86.] TIME. 



43 



minutes = 86 400 seconds. In theoretical mechanics the second 

 is generally used as the unit of time. 



83. To reduce mean time to apparent time, it is only neces- 

 sary to subtract from mean time the so-called equation of time, 

 whose value for any particular date is given in the Ephemeris. 



84. The relation between mean solar time and sidereal time 

 is readily found by considering that the tropical year, i.e. the 

 interval between two successive passages of the sun through 

 the mean vernal equinox, has 365.2422 mean solar days, and 

 of course just one more sidereal day. Hence i solar day 

 = 366.2422/365.2422 = 1.002738 sidereal day; in other words, 

 the sidereal day contains 86 164.1 seconds of mean time, while 

 the solar day contains 86 400 such seconds.* 



85. It will have been noticed that all these methods of 

 measuring time are ultimately based on the assumption that 

 the rotation of the earth on its axis is perfectly uniform. Obser- 

 vation shows this assumption to be true, or at least to have a 

 very high degree of approximation. 



It might be asked how we can know, without using some unit of time 

 for comparison, that the earth's rotation on its axis is uniform ; in other 

 words, that the mean solar day is constant. Our absolute unit of time 

 would seem to be obtained by reasoning in a circle. This objection is 

 not quite without foundation ; and as similar difficulties arise in the 

 case of other fundamental data of mechanics, it may be well to consider 

 the matter a little more in detail. 



86. The simplest answer is that we assume the constancy of the 

 mean solar day and find this assumption fully justified by the fact that 

 while the whole structure of the astronomical and physical sciences rests 

 on this assumption, the theoretical predictions of these sciences are 

 found to be in close agreement with the results of direct observation. 



Historically, the assumption was originally adopted on account of its 



* For further particulars see W. CHAUVENET, Spherical and practical astronomy, 

 Vol. I., p. 52 sq. and pp. 651-654; also the American Ephemeris and Nautical 

 Almanac. 



