Page:Encyclopædia Britannica, Ninth Edition, v. 4.djvu/743

.] years. In the course of this long period no two years can be expressed by the same numbers in all the three cycles. Hence, when the number of any proposed year in each of the cycles is known, its number in the Julian period can be determined by the resolution of a very simple problem of the indeterminate analysis. It is unnecessary, however, in the present case to exhibit the general solution of the problem, because when the number in the period corresponding to any one year in the has been ascertained, it is easy to establish the correspondence for all other years, without having again recourse to the direct solution of the problem. We shall therefore find the number of the Julian period corresponding to of. We have already seen that the of had 10 for its number in the solar cycle, 2 in the lunar cycle, and 4 in the cycle of indiction; the question is therefore to find a  such, that when it is  by the three s 28, 19, and 15 respectively, the three s shall be 10, 2, and 4.

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Reformation of the Calendar.—The ancient calendar was founded on two suppositions, both erroneous, namely, that the year contains 365$9 x + 8⁄19$ days, and that 235 s are exactly equal to nineteen solar years. It could not therefore long continue to preserve its correspondence with the s, or to indicate the days of the with the same accuracy. About  the  had already perceived the anticipation of the es, and remarked that these phenomena then took place about three days earlier than at the time of the  of. Five centuries after the time of, the divergence of the true from the 21st of, which now amounted to seven or eight days, was pointed out by John of Sacrobosco, in a work published under the title De Anni Ratione; and by Roger Bacon, in a  De Reformatione Calendarii, which, though never , was transmitted to. These works were probably little regarded at the time; but as the errors of the calendar went on increasing, and the true length of the year, in consequence of the progress of, became better known, the project of a reformation was again revived in the ; and in  invited , the most celebrated  of the age, to , to superintend the reconstruction of the calendar. The premature death of caused the design to be suspended for the ; but in the following century numerous s appeared on the subject, among the s of which were Stöffler, Albert Pighius, John Schöner, Lucas Gauricus, and other s of celebrity. At length perceiving that the measure was likely to confer a great  on his, undertook the long-desired reformation; and having found the s of the principal  s ready to adopt his views, he issued a  in the  of  , in which he abolished the use of the ancient calendar, and substituted that which has since been received in almost all   under the name of the Gregorian Calendar or New Style. The of the system adopted by  was, or , a learned  and  of , who died, however, before its introduction; but the individual who most contributed to give the ecclesiastical calendar its present form, and who was charged with all the calculations necessary for its verification, was , by whom it was completely developed and explained in a great folio treatise of 800 pages,  in , the title of which is given at the end of this article. It has already been mentioned that the error of the Julian year was corrected in the calendar by the suppression of three s in 400 years. In order to restore the commencement of the year to the same place in the s that it had occupied at the time of the of,  directed the day following the  of, that is to say the 5th of , to be reckoned the 15th of. By this regulation the which then happened on the 11th of  was restored to the 21st. From to  the difference between the old and new style continued to be ten days; but  being a leap year in the Julian calendar, and a  in the Gregorian, the difference of the styles during the  was eleven days. was also in the new calendar, and, consequently, the difference in the  is twelve days. From 1900 to 2100 inclusive it will be thirteen days. The restoration of the to its former place in the year, and the correction of the  period, were attended with no difficulty; but  had also to adapt the lunar year to the new rule of. The lunar cycle