392 THE PRINCIPLES OF SCIENCE. [chap. 



have frequently explained, upon tbe assumption that every 

 error acting in one direction will probably be balanced by 

 other errors acting in an opposite direction. If then \ve 

 know or can possibly discover any causes of error not 

 agreeing with this assumption, we shall be justified in 

 excluding results which seem to be affected by this cause. 

 In reducing large series of astronomical observations, it is 

 not uncommon to meet with numbers differing from others 



o 



by a whole degree or half a degree, or some considerable in- 

 tegral quantity. These are errors v/hich could hardly arise 

 in the act of observation or in instrumental irregularity ; 

 but they might readily be accounted for by misreading 

 of figures or mistaking of division marks. It would be 

 absurd to trust to chance that such mistakes would 

 balance each other in the loncj run, and it is therefore better 

 to correct arbitrarily the supposed mistake, or better still, 

 if new observations can be made, to strike out the diver- 

 gent numbers altogether. When results come sometimes 

 too great or too small in a regular manner, we should 

 suspect that some part of the instrument slips through a 

 definite space, or that a definite cause of error enters at 

 times, and not at others. We should then make it a point 

 of prime importance to discover the exact nature and 

 "amount of such an error, and either prevent its occurrence 

 for the future or else introduce a corresponding correction. 

 In many researches the whole difficulty will consist in 

 this detection and avoidance of sources of error. Professor 

 Eoscoe found that the presence of phosphorus caused 

 serious and almost unavoidable errors in the determination 

 of the atomic weight of vanadium.^ Herschel, in reducing 

 his observations 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 reflector telescopes, and after a careful in- 

 vestigation was obliged to be contented with introducing 

 a correction experimentally determined.^ 



Wlien observations are sufficiently numerous it seems 

 desirable to project the apparent errors into a curve, and 

 then to observe whether this curve exhibits the symmet- 



1 Bakerian Lecture, Philoi'ophical 2'ransactions (1868), vol. clviii. 

 p. 6. 



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



