200 THE PRINCIPLES OF SCIENCE. 



mains unreduced we may attempt to invent some widely 

 different mode of arriving at the same physical quantity, 

 so that we may be almost sure that the same cause of 

 error will not affect both the new and old results. In 

 some cases it is possible to find five or six essentially 

 different modes of arriving at the same determination. 



Supposing that the discrepancy still exists we may well 

 begin to suspect that our direct measurements are correct, 

 but that the data employed in the theoretical calculations 

 are inaccurate. We must now review the grounds on 

 which these data depend, consisting as they must ulti- 

 mately do of direct measurements. A comparison of the 

 various recorded results will show the degree of proba- 

 bility attaching to the mean result employed ; and if there 

 is any ground for imagining the existence of error, we 

 should repeat the observations, and vary the forms of 

 experiment just as in the case of the previous direct 

 measurements. The continued existence of the discre- 

 pancy must show that we have not really attained to a 

 complete acquaintance with the theory of the causes in 

 action, but two different cases still remain. We may have 

 misunderstood the action of those causes which do exist, 

 or we may have overlooked the existence of one or more 

 other causes. In the first case our hypothesis appears to be 

 wrongly chosen and inapplicable ; but whether we are to 

 reject it will depend upon whether we can form any other 

 hypothesis which yields a more accurate accordance. The 

 probability of an hypothesis, it will be remembered (vol. i. 

 p. 279), is to be judged entirely by the probability that if 

 the supposed causes exist the observed result follows ; 

 but as there is now very little probability of reconciling 

 the original hypothesis with our direct measurements the 

 field is open for new hypotheses, and any one which gives 

 a closer accordance with measurement will so far have 

 claims to attention. Of course we must never estimate 



