and the Sun's Distance. 553 



Foucault's experiment on the velocity of light has been 

 popularly announced as making a " revolution in astronomical 

 science." But it appears from the preceding sketch that it has 

 raised no new question in astronomy, though it may have at- 

 tracted popular attention to an old difficulty, and possibly given 

 a solution to it. The three astronomical methods present solar 

 distances which, even if we select the most trustworthy decision 

 of each, differ by three or four millions of miles — that is, by 

 3 or 4 per cent, of the whole quantity. Though the best pro- 

 ducts of the first and third methods were at one time within a 

 million of miles of each other, an increase of lunar observations, 

 and especially improvements in the lunar tables, have now 

 carried that difference up to four millions of miles. If Fou- 

 cault's experiment were allowed to give the casting vote, it would 

 decide in favour of the third method, thus making the reflection 

 of Laplace, which I have already quoted, still more memorable. 



In regard to the commonly received distance of the sun, which 

 is based upon Encke's profound discussion of all the observa- 

 tions made at the last two transits of Venus, the case stands 

 thus. Encke decides, from the weights of the observations, dis- 

 cussed in the light of the mathematical principle of least squares, 

 that the probable error of the sun's distance, as given by the 

 transits, does not exceed -^ of the whole quantity. Astrono- 

 mers have also reason to believe that the adopted value of aber- 

 ration is correct within y-J^ of the whole quantity. Moreover, 

 Foucault is confident of his determination of the velocity of light 

 within -g^j. of the whole quantity ; nay, he expects to improve 

 his instruments so as to banish all errors larger than ^L^ of the 

 whole quantity. Neither the velocity of light, aberration, nor 

 the sun's distance can be suspected cf an error to the extent of 

 3 or 4 per cent. ; and yet one at least must be wrong to this 

 degree, as the best values of the three elements are irreconcilable 

 with each other. Which shall be changed ? 



It may excite surprise in those who have heard of the accu- 

 racy of astronomy, without weighing the exact significance of 

 the word as applied to so large a subject, that there should still 

 be a lingering uncertainty, to the extent of three or four millions 

 of miles, in the sun's distance from the earth. But the error, 

 whatever it is, is propagated from the solar system into the deep- 

 est spaces which the telescope has ever traversed. The sun's 

 distance is the measuring-rod with which the astronomer metes 

 out the distances of the fixed stars and the dimensions of stellar 

 orbits. An error of 3 per cent, in the sun's distance entails an 

 error of 3 per cent, in all these other distances and dimensions. 

 Trifling as 3 per cent, may seem, the correction runs up to 

 600,000 millions of miles in the distance of the nearest fixed star ! 



