658 THE PRINCIPLES OF SCIENCE. [CHAP. 



have measured light undulations, and by several methods 

 we learn the velocity with which light travels. Since an 

 undulation of the middle green is about five ten-millionths 

 of a metre in length, and travels at the rate of nearly 

 300,000,000 of metres per second, it follows that about 

 600,000,000,000,000 undulations must strike in one 

 second the retina of an eye which perceives such light. 

 But how are we to verify such an astounding calculation 

 by directly counting pulses which recur six hundred 

 billions of times in a second? 



Discordance of Theory and Experiment. 



When a distinct want of accordance is found to exist 

 between the results of theory and direct measurement, 

 interesting questions arise as to the mode in which we can 

 account for this discordance. The ultimate explanation 

 of the discrepancy may be accomplished in at least four 

 ways as follows : 



(1) The direct measurement may be erroneous owing to 

 various sources of casual error. 



(2) The theory may be correct as 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 recommendations may be 

 made. 



If the experimental measurements are not numerous, 

 repeat them and take a more extensive mean result, the prob- 

 able accuracy of which, as regards casual errors, will increase 

 as the square root of the number of experiments. Supposing 



