THE LAW OF ERROR. 457 



should then make it a point of prime importance to dis- 

 cover the exact nature and amount of such an error, and 

 either prevent its occurrence for the future or else intro- 

 duce a corresponding correction. In many researches the 

 whole difficulty will consist in this detection and avoidance 

 of sources of error. Thus Professor Roscoe found that the 

 presence of phosphorus caused serious and almost una- 

 voidable errors in the determination of the atomic weight 

 of vanadium 1 ". Sir John Herschel, in reducing his obser- 

 vations of double stars at the Cape of Good Hope, was 

 perplexed by an unaccountable difference of the angles of 

 position as measured by the Seven-feet Equatorial and 

 the Twenty-feet Keflector Telescopes, and after a careful 

 investigation was obliged to be contented with introducing 

 a correction experimentally determined 8 . 



Even the most patient and exhaustive investigations 

 will sometimes fail to disclose any reason why some results 

 diverge in an unusual and unexpected manner from others. 

 The question again recurs Are we arbitrarily to exclude 

 them 1 The answer should be in the negative as a general 

 rule. The mere fact of divergence ought not to be taken 

 as conclusive against a result, and the exertion of arbitrary 

 choice would open the way to the most fatal influence of 

 bias, and what is commonly known as the 'cooking' of 

 figures. It would amount in most cases to judging fact 

 by theory instead of theory by fact. The apparently 

 divergent number may even prove in time to be the true 

 one. It may be an exception of that peculiarly valuable 

 kind which upsets our false theories, a real exception, ex- 

 ploding apparent coincidences, and opening the way to a 

 wholly new view of the subject. To establish this position 

 for the divergent fact will of course require additional re- 

 search ; but in the meantime we should give it a fair 



r Bakerian Lecture, 'Philosophical Transactions' (1868), vol. clviii. p. 6. 

 8 ' Results of Observations at the Cape of Good Hope,' p. 283. 



