to the heat developed by the sudden compression of the air in the passage of the wave, this heat having the effect of increasing the elasticity of the air and accelerating the impulse. It is now perceived that this discrepancy really involves the doctrine of the equivalence of heat and energy, and it was applied by Mayer, at least by implication, to give an estimate of the mechanical equivalent of heat. The estimate thus derived agrees satisfactorily with direct determinations by Dr. Joule and other physicists, so that the explanation of the residual phenomenon which exercised Newton’s ingenuity is now complete, and forms an important part of the new science of thermodynamics.
As Herschel observed, almost all great astronomical discoveries have been disclosed in the form of residual differences. It is the practice at well-conducted observatories to compare the positions of the heavenly bodies as actually observed with what might have been expected theoretically. This practice was introduced by Halley when Astronomer Royal, and his reduction of the lunar observations gave a series of residual errors from 1722 to 1739, by the examination of which the lunar theory was improved. Most of the greater astronomical variations arising from nutation, aberration, planetary perturbation were discovered in the same manner. The precession of the equinox was perhaps the earliest residual difference observed; the systematic divergence of Uranus from its calculated places was one of the latest, and was the clue to the remarkable discovery of Neptune. We may also class under residual phenomena all the so-called proper motions of the stars. A complete star catalogue, such as that of the British Association, gives a greater or less amount of proper motion for almost every star, consisting in the apparent difference of position of the star as derived from the earliest and latest good observations. But these apparent motions are often due, as explained by Baily,12 the author of the catalogue, to errors of observation and reduction. In many cases the best astronomical authorities have differed as to the very direction of the supposed proper motion of stars, and as regards the amount of the motion, for instance of α Polaris, the most different estimates have been formed. Residual quantities will often be so small that their very existence is doubtful. Only the gradual progress of theory and of measurement will show clearly whether a discrepancy is to be referred to casual errors of observation or to some new phenomenon. But nothing is more requisite for the progress of science than the careful recording and investigation of such discrepancies. In no part of physical science can we be free from exceptions and outstanding facts, of which our present knowledge can give no account. It is among such anomalies that we must look for the clues to new realms of facts worthy of discovery. They are like the floating waifs which led Columbus to suspect the existence of the new world.