(2) What is the weight of a piece of fir, whose girt is 20 inches, and length 40 feet? (3) What is the weight of an iron shot, of 7 inches dia meter? (4) What is the diameter of an iron shot, weighing 42 lb. avoirdupois? (5) What is the weight of an iron bumb of 3 inches thick, the greatest diameter being 16 inches? (6) Required the weight of one of the Portland key-stones lo the middle arch of Westminster Bridge, the diameter of the arch being 76 feet, the height of the key-stone 5 feet, the chord of its greatest breadth, to the front of the arch, 3 feet 4 inches, and its depth of the arch 4 feet. (7) In the walls of Balbec, in Turkey, there are three stones, laid end to end, now in sight, that measure in length 61 yards; one of which in particular is 63 feet long, 12 feet thick, and yard over: Now if this block was marble, what power would balance it, so as to prepare it for moving? Case 2. The weight of any body being given, to find the solidity and the specific gravity thereof, RULE. Divide the given weight by the tabular weight corresponding to the name of the same kind, and the quotient will be the solidity in cubic inches, EXAMPLES, (8) What will a block of marble, weighing 8 tons 14 cwt. come to, at 6s, per foot solid? (9) Suppose that a man of war, with all its ordnance, rigging, and appointments, draws so much water as to displace 1300 tons of sea water, London beer measure. The weight of the vessel is required. (10) What will a chain of standard gold weigh in water that raises a fluid an inch, in a vessel 3 inches square, when put into it; and supposing the workman had adulterated the said chain with 142 ounces of silver, how much higher would the water, upon its immersion, be raised in the vessel? (11) Hiero, king of Sicily, ordered his jeweller to make him a crown containing 63 ounces of gold; the workman do thought of substituting part silver therein, to have a proper perquisite: which taking air, Archimedes was appointed to examine it; who, on putting it into a vessel of water, found it raised the fluid, or that itself contained 8,2245 cubic inches of metal; and having discovered that the cubic inch of gold more critically weighed 10,36 ounces, and that of silver but 5,85 ounces, he, by calculation, found what part of his majesty's gold had been changed; and you are desired to repeat the process. *N 266 PART V. LXXVIII. CHRONOLOGY Is the art of estimating and comparing together the times when any memorable transaction hath happened, such as related in history, whether civil or ecclesiastical. It also takes a view of the various fasti, calendars, and methods of computing time, practised by different nations, compares them together, and settles such order and harmony among them, that the exact time in which any remarkable event happened may be certainly known. Some have dated their events from the creation of the world Others from the deluge or flood The Greeks from their olympiads, of 4 the} years each + } The Romans from the building of Rome The Mohammedans from the flight of } PROBLEM I. To find whether any given year be leap year. RULE. Divide the given year by 4: if 0 remain, it is leap year; but if 1, 2, 3, remain, it is so many years after. (1) Is 1795 leap year? (2) Is 1796 leap year? EXAMPLES. Note 1.-Every fourth year is leap year, so called from leaping or advancing a day more that year than any other; that year has then 366 days in it, and Febru ary 29. PROBLEM II. To find the dominical letter till the year 1800. RULE. To the given year add its fourth part, omitting fractions; divide that sum by 7; the remainder taken from 7 leaves the index of the letter in the common year's reckoning. 1 2 3 4. 5 6 7 But in leap years, this letter and its preceding one (in the retrograde order which these letters take) are the dominical letters. EXAMPLES. (3) For the year 1795, I demand the dominical letter. (4) For the year 1796, I demand the dominical letter, 2. The dominical letter is that letter of the alphabet which points out in the calendar the Sundays throughout the year; thence also called the Sunday letter. Of these letters are consequently seven before mentioned, beginning with the first letter of the alphabet; and as in leap year there is an intercalary day, there are then two, one serving January and February, and its following letter the remaining part of the year. N 2 PROBLEM III. To know on what day in the week any proposed day of the month will fall. RULE. First find the dominical letter, then the day of the week the first of the proposed month falls on, which is known by the two following lines: At Dover dwell George Brown, Esquire, Good Christopher Finch, and David Frier. Where the first letter of each word answers to the letter belonging to the first day of the months in order, from January to December. 3. You must observe that the 1st, 8th, 15th, 22d, and 29th day of any month fall on the same day of the week. EXAMPLES. (5) In 1795, on what day of the week does the 19th of May fall, it being queen Charlotte's birth-day? (6) On what day of the week does the 4th of June fall in 1796, being king George the Third's birth-day? PROBLEM IV. To find the year of the solar, lunar, or golden number, and indiction cycles. RULE. To the given year add 9 for the solar, 1 for the lunar, 3 for the indiction; divide the sums in order by 28, 19, and 15: the remainder in each shows the year of its respective cycle. EXAMPLE. (7) Required the year of the solar, lunar, and indiction cycles, for the years 1795 and 1796. 4. The solar cycle, or the cycle of the sun, is a period of 28 years; in which time all the varieties of the |