The daily morning journal and courier., 1896-01-09
CrCLE ON CYCLE.
How Professor Totten Would Preserve the
 Calendar,

Calendar Almanac is so interesting and comprehensive in its survey of time in general, and of it's fundamental ele- ments of record, that we publish it as perhaps the best review we can offer our readers Of the work in question macs with a simple key to pick out that one belonging to any year, past or fu- ture. As to the preservation of the cal endar he says as follows
 The Solar Equlnoctial, Tropical, Civ il or Calendar year is the time in which the sun returns from one Venal Equt- noX to the next, but as we have changed the origin of the year to Jan uary 1st we measure it from January list to December S1st inclusive and end ed. Its average, termed the Mean So- lar year, is what we aim to keep as a chronological measure throughout all time, past and future, just as in our watches we aim to keep the absolute value of the days at twenty-four hours each, no matter what the time or the year, or the position of the sun With reference to our zenith at noon, may be. Now it is in terms of these days which the earth accurately keeps, that we measure the calendar year at S65 days each, excepting such occasional years as may, for the preservation of the monthly dates at their proper sea- sons, be necessarily introduced at value of 366 days each.
 Julius Caesar took the value of the mean solar year at S65.25 such days: hence in the Julian system the intercal- ary day is introduced every fourth year. because 4X365.25 equals 965 plus 365 plus 365 plus 366 equals 1461 days; it's function, therefore, is Y divided by i equals the number of leap-years. The relation between this leap-period of four Julian years equals 1461 days, and the Sothic or Canicular era of 146l vague years of 365 days each, without any intercalation Gin which the Nabon- assan Cor vague) year of 365 days falls back one round Julian year0 is shown by the equation S65 25X1460 equals 365x 1461 equals ,265 days. Hence every 1462d Nabonassan year begins with it's Thoth 1st, or New-years day, at it's proper Heliacal place February 26th) on the corresponding Julian or old style year. This is nearly 1131 days late as to absolute accuracy on the extended Gregorian system, for 1460 multiplied by 36524225561 days are but 533 25S 6932 days. Nevertheless as a measure of mere duration, the vague Nabonassan year in it's relation to the Julian or old style reckoning is without known compeer for simplicity of reckoning.
 But of course the Julian system was a great advance upon the Nabonassan in 50 far as the preservation of the sea sons at their proper dates is concerned. Yet between his day (45 B. O and that of Gregory d5S2 A. D.) the Julian cal- endar had lost twelve days because Caesars mean solar year value was too great by .0077449S979 days; hence Greg ory who aimed merely to perpetuate certain calendric data relating specifi- cally to the Council of Nice (325 B, O added but ten of these days by chang ing October ,, 15S2 A. D. O. $. toOctober 18th N. S, and ordained the future suppression of the intercalary day upon all centurial years except such as are divisible by 400 without a remain der. This was intended to fix the ver- nal equinox at March Fist Julian, as it was in 325 A. D., or at March 22d Greg brian for that same year, and would have accomplished the object had Gregory's value for the mean solar year (3652425 days) been correct. As 9 matter of fact the dates upon the old style (Juliam, and new style Gre gorian) agreed from March 1, 200 AID to February 2s, 300 A. D., and were ten days apart from March i, 1500 A. D. to February 2S, 1700 A. D. Grego- ry's calendric function is divided by minus 3 divided by 400 equals 97 leap-years in 400, leaving 303 common years in that period.
 However, the Gregorian value for the mean solar year was greater than the truth by O002443S979 days, for its actual value is 365. 24225561021, plus days equals 365d 5h 4Sm sos 53t 6f 4Of If, therefore, we take the error at the round number of .00025 days it will amount to one day too much in 4091.S, plus, years. Herschel, therefore, pro- posed that every 10th Gregorian inter- calation should be omitted; or, as 10x400 equals 400O, that every even 4000 A. D. year should be reckoned as a common year. If this suggestion be adopted, then by reckoning both forward and backward from 1 B. c. as an origin% the first A. D. application will fall upon 4000 A. D. and the first proleptic B. C. application will fall at 4001 B. C., etc The full function for Herschel's inter- calary rule is therefore divided by 4. minus Y divided by 400, minus di- vided by 4000 equals 969 leap-years in 4000, leaving 3031 common years in the same period.
 The application of Herschel's rule leaves a residual error of but O0561021 days every 1000 years by which it is short of absolute accuracy, and this will not grow into the necessity of add ing an intercalary day until IFS, ,246 years have elapsed. It, however, forms the basis for another intercalary rule, and because of it's relation to certain fundamental metric functions found in the primary measures of the Great Pyramid of Gizeh, by my friend, Pro- lessor C. Piazzi Smyth, late Astrono- rner Royal of Scotland, I shall take the liberty of naming it the PiazZian inter calation. Its function Is as follows Y divided by 4, minus divided by 400. minus Y divided by 40G0, plus di- vided by 4O0x4CO equals SS761 leap-years in 160.0OO, leaving 12t, ,239 common ones in it's period upon the calendar The