416 THE PRINCIPLES OF SCIENCE. 



made a number of measurements which are equally good 

 in his opinion, and it is quite apparent that in using an 

 instrument or apparatus of considerable complication the 

 observer will not necessarily be able to judge whether 

 slight causes have affected its operation or not. 



In this question, as indeed throughout inductive logic, 

 we deal only with probabilities. There is no infallible 

 mode of arriving at the absolute truth, which lies beyond 

 the reach of human intellect, and can only be the distant 

 object of our long continued and painful approximations. 

 Nevertheless there is a mode pointed out alike by common 

 sense and the highest mathematical reasoning, which is 

 more likely than any other, as a general rule, to bring us 

 near the truth . The apia-rov jmerpov, or the aurea mediocritas, 

 was highly esteemed in the ancient philosophy of Greece 

 and Rome ; but it is not probable that any of the ancients 

 should have been able clearly to analyse and express the 

 reasons why they advocated the mean as the safest course. 

 But in the last two centuries this apparently simple 

 question of the mean has been found to afford a field for 

 the exercise of the utmost mathematical skill. Roger 

 Cotes, the editor of the ' Principia/ appears to have had 

 some insight into the value of the mean ; but profound 

 mathematicians such as De Moivre, Daniel Bernoulli!, La- 

 place, Lagrange, Gauss, Quetelet, De Morgan, Airy, Leslie, 

 Ellis and others have hardly exhausted the subject. 



Several uses of the Mean Result. 



The elimination of errors of unknown sources, is almost 

 always accomplished by the simple arithmetical process 

 of taking the mean, or, as it is often called, the average 

 of several discrepant numbers. To take an average is to 

 add the several quantities together, and divide by the 

 number of quantities thus ndded, which gives a quotient 



