74 SCIENCE AND METHOD. 



the vessel were revolving and the currents revolved 

 in circles about its axis — the case would be altered, 

 for each grain would retain its original height and 

 its original distance from the axis. 



We should arrive at the same result by picturing 

 the mixing of two liquids or of two fine powders. 

 To take a rougher example, it is also what 

 happens when a pack of cards is shuffled. At 

 each shuffle the cards undergo a permutation similar 

 to that studied in the theory of substitutions. 

 What will be the resulting permutation ? The prob- 

 ability that it will be any particular permutation (for 

 instance, that which brings the card occupying the 

 position (fi (n) before the permutation into the position 

 u), this probability, I say, depends on the habits of 

 the player. But if the player shuffles the cards long 

 enough, there will be a great number of successive 

 permutations, and the final order which results will 

 no longer be governed by anything but chance ; I 

 mean that all the possible orders will be equally 

 probable. This result is due to the great number 

 of successive permutations, that is to say, to the 

 complexity of the phenomenon. 



A final word on the theory of errors. It is a case 

 in which the causes have complexity and multiplicity. 

 How numerous are the traps to which the observer 

 is exposed, even with the best instrument. He must 

 take pains to look out for and avoid the most flagrant, 

 those which give birth to systematic errors. But 

 when he has eliminated these, admitting that he 

 succeeds in so doing, there still remain many which, 

 though small, may become dangerous by the ac- 

 cumulation of their effects. It is from these that 



