In tracing out the history of human knowledge, says Dr. Lardner, we have frequently to point out with some little surprise, joined to a feeling of profound humility, the important part played by chance in the advancement of science. In searching zealously after mere trifles which, when found, are of no consequence, we frequently lay our hands on inestimable treasures. The frequency of this fact impresses the mind with the notion that some secret and unceasing power exists, in accordance with which human knowledge and science are continually progressing. It is in physical, as in moral philosophy. In our ignorance—like the dog mentioned by Æsop, which, seeing in the water the reflection of the prey it held in its mouth, dropped the substance and tried to seize the shadow—we are continually searching after trifles; but, more fortunate than the animal of whom we have been speaking, the shadow that we try to seize is often transformed into a rich treasure. We can say with every confidence that “the Providence which shapes our ends,” knows our wants better than we do ourselves, and bestows on us the things we _ought to have_ asked for instead of those we _have_ asked for. We shall find a very simple proof of this in the history of the discovery of the velocity of light. A short time after the invention of the telescope and the consequent discovery of Jupiter’s satellites, Römer, a celebrated Danish astronomer, was engaged in a series of observations, the object of which was to determine the time which one of these bodies took to revolve round its planet. The method employed by Römer was to observe the successive occultations of the satellite, and to notice the interval that elapsed between each of them. But it at last happened that the interval between the two occultations, which was about forty-five hours, became prolonged by periods of 8, 13, and 16 minutes, during that half of the year when the earth was receding from the planet, while it became proportionally cut short during the rest of the year. Römer was struck by a happy idea; he suspected instantly that the moment when he remarked the disappearance of the satellite was not always coincident with the instant when it really took place, but that it sometimes appeared to happen later—that is to say, after an interval of time sufficiently long to allow the light that had left the satellite immediately after its disappearance, to reach the eye of the observer. Hence it became evident that the farther off the earth was from the satellite, the longer was the interval of time between its disappearance and that of the arrival of the last portions of its light upon the earth; but that the moment of the disappearance of the satellite is that of the commencement of the occultation, and that the moment of the arrival of the last portions of light is that when the commencement of the occultation is observed.