198 THE PRINCIPLES OF SCIENCE. 



then, they might have been used to predict or to correct 

 that most important constant. But if other more direct 

 methods of experiment give the mechanical equivalent of 

 heat with superior accuracy, then the experiments on 

 fluids will be turned to a better use in detecting and 

 assigning various quantities relating to the theory of 

 fluids. We will further consider questions of this kind 

 in succeeding sections. 



There are of course many quantities assigned on theo- 

 retical grounds which we are quite unable to verify with 

 corresponding accuracy. The thickness of a film of gold 

 leaf, the average depths of the oceans, the velocity of a 

 star's approach to or regression from the earth as inferred 

 from spectroscopic data, or other quantities indirectly 

 determined (see vol. i. pp. 345-349), might be cases in 

 point ; but many others might be quoted where direct 

 verification seems impossible. Newton and many sub- 

 sequent physicists have accurately measured the lengths 

 of light undulations, and by several distinct 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 necessarily 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 1 



Discordance of Theory and Experiment. 



When a distinct want of accordance is found to exist 

 between the results of theory and direct measurement, 

 several interesting questions may arise as to the mode in 

 which we can account for this discordance. The ultimate 



