it does not conflict with other probable theories, must be taken into account, as we shall see in the next book. The requisite condition of a good hypothesis, that it must admit of the deduction of facts verified in observation, must be interpreted in the widest manner, as including all ways in which there may be accordance or discordance. All our attempts at reconciliation having failed, the only conclusion we can come to is that some unknown cause of a new character exists. If the measurements be accurate and the theory probable, then there remains a residual phenomenon, which, being devoid of theoretical explanation, must be set down as a new empirical fact worthy of further investigation. Outstanding residual discrepancies have often been found to involve new discoveries of the greatest importance.
Accordance of Measurements of Astronomical Distances.
One of the most instructive instances which we can meet, of the manner in which different measurements confirm or check each other, is furnished by the determination of the velocity of light, and the dimensions of the planetary system. Roemer first discovered that light requires time to travel, by observing that the eclipses of Jupiter’s satellites, although they occur at fixed moments of absolute time, are visible at different moments in different parts of the earth’s orbit, according to the distance between the earth and Jupiter. The time occupied by light in traversing the mean semi-diameter of the earth’s orbit is found to be about eight minutes. The mean distance of the sun and earth was long assumed by astronomers as being about 95,274,000 miles, this result being deduced by Bessel from the observations of the transit of Venus, which occurred in 1769, and which were found to give the solar parallax, or which is the same thing, the apparent angular magnitude of the earth seen from the sun, as equal to 8″·578. Dividing the mean distance of the sun and earth by the number of seconds in 8m. 13s.3 we find the velocity of light to be about 192,000 miles per second.
Nearly the same result was obtained in what seems a different manner. The aberration of light is the apparent change in the direction of a ray of light owing to the composition of its motion with that of the earth’s motion round the sun. If we know the amount of aberration and the mean velocity of the earth, we can estimate that of light, which is thus found to be 191,100 miles per second. Now this determination depends upon a new physical quantity, that of aberration, which is ascertained by direct observation of the stars, so that the close accordance of the estimates of the velocity of light as thus arrived at by different methods might seem to leave little room for doubt, the difference being less than one per cent.
Nevertheless, experimentalists were not satisfied until they had succeeded in measuring the velocity of light by direct experiments performed upon the earth’s surface. Fizeau, by a rapidly revolving toothed wheel, estimated the velocity at 195,920 miles per second. As this result differed by about one part in sixty from estimates previously accepted, there was thought to be room for further investigation. The revolving mirror, used by Wheatstone in measuring the velocity of electricity, was now applied in a more refined manner by Fizeau and by Foucault to determine the velocity of light. The latter physicist came to the startling conclusion that the velocity was not really more than 185,172 miles per second. No repetition of the experiment would shake this result, and there was accordingly a discrepancy between the astronomical and the experimental results of about 7,000 miles per second. The latest experiments, those of M. Cornu, only slightly raise the estimate, giving 186,660 miles per second. A little consideration shows that both the astronomical determinations involve the magnitude of the earth’s orbit as one datum, because our estimate of the earth’s velocity in its orbit depends upon our estimate of the sun’s mean distance. Accordingly as regards this quantity the two astronomical results count only for one. Though the transit of Venus had been