April 1, 1893.] 



KNOWLEDGE 



77 



based on an accurate representation of the constitution of 

 gases. 



If Dj and D., represent the densities of the two gases, 

 Dj = Mj N, and D. = M-. No ; as also Nj = N., it follows 

 that Dj : II, : : ]\Ij : M.,, or "in other words the densities of two 

 gases which have the same pressure and temperature are 

 proportional to tlie masses of the molecules composing 

 these gases. 



This is the expression in the language of the mechanical 

 theory of the law, proved by Gey-Lussac, that the densities 

 of gases are directly proportional to their molecular 

 weights. 



It was discovered by Charles that all gases expand 

 equally under the inthieiice of heat. This follows at once 

 from the kinetic theory, for when two gases have the same 

 temperature the kinetic energy of their molecules is the 

 same, there is no tendency for heat (or what comes to the 

 same thing, energy of motion possessed by the gas particles) 

 to pass from one gas to the other. 



Then Mj V^- = M„ Vj^ and the absolute temperature is 

 proportional to Vj- when measured by a gas thermometer 

 containing the tirst gas, and to V,,- when the thermometer 

 contains the second gas. Now as ^\~ is proportional to 

 Vo", the absolute temperatures, as indicated by those two 

 gas thermometers, must be proportional, and if the 

 readings on the thermometers coincide at any one 

 temperature, say that of melting ice, then they must 

 coincide at every other temperature ; in other words, 

 Charles' law holds good. 



The length of the mean free path can be deduced from 

 the kinetic theory. Clausius, reasoning from the theory 

 of probability, shows that the ratio of the free path (i.e., 

 the course of the molecule between two collisions) to the 

 diameter of a molecule is the same as the ratio of the 

 whole volume of the gas to 8^ times the volume actually 

 occupied by the molecules themselves. We can find this 

 latter quantity, for the volume taken up by the molecules 

 will not differ much from the volume into which the gas 

 is condensed when it becomes liquid, as we may consider 

 the particles of a liquid to be almost in contact. Thus the 

 volume of steam, at atmospheric pressure, is about 1700 

 times that of the water from which it is produced, or the 

 ratio of the volume of the gas to the volume occupied by 

 its constituent molecules is, in this case, nearly 1700 :1. 

 Knowing, in the case of gases, these two volumes, the size 

 of the particles of gas follows. For example, the number 

 of molecules of hydrogen gas in one cubic inch at standard 

 temperature and pressure is about 300 millions of millions 

 of millions— 300,000,000,000,000,000,000. In the case of 

 oxygen, as stated above, the velocity of the particles is 

 about 1500 feet per second, and in this gas the mean free 

 path is about ^-u'noTy inch. Thus, in one second, each 

 oxygen molecule has about 7600 million encounters with 

 other molecules. 



These enormous numbers give us a striking mental 

 picture of the jostling crowds of molecules through which 

 we move, and enable us to realize the little likelihood of 

 finding any marked difference in the relative quantities of 

 the oxygen and nitrogen particles in any given portions of 

 the air around us. 



Let us consider what happens in experiments showing 

 the diffusion of gases. Take a cylinder made of porous 

 earthenware, such as is used for tobacco pipes, or in the 

 cells of some voltaic batteries. Close it, except at one 

 point in the end, where a glass tube is to be fitted in air- 

 tight. Now put the open end of the glass tube into water, 

 while the porous cylinder remains in the air. The water 

 will rise a short distance up into the tube, owing to the 

 action of capillary forces, and thus things will remain. 



Now bring over the cylinder or jar containing hydrogen 

 (ordinary coal gas will do), and the state of affairs is very 

 different. At once air-l)ubbles are seen rising through the 

 water, they are forced out of the tube before the entering 

 hydrogen, and whenever the jar is removed so that air 

 once more surrounds the outer surface of the cylinder, 

 the water rapidly rises in the glass tube. What has 

 happened is, that first of all, when the apparatus was in 

 air, as many gas particles entered through the pores of 

 the cylinder as made their escape outwards by the same 

 means ; the pressure in the tube was the same as outside. 

 When, however, hydrogen gas was made to surround the 

 cylinder, gas entered much faster than the air could escape 

 — about four times as quickly ; thus the air was forced 

 down the tube, and up through the water in the trough. 

 When, again, the jar of gas was removed, the hydrogen 

 rapidly escaped through the porous surface, while the more 

 sluggish air entered slowly ; hence the pressure fell inside 

 the tube, and the water rose, pushed up by the pressure of 

 the atmosphere. Graham made many experiments in the 

 diffusion of gases, and reached the result mentioned above, 

 that the rates of diffusion are inversely as the square roots 

 of the densities. The above simple experiment is a striking 

 exemplification of the kinetic theory, and gives one some 

 idea of the very rapid movement the gas particles must 

 have, and how independent each one must be of 

 another. 



The viscosity of a gas is the name given to that property 

 which causes bodies moving in it to gradually come to 

 rest. It is this viscosity also which affects the flow of gas 

 through a narrow tube. When air passes through a tube 

 the layer next the tube moves slowly, or almost impercep- 

 tibly ; the succeeding layers increase in velocity till we 

 reach the axis of the tube. The measurement of the 

 viscosity of gases is important, as from a knowledge of the 

 value of this qixantity, and with the help of the mecbanical 

 theory of gases, the length of the mean free path of the 

 gas particles can be calculated. Measurements of the 

 viscosity of gases have been made by Maxwell, and also by 

 0. Meyer in Germany. The methods employed were first 

 that of observing the rate of flow of gases through tubes 

 of known dimensions imder given pressures and hence 

 deducing the gaseous friction ; and second, causing a disc 

 to vibrate in its own plane in the gas, and observing the 

 damping of its motion due to viscosity. 



Consider a stratum of gas of unit thickness — 1 centi- 

 metre — extending between two flat surfaces of indefinite 

 extent. Let one of these plane surfaces be moving 

 relatively to the other, with unit velocity — 1 c. m. per 

 second — the tangential force on either surface per unit of 

 surface — 1 square c. m. — is the measure of the viscosity. 

 Expressed otherwise, we may say that the viscosity is the 

 quantity of momentum which must be supplied per unit 

 area in unit time, in order to keep wp the unit rate of 

 change of velocity between layers a unit distance apart. 



The viscosity of a gas depends on the transfer of the 

 momentum of its particles exactly as the diffusion of the 

 gas depends on the transfer of the actual masses of the 

 particles themselves. One of the best illustrations of the 

 effect of viscosity is that given by Prof. Balfour Stewart. 



Imagine a number of rail- 



e way trains — a, h, c, <l, e — 



on parallel rails ; train a 

 ~ being at rest, // moving 



<■ slowly, c a little faster, and 



J soon,thespeedof the trains 



increasing as we mo ve away 

 "- ; — fi'om a. Suppose passen- 

 gers are continually passing 



