THE EXACT MEASUREMENT OF PHENOMENA. 337 



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 sideral day 

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

 hundred millionth part, 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 u , 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 astronomers ; 

 Tycho, for instance, detected the slow diminution of the 

 obliquity of the> earth's axis, by the comparison of ob- 

 servations at long intervals. Living astronomers use the 

 method as much as earlier ones ; but so superior in ac- 

 curacy are all observations taken during the last hundred 

 years to all previous ones, that it is often found pre- 

 ferable to take a shorter interval, rather than incur the 

 risk of greater instrumental errors in the earlier observa- 

 tions. 



u Montucla, 'Histoire des Mathematiques,' vol. i. p. 258. 



z 



