260 ON MB STONE'S EXPLANATION OF THE LARGE AND [31 



The difference between the Right Ascensions of the two bodies at any 

 moment is called the Equation of Time. 



The instant of Mean Noon is determined by the transit of this imaginary 

 Mean Sun over the meridian of a given place just as the instant of 

 Apparent Noon is determined by the transit of the true Sun over the 

 same meridian. 



Hence, the mean time, according to the definition of it above given, 

 may be determined by observation of the transit of the true Sun over the 

 meridian, subject only to the small error to which all transit observations 

 are liable, and also to the extremely small error which is possible in the 

 theoretical expression for the equation of time. When this mode of deter- 

 mining the mean time is employed, no accumulation of error in proportion 

 to the interval of time from a given epoch is possible. 



If, as it is frequently convenient to do, we wish to determine the mean 

 solar time by means of the sidereal time supposed to be known, without 

 having to make a transit observation of the Sun, we must employ the 

 sidereal time at mean noon calculated from the proper formula or from 

 the Solar Tables. This sidereal time at mean noon is equal to the Sun's 

 mean longitude at mean noon corrected by the equation of the equinoxes 

 in Right Ascension. 



In order to find the mean time correctly in this way it is necessary to 

 employ the correct value of the Sun's mean longitude, and any error in 

 the assumed value of this quantity will produce an equivalent error in the 

 mean time deduced. 



Any such error can be at once checked and corrected by observation 

 of the Sun's transit over the meridian. 



If we wilfully refuse to check our results by solar observations, the 

 error in the determination of the mean time by means of the sidereal time 

 would, no doubt, increase in proportion to the interval of tune from a 

 certain epoch. Practically, however, it would be intolerable to use Solar 

 Tables which were grossly erroneous, and long before the error of time 

 became important the tables would be replaced by more accurate ones. 



For many years previously to 1864 Bessel's formula had been employed 

 in the Nautical Almanac for the calculation of the sidereal time at Green- 

 wich mean noon. 



