66 G. F. C. SEARLE, M.A., F.R.S., ON THE 
almost entirely new ideas as to the character of matter, and 
hence demand consideration in any account of what is known 
about the universe. Their bearing on our subject will be 
considered presently. 
§ 7. Abrupt Changes—The elements differ one from another 
by abrupt steps just as polygons of 3, 4,5 . . . sides 
differ. We cannot pass from one element to another by an 
infinite series of infinitely small steps. If we could, there 
would be no science of chemistry. The idea has been held that 
living organisms have been derived from earher forms by a 
continuous process of evolution, but nothing like this occurs 
among the elements, for there the steps are abrupt. The 
transformations of the radio-active substances appear to be due 
to abrupt changes in the number of electrified particles in the 
molecule. ‘These abrupt steps and others we shall meet in our 
survey are of great interest. Thus the abrupt changes of the 
molecules of radio-active elements warn us that deductions 
based upon observed uniformity may be unsound, even though 
the period of observation may have extended over hundreds of 
years. If we start to-day with a gramme of radium, there 
will still be half a gramme left after 1,800 years, and if we 
were to observe for this period one of the molecules forming part 
of the remaining half gramme, we should naturally conclude that 
this molecule would continue for all time “unbroken and 
unworn.” But, if we maintained our watch for another 
century, we might witness the catastrophe which results in the 
expulsion of a positively charged particle and our earlier 
conclusion would then be proved to be false. 
§ 8. The Universe as a single System—The view that all 
matter is built up of a single primordial substance is a great 
step in advance, but it does not at once replace complexity by 
simplicity, for the fact remains that the number of molecules in 
the universe is inconceivably great. You will not think the 
word inconceivable to be inappropriate in view of the estimate 
that a drop of water no larger than a grain of mustard seed 
contains enough molecules to supply each inhabitant of the 
earth with one molecule every second for many thousands of 
years. Who then shall grasp the number of molecules in the 
whole universe ? 
But the results of scientific investigation lead us to regard 
all these molecules in their vast array ‘less as 80 many separate 
entities than as forming one great and indivisible whole. One 
instance will make this clear. We believe that if there were 
only two molecules in the whole universe the force of gravita- 
