INTRODUCTORY LECTURE ON EXPERIMENTAL PHYSICS. 253 



Calculus, which is the appropriate expression of the relations of continuous 

 quantity. 



The theory of atoms and void leads us to attach more importance to the 

 doctrines of integral numbers and definite proportions ; but, in applying dynamical 

 principles to the motion of immense numbers of atoms, the limitation of our 

 faculties forces us to abandon the attempt to express the exact history of each 

 atom, and to be content with estimating the average condition of a group of 

 atoms large enough to be visible. This method of dealing with groups of atoms, 

 which I may call the statistical method, and which in the present state of our 

 knowledge is the only available method of studying the properties of real bodies, 

 involves an abandonment of strict dynamical principles, and an adoption of the 

 mathematical methods belonging to the theory of probability. It is probable 

 that important results will be obtained by the application of this method, which 

 is as yet little known and is not familiar to our minds. If the actual history 

 of Science had been different, and if the scientific doctrines most familiar to 

 us had been those which must be expressed in this way, it is possible that 

 we might have considered the existence of a certain kind of contingency a self- 

 evident truth, and treated the doctrine of -philosophical necessity as a mere 

 sophism. 



About the beginning of this century, the properties of bodies were investi- 

 gated by several distinguished French mathematicians on the hypothesis that 

 they are systems of molecules in equilibrium. The somewhat unsatisfactory nature 

 of the results of these investigations produced, especially in this country, a 

 reaction in favour of the opposite method of treating bodies as if they were, 

 so far at least as our experiments are concerned, truly continuous. This method, 

 in the hands of Green, Stokes, and others, has led to results, the value of which 

 does not at all depend on what theory we adopt as to the ultimate constitution 

 of bodies. 



One very important result of the investigation of the properties of bodies 

 on the hypothesis that they are truly continuous is that it furnishes us with 

 a test by which we can ascertain, by experiments on a real body, to what 

 degree of tenuity it must be reduced before it begins to give evidence that its 

 properties are no longer the same as those of the body in mass. Investigations 

 of this kind, combined with a study of various phenomena of diffusion and of 

 dissipation of energy, have recently added greatly to the evidence in favour of 

 the hypothesis that bodies are systems of molecules in motion. 



