Page:Encyclopædia Britannica, Ninth Edition, v. 4.djvu/745

] here given, this distinction is made by means of an accent placed over the last figure. At the reformation the epacts were given by the line D. was a ; the  accordingly took place as usual, and there was no interruption in the order of the epacts; the line D was employed till. In the omission of the  rendered it necessary to diminish the epacts by unity, or to pass to the line C. In  the solar equation again occurred, in consequence of which it was necessary to descend one line to have the epacts diminished by unity; but in  the lunar equation also occurred, the anticipation of the  having amounted to a day: the  accordingly happened a day earlier, which rendered it necessary to take the epacts in the next higher line. There was, consequently, no alteration; the two equations destroyed each other. The line of epacts belonging to is therefore C. In 1900 the solar equation occurs, after which the line is B.  2000 is a, and there is no alteration. In 2100 the equations again occur together and destroy each other, so that the line B will serve three centuries, from 1900 to 2200. From that year to 2300 the line will be A. In this manner the line of epacts belonging to any given century is easily found, and the method of proceeding is obvious. When the solar equation occurs alone, the line of epacts is changed to the next lower in the table; when the lunar equation occurs alone, the line is changed to the next higher; when both equations occur together, no change takes place. In order that it may be perceived at once to what centuries the different lines of epacts respectively belong, they have been placed in a column on the left hand side of the following table.    

—Extended Table of Epacts.

   The use of the epacts is to show the days of the, and consequently the 's age on any day of the year. For this purpose they are placed in the calendar (TableIV.) along with the days of the month and dominical letters, in a retrograde order, so that the stands beside the 1st of, 29 beside the 2nd, 28 beside the 3rd, and so on to 1, which corresponds to the 30th. After this comes the, which corresponds to the 31st of , then 29, which belongs to the 1st of , and so on to the end of the year. The reason of this distribution is evident. If the last of any year ends, for example, on the 2nd of, the  falls on the 3rd; and the 's age on the 31st, or at the end of the year, is twenty-nine days. The epact of the following year is therefore twenty-nine. Now that having commenced on the 3rd of, and consisting of thirty days, will end on the 1st of. The 2nd of is therefore the day of the, which is indicated by the epact twenty-nine. In like manner, if the fell on the 4th of, the epact of the following year would be twenty-eight, which, to indicate the day of next , must correspond to the 3rd of. When the epact of the year is known, the days on which the occur throughout the whole year are shown by Table IV., which is called the Gregorian Calendar of Epacts. For example, the golden number of, is $\left ( \frac{\scriptstyle 1832+1}{\scriptstyle\text {19}} \right )_r $ = 9,|undefined and the epact, as found in TableIII., is twenty-eight. This epact occurs at the 3rd of, the 2nd of , the 3rd of , the 2nd of , the 1st of , &c.; and these days are consequently the days of the ecclesiastical in. The  generally take place one or two days, sometimes even three days, earlier than those of the calendar.|undefined