, and thereby communicating to them a series of impulses 

 which follow each other in such rapid succession that they produce an effect 

 which cannot be distinguished from that of a continuous pressure. 



If the velocity of the molecules is given, and the number varied, then since 

 each molecule, on an average, strikes the sides of the vessel the same number 

 of times, and with an impulse of the same magnitude, each will contribute an 

 equal share to the whole pressure. The pressure in a vessel of given size is 

 therefore proportional to the number of molecules in it, that is to the quantity 

 of gas in it. 



This is the complete dynamical explanation of the fact discovered by Robert 

 Boyle, that the pressure of air is proportional to its density. It shews also 

 that of different portions of gas forced into a vessel, each produces its own 

 part of the pressure independently of the rest, and this whether these portions 

 be of the same gas 'or not. 



Let us next suppose that the velocity of the molecules is increased. Each 

 molecule will now strike the sides of the vessel a greater number of times in 

 a second, but, besides this, the impulse of each blow will be increased in the 

 same proportion, so that the part of the pressure due to each molecule 

 will vary as the square of the velocity. Now the increase of velocity cor- 

 responds, on our theory, to a rise of temperature, and in this way we can 

 explain the effect of warming the gas, and also the law discovered by Charles 

 that the proportional expansion of all gases between given temperatures is the 

 same. 



The dynamical theory also tells us what will happen if molecules of different 

 masses are allowed to knock about together. The greater masses will go slower 

 than the smaller ones, so that, on an average, every molecule, great or small, 

 will have the same energy of motion. 



The proof of this dynamical theorem, in which I claim the priority, has 



