xiii.] MEASUREMENT OF PHENOMENA. 289 



without error of juxtaposition, which is especially thy 

 case with the motions of the earth and heavenly bodies. 

 In determining the length of the sidereal day, we deter- 

 mine the ratio between the earth's revolution round the 

 sun, and its rotation on its own axis. We might ascertain 

 the ratio by observing the successive passages of a star 

 across the zenith, and comparing the interval by a good 

 clock with that between two passages of the sun, the 

 difference being due to the angular movement of the 

 earth round the sun. In such observations we should 

 have an error of a considerable part of a second at each 

 observation, in addition to the irregularities of the clock. 

 But the revolutions of the earth repeat themselves day 

 after day, and year after year, without the slightest in- 

 terval between the end of one period and the beginning 

 of another. The operation of multiplication is perfectly 

 performed for us by nature. If, then, we can find an obser- 

 vation of the passage of a star across the meridian a hun- 

 dred years ago, that is of the interval of time between 

 the passage of the sun and the star, the instrumental 

 errors in measuring this interval by a clock and telescope 

 may be greater than in the present day, but will be 

 divided by about 36,524 days, and rendered excessively 

 small. It is thus that astronomers have been able to 

 ascertain the ratio of the mean solar to the sidereal day 

 to the 8th place of decimals (1-00273791 to i), or to the 

 hundred millionth pait, probably the most accurate result 

 of measurement in the whole range of science. 



The antiquity of this mode of comparison is almost as 

 great as that of astronomy itself. Hipparchus made the 

 first clear application of it, when he compared his own 

 observations with those of Aristarchus, made 145 years 

 previously, and thus ascertained the length of the year. 

 This calculation may in fact be regarded as the earliest 

 attempt at an exact determination of the constants of 

 nature. The method is the main resource of astrono- 

 mers; Tycho, for instance, detected the slow diminution 

 of the obliquity of the earth's axis, by the comparison 

 of observations at long intervals. Living astronomers 

 use the method as much as earlier ones ; but so superior 

 in accuracy are all observations taken during the last 

 hundred years to all previous ones, that it is often 



