As matters stand at present, the majority of astronomers would probably consider that these secular perturbations are not yet known with an exactness sufficient to render this method superior to the others that have been named—perhaps as yet not even their rival. Leverrier, on the other hand, himself puts such confidence in it that he declined to sanction or coöperate in the operations for observing the recent transit of Venus, considering all labor and expense in that direction as merely so much waste.
But, however the case may be now, there is no question that as time goes on, and our knowledge of the planetary motions becomes more minutely precise, this method will become continually and cumulatively more exact, until finally, and not many centuries hence, it will supersede all the others that have been described. The parallax of the sun, determined by Leverrier in this method, in 1872, comes out 8.86".
The last of the methods mentioned in the synopsis given on page 405 is interesting as an example of the manner in which the sciences are mutually connected and dependent. Before the experiments of Fizeau in 1849, and of Foucault a few years later, our knowledge of the velocity of light depended on our knowledge of the dimensions of the earth's orbit: it had been found by astronomical observations upon the eclipses of Jupiter's satellites that light occupied a little more than 16 minutes in crossing the orbit of the earth, or about 8 minutes in coming from the sun; and hence, supposing the sun's distance to be 95,600,000 miles, as was long believed, the velocity of light must be about 192,000 miles per second; thus optics was indebted to astronomy for this fundamental element. But when Foucault in 1862 announced that, according to his unquestionably accurate experiments, the velocity of light could not be much more than 186,000 miles per second, the obligation was returned, and the suspicions as to the received value of the sun's parallax, which had been raised by the lunar researches of Hansen and Leverrier, were changed into certainty. The most recent experimental determinations of the velocity of light by Cornu in 1873-'74 fix the solar parallax between 8.80" and 8.85", according as we use Peters's "constant of aberration" or Delambre's value of the "equation of light," which is the name given to the time required for light to traverse the interval between the sun and the earth.
Collecting all the evidence at present attainable, it would seem that the solar parallax cannot differ much from 8.86", though it may be as much as 0.04" greater or smaller; this would correspond, as has
by the square of the number of sidereal months in a year, and by the ratio between the masses of the sun and earth. It is to be noted, however, that T and t are the periods of the earth and moon, as they would be if wholly undisturbed in their motions, and hence differ slightly from the periods actually observed—the differences are small, but somewhat troublesome to calculate with precision.