xxv.] ACCORDANCE OF THEORIES. 559 



that no considerable modification of the result is thus 

 effected, we may suspect the existence of more deep-seated 

 sources of error in our method of measurement. The next 

 resource will be to change the size and form of the appa- 

 ratus employed, and to introduce various modifications in 

 the materials employed or the course of procedure, in the 

 hope (p. 396) that some cause of constant error may thus 

 be removed. If the inconsistency with theory still remains 

 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 

 begin to suspect that our direct measurements are correct, 

 and 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 

 recorded data will show the degree of probability 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 con- 

 tinued existence of the discrepancy must show that we 

 have not 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 we know to 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 another hypothesis which 

 yields a more accurate accordance. The probability of an 

 hypothesis, it will be remembered (p. 243), is to be judged, 

 in the absence of a priori grounds of judgment, by the 

 probability that if the supposed causes exist the observed 

 result follows; but as there is now little probability of 

 reconciling the original hypothesis with our direct measure- 

 men L'3 the field is open for new hypotheses, and any one 

 which gives a closer accordance with measurement will so 



