456 THE PRINCIPLES OF SCIENCE. 



for the elimination of the error. As Flamsteed says <i, ' Om 

 good instrument is of as much worth as a hundred in- 

 different ones/ But an instrument is good or bad only in 

 a comparative sense, and no instrument gives invariable 

 and truthful results. Hence we must always ultimately 

 fall back upon general probabilities for the selection of the 

 final mean, when our other precautions are exhausted. 



Very difficult questions sometimes arise when one or 

 more results of a method of experiment diverge widely 

 from the mean of the rest. Are we or are we not to ex- 

 clude them in adopting the supposed true mean result of 

 the method. The drawing of a mean result rests, as I 

 have frequently explained, upon the assumption that every 

 error acting in one direction will probably be balanced by 

 other errors acting iri an opposite direction. If then we 

 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 

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

 tegral quantity. These are errors which 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 long 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 divergent numbers altogether. When results 

 come sometimes too great or too small in a regular 

 manner, we should suspect that some part of the instru- 

 ment slips through a definite space, or that a definite 

 cause of error enters at times, and not at others. We 

 <i Baily, ' Account of Flamsteed/ p. 56. 



