368 



Prof. G. H. Darwin. On an Apparatus for [Dec. 15, 

 Special time.' 



Mean solar 

 time. 



O h = 



+ 0-/3) 



+ 10 h ) + O 10 



22 h = 

 23 h = 



In the column of special time it is supposed that 24 h is added or 

 subtracted, so that the result is less than 24 h . For example, if # 

 is 10, the hour column of special time will run 22 h , 23 h , O h , . . . ., 9 h , 

 10 h , ll h , . . . ., 20 h , 21 h . 



If the series of days be long x will have all integral values between 

 and 23 with equal frequency, and since has all values between 

 + J and J with equal frequency, the excess of the solar hour 

 above the nearest exact special hour (which may be called the 

 error) will have all its possible values with equal frequency. If the 

 mean solar hours be arranged in a schedule of columns headed 

 O h , l h , . . . ., 23 h of special time, each column will be subject to errors 

 which follow the same law of frequency. 



