March 4, 187 5 J 



NA TURE 



157 



ON THE DYNAMICAL EVIDENCE OF THE 

 MOLECULAR CONSTITUTION OF BODIES* 



■^ITHEN any phenomenon can be described as an example of 

 some general principle whicli is applicable to other phe- 

 nomena, that phenomenon is said to be explained. Explanations, 

 however, are of very various orders, according to the degree of 

 generality of the principle which is made use of. Thus the per- 

 son who first observed the effect of throwing water into a fire 

 would feel a certain amount of mental satisfaction when he 

 found that the results were always similar, and that they did not 

 depend on any temporary and capricious antipathy between the 

 water and the fire. This is an explanation of the lowest order, 

 in which the class to which the phenomenon is referred consists 

 of other phenomena which can only be distinguished from it by 

 the place and time of their occurrence, and the principle involved 

 is the very general one that place and time are not among the 

 conditions which determine natural processes. On the other 

 hand, when a physical phenomenon can be completely described 

 as a change in the configuration and motion of a material sys- 

 tem, the dynamical explanation of that phenomenon is said to be 

 complete. We cannot conceive any further explanation to be 

 either necessary, desirable, or possible, for as soon as we know 

 what is meant by the words configuration, motion, mass, and 

 force, we see that the ideas which they represent are so elemen- 

 tary that they cannot be explained by means of anything else. 



The phenomena studied by chemists are, for the most part, 

 such as have not received a complete dynamical explanation. 



Many diagrams and models of compound molecules have 

 been constructed. These are the records of the efforts of che- 

 mists lo imagine configurations of material systems by the 

 geometrical relations of which chemical phenomena may be 

 illustrated or explained. No chemist, however, professes to see 

 in these diagrams anything more than symbolic representations 

 of the various degrees of closeness with which the different com- 

 ponents of the molecule are boimd together. 



In astronomy, on the other hand, the configurations and mo- 

 tions of the heavenly bodies are on such a scale that we can 

 ascertain them by direct^observation. Newton proved that the 

 observed motions indicate a continual tendency of all bodies to 

 approach each other, and the doctrine of universal gravitation 

 which he established not only explains the observed motions of 

 our system, but enables us to calculate the motions of a system 

 in which the astronomical elements may have any values what- 

 ever. 



When we pass from'astronomical to electrical science, we can 

 still observe the configuration and motion of electrified bodies, 

 and thence, following the strict Newtonian path, deduce the 

 forces with which they act on each other ; but these forces are 

 found to depend on the distribution of what we call electricity. 

 To form what Gauss called a " constrairbar Vorstellung " of the 

 invisible process of electric action is the great desideratum in this 

 part of science. 



In attempting the extension'of dynamical' methods to the 

 explanation of chemical phenomena, we have to form an idea of 

 the configuration and motion of a number of material systems, 

 each of which is so small that it cannot be directly observed. 

 We have, in fact, to .determine, from the observed external 

 actions of an unseen piece of machinery, its internal construction. 



The method which has been for the most part employed in 

 conducting such inquiries is that of forming an hypothesis, and 

 calculating what would happen if the hypothesis were true. If 

 these results agree with the actual phenomena, the hypothesis is 

 said to be verified, so long, at least, as some one else does not 

 invent another hypothesis which agrees still better with the 

 phenomena. 



The reason why so many of our physical theories have been 

 built up by the method of hypothesis is that the speculators have 

 not been provided with methods and terms sufficiently general 

 to express the results of their induction in its early stages. 

 They were thus compelled either to leave their ideas vague 

 and therefore useless, or to present them in a form the details of 

 which could be supplied only by the illegitimate use of the 

 imagination. 



In the meantime the mathematicians, guided by that instinct 

 which teaches them to store up for others the irrepressible secre- 

 tions of then- own minds, had developed with the utmost gene- 

 rality the dynamical theory of a material system. 



