36 PHILOSOPHICAL TRANSACTIONS. [aNNO 1750. 



But the regulating these things for those who use the Gregorian account, is 

 an affair of more intricacy ; and for them it will require more consideration to 

 determine, when the epacts are to be more than ordinarily augmented, and at 

 what, times they are to continue in their usual course ; nay, to know when they 

 are not only not to be extraordinarily augmented, but also when they are to be 

 diminished by a unit, by increasing one of them by 10 only instead of 11 as 

 usual : and this happens much oftener with the Gregorians, than the increasing 

 one of them by 12 instead of 1 1. For in every Gregorian solar year, whose date 

 consists of any number of entire hundreds not divisible by 4, it is supposed that 

 the equinox has anticipated one whole day ; and therefore 1 day, that which 

 ought to be the intercalary one, is omitted ; and consequently the preceding 

 solar year, where one day was lost, exceeded the lunar year by lO days only, 

 instead of 1 1 . 



In order therefore to adapt the before-mentioned rule to the Gregorian ac- 

 count, and to know in what years the epacts should either be extraordinarily 

 augmented or diminished, and the golden numbers should either be set back- 

 wards or forwards in the calendar ; the following rules and directions must be 

 observed. 



First, that in the years 1800, 2100, 2700, 3000, &c. where the number of 

 entire hundreds is divisible by 3, but not by 4, the Gregorian solar, as well as 

 the lunar year, will have lost a day ; and consequently the difference between 

 them will be the same as usual : therefore in those years there must be no alter- 

 ation, either in the epacts or the golden numbers ; but the former must go on 

 in the same manner, and the latter stand prefixed to the same days in the calen- 

 dar, for another, as they did for the last 100 years. 



2dly. The like will happen in the years 2000, 2800, 3200, &c. where the 

 number of entire hundreds is divisible by 4, but not by 3 : for neither the Gre- 

 gorian solar nor the lunar year is to be altered ; and therefore the epacts must 

 go on, and the golden numbers stand, as they did before. 



But 3dly, in the years 2400, and 36oo, whose number of entire hundreds is 

 divisible both by 3 and 4, the Gregorian solar year goes on as usual, and the 

 lunar year has lost a day. The difference therefore between them being 12, 

 the epact of the preceding year must be augmented by that number instead of 

 11, in order to form the epact of the then present year; by which a new set of 

 epacts will be introduced, exceeding their precedent corresponding epacts by 1 : 

 and the golden numbers must be set 1 day back in the calendar. 



4thly and lastly, in the years IQOO, 2200, 2300, 2500, &c. where the num- 

 ber of hundreds is divisible neither by 3 nor 4 ; the Gregorian solar. year having 

 lost one day, and the lunar none, the difference between them being only 1 o ; 



