THE LAW OF ERROR. 441 



If any case should arise in which the observer knows 

 the number and magnitude of the independent errors 

 which may occur, he ought certainly to calculate from the 

 Arithmetical Triangle the special Law of Error which would 

 apply. But the general law, of which we are in search, 

 is to be used in the dark, when we have no knowledge 

 whatever of the sources of error. To assume any special 

 number of causes of error is then an arbitrary proceeding, 

 and mathematicians have chosen the least arbitrary course 

 of imagining the existence of an infinite number of in- 

 finitely small errors, just as, in the inverse method of 

 probabilities, an infinite number of infinitely improbable 

 hypotheses were submitted to calculation (p. 296). 



The reasons in favour of this choice are of several 

 different kinds. 



1. It cannot be denied that there may exist infinitely 

 numerous causes of error in any act of observation. 



2. The resulting law on the hypothesis of a large finite, 

 or even a moderate finite number of causes of error, does 

 not appreciably differ from that given by the hypothesis 

 of infinity. 



3. We gain by the hypothesis of infinity a general law 

 capable of ready calculation, and applicable by uniform 

 rules to all problems. 



4. This law, when tested by comparison with extensive 

 series of observations, is strikingly verified, as will be 

 shown in a later section. 



When we imagine the existence of any large number of 

 causes of error, for instance one hundred, the numbers of 

 combinations become impracticably large, as may be seen 

 to be the case from a glance at the Arithmetical Triangle 

 (p. 208), which proceeds only up to the seventeenth line. 

 M. Que tet, by suitable abbreviating processes, succeeded 

 in calculating out a table of probability of errors on the 



