ACCORDANCE OF QUANTITATIVE THEORIES, <bc. 199 



explanation of the discrepancy may be accomplished in 

 any one of at least four distinct ways, as follows : 



(1) The direct measurement may be erroneous owing to 

 various sources of casual error. 



(2) The theory may be correct so far as regards the 

 general form of the supposed laws, but some of the con- 

 stant numbers or other quantitative data employed in the 

 theoretical calculations may be inaccurate. 



(3) The theory may be false, in the sense that the 

 forms of the mathematical equations assumed to express 

 the laws of nature are incorrect. 



(4) The theory and the involved quantities may be 

 approximately accurate, but some regular unknown cause 

 may have interfered, so that the divergence may be re- 

 garded as a residual effect representing possibly a new 

 and interesting phenomenon. 



No precise rules can be laid down as to the best mode 

 of proceeding to explain the divergence, and the experi- 

 mentalist will have to depend upon his own insight and 

 knowledge ; but the following general recommendations 

 may perhaps be made. 



In the first place, if the experimental measurements are 

 not numerous, repeat them and take a more extensive 

 mean result, the probable accuracy of which, as regards 

 freedom from casual errors of experiment, will increase as 

 the square root of the number of experiments. Supposing 

 that no considerable modification of the result is thus 

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

 seated and constant source of error in our method of 

 measurement. The next resource will be to change the 

 size and form of the apparatus employed, and to introduce 

 various modifications in the materials employed or in the 

 course .of procedure, in the hope, as before explained 

 (vol. i. p. 462), that some cause of constant error may thus 

 be removed. If the inconsistency with theory still re- 



