SECT. 5.] Modes of establishing the Groups or Series. 79 



by itself is not sufficient, others are wanted as well. The 

 penny was supposed to be tossed up, as we say at random. 

 What is meant by this, and how is this process to be ideal 

 ized ? To ask this is to introduce no idle subtlety ; for it 

 would scarcely be maintained that the heads and tails would 

 get their fair chances if, immediately before the throwing, 

 we were so to place the coin in our hands as to start it 

 always with the same side upwards. The difference that 

 would result in consequence, slight as its cause is, would 

 tend in time to show itself in the results. Or, if we per 

 sisted in starting with each of the two sides alternately 

 upwards, would the longer repetitions of the same side get 

 their fair chance ? 



Perhaps it will be replied that if we think nothing what 

 ever about these matters all will come right of its own accord. 

 It may, and doubtless will be so, but this is falling back upon 

 experience. It is here, then, that we find ourselves resting on 

 the experimental assumption above mentioned, and which 

 indeed cannot be avoided. For suppose, lastly, that the 

 circumstances of nature, or my bodily or mental constitution, 

 were such that the same side always is started upwards, or 

 indeed that they are started in any arbitrary order of our 

 own ? Well, it will be replied, it would not then be a fair 

 trial. If we press in this way for an answer to such enquiries, 

 we shall find that these tacit restrictions are really nothing 

 else than a mode of securing an experimental result. They 

 are only another way of saying, Let a series of actions be 

 performed in such a way as to secure a sequence of a par 

 ticular kind, viz., of the kind described in the previous 

 chapters. 



5. An intermediate way of evading the direct appeal 

 to experience is sometimes found by defining the probability 

 of an event as being measured by the ratio which the 





