The system of leap years introduced by Cæsar makes the average length of a year 365.25 days, which differs by about eleven minutes from the true length of the tropical year, a difference so small that for ordinary purposes no better approximation to the true length of the year need be desired. But _any_ deviation from the true length, however small, must in the course of time shift the seasons, the vernal and autumnal equinox, to another part of the year, and the ecclesiastical authorities of mediæval Europe found here ground for objection to Cæsar's calendar, since the great Church festival of Easter has its date determined with reference to the vernal equinox, and with the lapse of centuries Easter became more and more displaced in the calendar, until Pope Gregory XIII, late in the sixteenth century, decreed another reformation, whereby ten days were dropped from the calendar, the day after March 11th being called March 21st, to bring back the vernal equinox to the date on which it fell in A. D. 325, the time of the Council of Nicæa, which Gregory adopted as the fundamental epoch of his calendar. The calendar having thus been brought back into agreement with that of old time, Gregory purposed to keep it in such agreement for the future by modifying Cæsar's leap-year rule so that it should run: Every year whose number is divisible by 4 shall be a leap year except those years whose numbers are divisible by 100 but not divisible by 400. These latter years--e. g., 1900--are counted as common years. The calendar thus altered is called Gregorian to distinguish it from the older, Julian calendar, and it found speedy acceptance in those civilized countries whose Church adhered to Rome; but the Protestant powers were slow to adopt it, and it was introduced into England and her American colonies by act of Parliament in the year 1752, nearly two centuries after Gregory's time. In Russia the Julian calendar has remained in common use to our own day, but in commercial affairs it is there customary to write the date according to both calendars--e. g., July 4/16, and at the present time strenuous exertions are making in that country for the adoption of the Gregorian calendar to the complete exclusion of the Julian one. The Julian and Gregorian calendars are frequently represented by the abbreviations O. S. and N. S., old style, new style, and as the older historical dates are usually expressed in O. S., it is sometimes convenient to transform a date from the one calendar to the other. This is readily done by the formula G = J + (N - 2) - N/4, where _G_ and _J_ are the respective dates, _N_ is the number of the century, and the remainder is to be neglected in the division by 4. For September 3, 1752, O. S., we have J = Sept. 3 N - 2 = + 15 - N/4 = - 4 ------------------ G = Sept. 14