68 Dr. W. F. G. Swann on Equipartition of 



different blocks as representing different states o£ the same 

 system. Now there is nothing a priori to tell us how the 

 points will be distributed over the region of the space con- 

 cerned. If they were distributed anything like uniformly,, 

 the law represented by (2), (3), &c. would be expected to 

 hold ; but if they are not so distributed, it is useless for us 

 to argue as to what would have been expected if they had 

 been so arranged. We must guard against a temptation to 

 expect a fortuitous distribution of the points on the basis 

 that the systems may have been chosen from pieces of 

 copper millions of miles apart, because it may be, and 

 probably would be, that it was just because the coordinates 

 were restricted in some way so as to cause the points to be 

 confined to special regions of the generalized space that we 

 should recognize the substance as copper. It will perhaps- 

 be well to probe this matter a little farther. When we think 

 of a piece of copper we are apt to picture it as distinct from 

 other elements, sodium, zinc, &c, not owing to a difference 

 in the fundamentals out of which it is composed but to the 

 fact that the electrons and so forth are describing, in the 

 atom, more or less definite paths peculiar to the element. 

 Nevertheless, in our mind's eye, we keep the sodium elec- 

 trons locked up in the sodium, and the copper electrons in 

 the copper. It is, however, possible for us to imagine the 

 various electrons of the copper dissected out and linked to- 

 gether in new configurations so as to form something else, 

 some element of lower atomic weight for example, and 

 even in the general case where we concern ourselves with 

 more general types of coordinates than those associated 

 with the centres of gravity of the electrons, the transition 

 from copper to the other element is capable of being- 

 pictured as the mere readjustment of the magnitudes of 

 these more generalized coordinates to the values or range 

 of values appropriate to the second element. It is the same 

 dynamical system which concerns us in each case, however. 

 Even though the operation of transmutation may be impos- 

 sible by dynamical evolution, the mathematical analysis on 

 which the infinite probability of the state represented by (2), 

 (3), &c is based will take cognizance of all such arrange- 

 ments, and indeed of all conceivable arrangements of the 

 coordinates. For all that the mathematics is concerned with 

 is how many coordinates there are : given this, it will make 

 no use of the fact that the substance is copper, for example,, 

 but, in estimating the probability, it will include in its 

 survey all the other possible elements, compounds, &c.,. 

 which can conceivably be produced by dissecting out the 



