CHAPTER X\1I. 



THE LAW OF ERROR. 



To bring error itself under law might seem beyond human 

 power. He who errs surely diverges from law, and it 

 might be deemed hopeless out of error to draw truth. One 

 of the most remarkable achievements of the human intel- 

 lect is the establishment of a general theory which not only 

 enables us among discrepant results to approximate to 

 the truth, but to assign the degree of probability which 

 fairly attaches to this conclusion. It would be a mistake 

 indeed to suppose that this law is necessarily the best 

 guide under all circumstances. Every measuring instru- 

 ment and every form of experiment may have its own 

 special law of error ; there may in one instrument be a 

 tendency in one direction and in another in the opposite 

 direction. Every process has its peculiar liabilities to 

 disturbance, and we are never relieved from the necessity of 

 providing against special difficulties. The general Law of 

 Error is the best guide only when we have exhausted all 

 other means of approximation, and still find discrepancies, 

 which are due to unknown causes. We must treat such 

 residual differences in some way or other, since they will 

 occur in all accurate experiments, and as their origin is 

 assumed to be unknown, there is no reason why we should 

 treat them differently in different cases. Accordingly the 

 ultimate Law of Error must be a uniform and general one. 

 It is perfectly recognised by mathematicians that in 

 each case a special Law of Error may exist, and should be 

 discovered if possible. "Nothing can be more unlikely 

 than that the errors committed in all classes of observa- 



