172 INDUCTION. 



whole a less departure from the ordinary course of events. 

 Yet, on such grounds as this have able writers been led to the 

 extraordinary conclusion, that nothing supported by credible 

 testimony ought ever to be disbelieved. 



5. We have considered two species of events, com- 

 monly said to be improbable ; one kind which are in no way 

 extraordinary, but which, having an immense preponderance 

 of chances against them, are improbable until they are affirmed, 

 but no longer ; another kind which, being contrary to some 

 recognised law of nature, are incredible on any amount of 

 testimony except such as would be sufficient to shake our 

 belief in the law itself. But between these two classes of 

 events, there is an intermediate class, consisting of what are 

 commonly termed Coincidences : in other words, those combi- 

 nations of chances which present some peculiar and unex- 

 pected regularity, assimilating them, in so far, to the results 

 of law. As if, for example, in a lottery of a thousand tickets, 

 the numbers should be drawn in the exact order of what are 

 called the natural numbers, 1 , 2, 3, &c. We have still to con- 

 sider the principles of evidence applicable to this case : whether 

 there is any difference between coincidences and ordinary 

 events, in the amount of testimony or other evidence necessary 

 to render them credible. 



It is certain, that on every rational principle of expecta- 

 tion, a combination of this peculiar sort may be expected quite 

 as often as any other given series of a thousand numbers ; that 

 with perfectly fair dice, sixes will be thrown twice, thrice, or 

 any number of. times in succession, quite as often in a thousand 

 or a million throws, as any other succession of numbers fixed 

 upon beforehand ; and that no judicious player would give 

 greater odds against the one series than against the other. 

 Notwithstanding this, there is a general disposition to regard 

 the one as much more improbable than the other, and as 

 requiring much stronger evidence to make it credible. Such 

 is the force of this impression, that it has led some thinkers 

 to the conclusion, that nature has greater difficulty in pro- 

 ducing regular combinations than irregular ones ; or in other 



