37] ON THE CHANGE IN THE ADOPTED UNIT OF TIME. 287 



and therefore the factor above referred to by Major- General Tennant will be 



360 + n + 360Tw ' 



whereas, according to Mr Stone's views, this factor should be 



n + Sn Sn 



n n ' 



where the difference from 1 is nearly 366 times greater than it should be. 



The same thing may be otherwise shewn thus : 



If N denote the number of mean solar days in a mean tropical year, 

 according to Bessel's determination, then N+ 1 will be the corresponding 

 number of sidereal days in the same interval. 



Consequently, the ratio of the length of a mean solar to that of a 

 sidereal day will be 



~N~ T W 



But if N + SN denote the number of mean solar days in a mean 

 tropical year, according to Le Verrier's determination, then JV'+S./V+l will 

 be the corresponding number of sidereal days in the same interval. 



And consequently the above-mentioned ratio will become 



N+SN+1_ t 1 

 N+8N 



Hence the ratio of the length of a mean solar to that of a sidereal day 

 will be changed in the ratio of 



i + 



N+SN SN 



whereas, according to Mr Stone, the ratio which measures this change would 



be 



N SN 



where, as before, the difference from 1 is nearly 366 times too great. 



