54 



KNOWLEDGE 



[Makch 1, 1893. 



research ; thougb it must be insisted on that the aotiial 

 constitution of matter is a yet impenetrated mystery, and 

 one which some able physicists consider to be quite beyond 

 the powers of man to solve. After Bernoulli's time, 

 Lesage, of Geneva, and Prevost applied the theory to 

 explain various phenomena. Herapath also worked in 

 the same field. 



In the year 1818, Dr. Joule, of worM-wide fame from 

 his researches on the dynamical theory of heat, explained 

 the pressure of gases as being due to the impact of their 

 molecules, and not only this, but he also calculated the 

 velocity which these particles must have in order to produce 

 the observed pressure. It is, however, to Clausius in 

 Germany, and to Clerk Maxwell in our own country, that 

 we chiefly owe the mathematical development of this 

 subject. These physicists, starting from the mathematical 

 theory of probability, and using a statistical method of 

 investigation, which they applied to companies of molecules, 

 arrived at results which agreed with the test of experiment, 

 and which could be applied to whole aggregates of 

 molecules existing under certain conditions, though the 

 beha\'iour of a single molecule, considered by itself, might 

 be unknown and untraceable. 



All portions of matter, whether in the sohd, liquid, or 

 gaseous state, consist of a finite number of very minute 

 parts or molecules. This particle or molecule is not 

 necessarily homogeneous throughout, but fi'om chemical 

 considerations we must suppose it to consist of two or 

 more atoms. These atoms, which together make up the 

 molecule of a substance, may consist of matter of the same 

 kind, or of a different kind. A molecule made up of 

 similar atoms forms a particle of an element, i.e., a body 

 which cannot be split up into two different sorts of 

 matter. A molecule made up of differing atoms forms 

 the smallest portion of a riiiiqiiiuniL A molecule may be 

 defined as the smallest conceivable portion of a substance 

 which can move about fi-eely by itself without its consti- 

 tuent atoms parting company. 



In solids the molecules can move with reference to each 

 other, but only with diificulty, and they are never outside 

 the influence of neighbouring molecules. Their excursions 

 from one spot are probably of the nature of vibrations. In 

 the case of liquids the constituent molecules are much 

 more free to move about amongst themselves. The 

 particles of the liquid can slide past each other, and the 

 liquid exhibits mobility — it takes the form of the vessel 

 which contains it. A molecule in a liquid can, in course 

 of time, penetrate to any part of the liquid mass, but its 

 course must be a slow one, as it will continually run 

 against other molecules, and have its path changed. 



When we come to consider gases, it is seen that here each 

 molecule leads a more independent existence. In a gas at 

 ordinary temperature and pressure, during the greater part 

 of the path of a molecule it is not in direct contact with 

 its fellows. 



As during this " free path " of the molecule it is not 

 acted on by any sensible force, it tends to move onwards in 

 a straight line. Hoon, however, it encoimters another 

 molecule, and from the collision between the two both the 

 velocity and direction of the moving molecules are altered. 

 Each starts off again in a new and different direction, 

 again in course of time to come into contact with other 

 molecules. The free motion of a molecule takes up con- 

 siderably more time than the duration of an encounter ; 

 but as the density of the gas increases there are more and 

 more gas molecules in a given space, and thus they strike 

 each other more fi-equently, the length of their undisturbed 

 path diminishes, and at length, if the gas is still further 

 condensed, it becomes a liquid in which no portion of a 



molecule's course can be called its free path ; it never gets 

 beyond the influence of its neighbours. 



In an encounter between two molecules, since the force 

 of the impact acts between the two masses, the motion of 

 the common centre of gravity of the two molecules must 

 be the same after the collision as it was before. Also it 

 follows from the principle of the conservation of energy, 

 that the velocity of each molecule relatively to their common 

 centre of gravity continues the same in magnitude but may 

 be changed in direction. 



It necessarily follows that the velocities must vary as 

 we pass from molecule to molecule. For even if we could 

 imagine all the molecules to be moving with the same 

 velocity at a given instant this velocity would soon be 

 changed by the successive encounters between the mole- 

 cules. Some of the constituent particles may have a 

 relatively very high velocity, others may be moving com- 

 paratively slowly, while most of them will have various 

 velocities intermediate between the highest and lowest. 



If the systems of moving molecules be divided into 

 groups according to the velocity which they may have at 

 the instant considered, a regular progression is observed as 

 to the number of molecules which fall into each separate 

 group. At the same time the motion of a simple molecule, 

 if it were possible to follow it, would be found to be 

 exceedingly changeable and irregular. The behaviour of 

 the groups may be stable but the individual molecules 

 making up these groups are continually changing ; a mole- 

 cule belonging to one group or another, according to its 

 velocity at a given instant, and of course belonging to 

 difl'erent groups at different parts of its career. This 

 statistical method of investigation resembles somewhat the 

 method of obtaining average characteristics of classes of 

 the community, these being made up of individuals differing 

 amongst themselves ; and the results attained are only 

 true when considered as giving broad characteristic out- 

 lines of masses of people. The distribution of the mole- 

 cules according to the speeds with which they are moving 

 is calculated by the theory of probability, and this 

 distribution is found to be of the same mathematical form 

 as that of the marks made on a target when these are 

 arranged according to their distances from the centre 

 aimed at, always supposing that the shots fired are nume- 

 rous, and that the riflemen have the same degree of sldll. 



To compare such systems of moving molecules together, 

 it is desirable to take the mean of the squares of all the 

 velocities, for the effect of a blow struck by a projectile 

 depends upon the square of its velocity. This is referred 

 to as the mean siiwiiv of the velocity, and the square I'oot 

 of this mean square is called the " velocity of mean 

 square." 



Clerk Maxwell has shown that if two sets of molecules 

 whose mass is difl'erent are in motion in the same vessel 

 they will, by continually striking against each other, 

 exchange energy until the average kinetic energy of one 

 molecule of either set is the same. 



Let Mj represent the mass of one molecule of the first 

 kind, and Mj the mass of a molecule of the second sort, 

 while Vj and V„ are equal to their respective velocities, 

 then ultimately'we shall have M, V, = = M. V„ \ 



In the case of any mass M, with a velocity V, the 

 kinetic fncri/!/ is equal to i M V-. So if we call M the mass 

 of a single molecule, and V its velocity of translation, its 

 average kinetic energy is expressed by i M V-. But this 

 is not the only energy which the molecule may possess, 

 for any given molecule (with perhaps one or two exceptions, 

 as that of mercury vapour) is made up of constituent parts, 

 it contains two or more atoms, and these may have relative 

 motions amongst themselves, and besides, the molecule as 