Of ill hypotheses as to the constitution of bodies, that is surely 

 the most warrantable which assumes no more than that they are 

 material systems, and proposes to deduce from the observed 

 phenomena just as much information about the conditions and 

 connections of the material system as these phenomena can 

 legitimately funiish. 



When examples of this method of physical specidation have 

 been properly set forth and explained, we shall hear fewer com- 

 plaints of the looseness of the reasoning of men of science, and 

 the method of inductive philosophy will no longer be derided as 

 mere guess-work. 



It is only a small part of the theory of the constitution of 

 bodies which has as yet been reduced to the form of accurate 

 deductions from known facts. To conduct the operations of 

 science in a perfectly legitimate manner, by means of methodised 

 experiment and strict demonstration, requires a strategic skill 

 which we must not look for, even among those to whom science 

 is most indebted for original observations and fertile suggestions. 

 It does not detract from the merit of the pioneers of science that 

 their advances, being made on unknown ground, are often cut 

 off, for a time, from that system of communications with an esta- 

 blished base of operations, which is the only security for any per- 

 manent extension of science. 



In studying the constitution of bodies we are forced from the 

 very beginning to deal with particles which we cannot observe. 

 For whatever may be our ultimate conclusions as to molecules 

 and atoms, we have experimental proof that bodies may be 

 divided into parts so small that we cannot perceive them.] 



Hence, if we are careful to remember that the word particle 

 means a small part of a body, and that it does not involve any 

 hypothesis as to the ultimate divisibility of matter, we may con- 

 sider a body as made up of particles, and we may also assert 

 that in bodies or parts of bodies of measurable dimensions, the 

 number of particles is very great indeed. 



The next thing required is a dynamical method of studying a 

 material system consisting of an immense number of particles, 

 by forming an idea of their configuration and motion, and of 

 the forces acting on the particles, and deducing from the dyna- 

 mical theory those phenomena whicli, though depending on the 

 configuration and motion of the invisible particles, are capable 

 of being observed in visible portions of the system. 



The dynamical principles necessary for this study were deve- 

 loped by the fathers of dynamics, from Galileo and Newton to 

 Lagrange and Laplace ; but the special adaptation of these 

 principles to molecular studies has been to a great extent the 

 work of Prof. Clausius of Bonn, who has recently laid us under 

 still deeper obligations by giving us, in addition to the results of 

 his elaborate calculations, a new dynamical idea, by the aid of 

 which I hope we shall be able to establish several important 

 conclusions without much symbolical calculation. 



The equation of Clausius, to which I must now call your 

 attention, is of the following form : — 



pV=iT-l-S.-S.{kR'-)- 



Here / denotes the pressure of a fluid, and V the volume of 

 the vessel which contains it. The product / V, in the case of 

 gases at constant temperature, remains, as Boyle's Law tells us, 

 nearly constant for different volumes and pressures. This 

 member of the equation, therefore, isthe product of two quan- 

 tities, each of which can be directly measured. 



The other member of the equation consists of two terms, the 

 first depending on the motion of the particles, and the second on 

 the forces with which they act on each other. 



The quantity T is the kinetic energy of the system, or, in 

 other words, that part of the energy which is due to the motion 

 of the parts of the system. 



The kinetic energy of a particle is half the product of its 

 mass into the square of its velocity, and the kinetic energy of 

 the system is the sum of the kinetic energy of its parts. 



In the second term, r is the distance between any two particles, 

 and A' is the attraction between them. (If the force is a repul- 

 sion or a pressure, R is to be reckoned negative.) 



The quantity \ K r, or half the product of the attraction 

 into the distance across which the attraction is exerted, is defined 

 by Clausius as the virial of the attraction. (In the case of 

 pressure or repulsion, the virial is negative. ) 



The importance of this quantity was first pointed out by 

 Clausius, who, by giving it a name, lias greatly facilitated the 

 application of his method to physical exposition. 



The virial of the system is the sum of the virials belonging to 

 every pair of particles which exist in the system. This is ex- 



