and September 14 is the date fixed by act of Parliament to correspond to September 3, 1752, O. S. Columbus discovered America on October 12, 1492, O. S. What is the corresponding date in the Gregorian calendar? 62. THE DAY OF THE WEEK.--A problem similar to the above but more complicated consists in finding the day of the week on which any given date of the Gregorian calendar falls--e. g., October 21, 1492. The formula for this case is 7q + r = Y + D + (Y - 1)/4 - (Y - 1)/100 + (Y - 1)/400 where _Y_ denotes the given year, _D_ the number of the day (date) in that year, and _q_ and _r_ are respectively the quotient and the remainder obtained by dividing the second member of the equation by 7. If _r_ = 1 the date falls on Sunday, etc., and if _r_ = 0 the day is Saturday. For the example suggested above we have Jan. 31 Feb. 29 Mch. 31 April 30 May 31 June 30 July 31 Aug. 31 Sept. 30 Oct. 21 --- D = 295 Y = 1492 + D = + 295 + (Y - 1) ÷ 4 = + 372 - (Y - 1) ÷ 100 = - 14 + (Y - 1) ÷ 400 = + 3 ------- 7) 2148 _q_ = 306 _r_ = 6 = Friday. Find from some history the day of the week on which Columbus first saw America, and compare this with the above. On what day of the week did last Christmas fall? On what day of the week were you born? In the formula for the day of the week why does _q_ have the coefficient 7? What principles in the calendar give rise to the divisors 4, 100, 400? For much curious and interesting information about methods of reckoning the lapse of time the student may consult the articles Calendar and Chronology in any good encyclopædia. [Illustration: THE YERKES OBSERVATORY, WILLIAMS BAY, WIS.] CHAPTER VII ECLIPSES 63. THE NATURE OF ECLIPSES.--Every planet has a shadow which travels with the planet along its orbit, always pointing directly away from the sun, and cutting off from a certain region of space the sunlight which otherwise would fill it. For the most part these shadows are invisible, but occasionally one of them falls upon a planet or some other body which shines by reflected sunlight, and, cutting off its supply of light, produces the striking phenomenon which we call an eclipse. The satellites of Jupiter, Saturn, and Mars are eclipsed whenever they plunge into the shadows cast by their respective planets, and Jupiter himself is partially eclipsed when one of his own satellites passes between him and the sun, and casts upon his broad surface a shadow too small to cover more than a fraction of it.