at a determination of the same physical quantity in several distinct modes it is often a delicate matter to decide which result is most reliable, and should be used for the indirect determination of other quantities. For instance, Joule’s and Thomson’s ingenious experiments upon the thermal phenomena of fluids in motion2 involved, as one physical constant, the mechanical equivalent of heat; if requisite, then, they might have been used to determine that important constant. But if 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 determining 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 theoretical 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 (pp. 296–99), are cases in point; but many others might be quoted where direct verification seems impossible. Newton and subsequent physicists 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