142 ESSAY ON PROBABILITIES. 



The experimenter, looking for a method of treating 

 observations which shall produce trustworthy results., 

 well knows that it matters nothing whether a method 

 be true or false, if demonstration can be given 

 that the consequences of the method are true. That 

 falsehood necessarily produces falsehood is a fallacy, 

 pardonable enough in everything but mathematics. 

 True reasoning on true hypotheses must necessarily 

 produce true results ; false reasoning, or false principles, 

 or both, may, and most probably will, lead to false con- 

 sequences, but may lead to the direct reverse. In 

 every part of knowledge, except mathematics, error 

 must be carefully avoided, because there is no method 

 of distinguishing between the cases in which it leads to 

 truth, and the contrary cases. But in the exact 

 sciences, the knowledge of the consequences of false- 

 hood and of those of truth are equally exact : and it is 

 possible to introduce an erroneous addition to the con- 

 ditions of a problem, to trace the consequences of such 

 error, and to annihilate them at any part of the process. 

 It is possible also to substitute for truth an erroneous 

 supposition, in such manner that the effect of successive 

 lapses of this kind shall be compensatory of each other, 

 or so that the more often the error is repeated, the nearer 

 is the result to the truth. The preceding case affords an 

 instance : let the law of error be what it may (provided 

 only that positive and negative errors are equally likely 

 and that of two errors the larger is always the less 

 probable), and let a moderately large number of observa- 

 tions be in question, and it follows that the results of the 

 real law, and those of the preceding supposition, are 

 nearly identical. Let the number of observations be 

 still larger, and the resemblance is still nearer, and so 

 on without limit. And this is true, even when the 

 law of error, as regards a single observation, or two or 

 three observations, varies to a large amount from that 

 which is used above. Consequently, for a tolerable 

 number of observations, it is absolutely indifferent 

 whether the real law of error be known, or whether 



