of these numbers. They boldly assume that the discrepancies are due to experimental errors, and they are justified by the fact that the more elaborate and skilful the researches on the subject, the more nearly their assumption is verified. Potassium is the only element whose atomic weight has been determined with great care, but which has not shown an approach to a simple ratio with the other elements. This exception may be due to some unsuspected cause of error.5 A similar assumption is made in the law of definite combining volumes of gases, and Brodie has clearly pointed out the line of argument by which the chemist, observing that the discrepancies between the law and fact are within the limits of experimental error, assumes that they are due to error.6
Faraday, in one of his researches, expressly makes an assumption of the same kind. Having shown, with some degree of experimental precision, that there exists a simple proportion between quantities of electrical energy and the quantities of chemical substances which it can decompose, so that for every atom dissolved in the battery cell an atom ought theoretically, that is without regard to dissipation of some of the energy, to be decomposed in the electrolytic cell, he does not stop at his numerical results. “I have not hesitated,” he says,7 “to apply the more strict results of chemical analysis to correct the numbers obtained as electrolytic results. This, it is evident, may be done in a great number of cases, without using too much liberty towards the due severity of scientific research.”
The law of the conservation of energy, one of the widest of all physical generalisations, rests upon the same footing. The most that we can do by experiment is to show that the energy entering into any experimental combination is almost equal to what comes out of it, and more nearly so the more accurately we perform the measurements. Absolute equality is always a matter of assumption. We cannot even prove the indestructibility of matter; for were an exceedingly minute fraction of existing matter to vanish in any experiment, say one part in ten millions, we could never detect the loss.