99. How many sheets of paper are there in a folio volume of 360 pages? Ans. 90. 100. How many sheets of paper are there in one thousand reams? Ans. 480000. 101. A quarto work contains 12600 pages; how many sheets of paper are there in it? Ans. 1575. 102. Thirty-five sheets are employed in an octavo book; how many pages does it contain? Ans, 560. 103. How many common reams are there in fifty printer's reams of paper? Ans. 53 reams, 15 quires. 104. An octavo work of 20 sheets contains eight hundred thousand letters; how many are there in a page? 61. TIME. 60 seconds (") make 1 minute. m. Ans. 2500. hA day is the length of time which elapses while the earth revolves once about its axis, which is about 23h. 56m. 4". although commonly reckoned 24 hours. Hours, minutes, and seconds, are divisions and subdivisions of a day, an hour being one twenty-fourth part of a day; a minute, one sixtieth part of an hour; and a second, one sixtieth part of a minute. The week is a religious institution, appointed by the ALMIGHTY immediately after the creation; and the observance of every seventh day as a day of holy rest is repeatedly enjoined in the Scriptures. A month is properly a portion of time regulated by the moon: thus a lunar periodical month is 27d. 7h. 43m. 8". being the time the moon takes in going from any point in the ecliptic to the same point again. A lunar synodical month or lunation consists of 29d. 12h. 44m. 3′′. 11′′. being the space of time which passes from one new moon to the next; to these may be added the solar month, of 30d. 10h. 29m. 5′′. which is the time the sun takes to pass through one sign, or one twelfth part of the ecliptic; and likewise the civil month of 28 days, as in the Table. A year is the space of time in which the earth makes one complete revolution round the sun, and in which all the seasons return: this is called the solar year, and consists of 365d. 5h. 48m. 48". The Julian year of 365d. 6h. is commonly reckoned 365 days only; and for seconds 60= 1 minute. 3600 60 = 1 hour. 86400= 1440 = 24 = 1 day. 105. In 12 weeks, how many seconds? Multiply by 7, 24, 60, and 60. Ans. 7257600. 106. In 1234567 seconds, how many weeks? Ans. 2w. 6h. 56m. 7". Divide by 60, 60, 24, and 7. 107. In 1mo. 2w. 3d. 4h. 5m. how many minutes? Ans. 65045. 108. How many seconds are there in a Julian year? Ans. 31557600. 109. October the 25th, 1809, the King completed the 49th of his reign; how many minutes are there in that space of time, reckoning Julian years? Ans. 25772040. year 110. How many hours have elapsed since the birth of Christ to Christmas 1810, allowing the years to be of the Julian kind? COMPOUND ADDITION. 62. A compound number is that which consists of different denominations in money, weights, measures, &c. the odd 6 hours, a day is added to February every fourth year, which year is called Bissextile, or Leap year. Thus February, in the Leap year, has 29 days; and consequently the Leap year consists of 366. To find Leap year, this is the rule. Divide the date by four, and you'll discover To find the number of days in each month. Compound Addition teaches to find the sums of such compound numbers as are of the same kind. RULE I. Place the numbers to be added so that all those of the same denomination may stand under one another in a column; and let two dots (thus . .) be put between each two numbers of different denominations. II. Add all the numbers in the least denomination together, and reduce the sum to the next higher denomination, and set down the remainder, if any. III. Carry the number arising from this reduction to the next superior denomination; add it up, reduce the sum to the next superior denomination, set down the remainder, carry, &c. as before. IV. Proceed in this manner with all the denominations to the highest, which must be added and put down like simple Addition. Method of Proof. Cut off the top line, and proceed as in simple Addition . Here we add up each separate denomination by simple Addition, and the truth of the rule may be shewn from any of the examples included under it. We will take the first example in Money, in which the sum of the farthings is 11; the sum of the pence 26; the sum of the shillings 71; and the sum of the pounds 224. Now as we always estimate any sum, namely, pounds, shillings, pence, or farthings, in the highest of these denominations it is reducible to, these farthings, pence, and shillings, must if possible be reduced higher. Let us try. Thus, 11 farthings 224 pounds =224 0 0 These added give 227 13 4 as in the example. Here note, that the 2 pence in the first line above is the 2 carried from farthings to pence, (in Ex. 1.) the 2 shillings in the second line is the 2 carried from pence to shillings; and the 3 pounds in the third line is the 3 carried from shillings to pounds: if this illustration be well understood, the reason of the following modes of operation will be extremely plain. d The coins used in England are gold, silver, and copper; the gold coins are, a guinea, halfguinea, and seven shilling piece. The silver coins are, a crown, halfcrown, shilling, and sixpence. The copper coins are, a twopenny piece, penny, halfpenny, and farthing. These are called real coins; but any denomination of money, which is not represented by a single coin, is called imaginary; thus a guinea, a crown, &c. are real coins; but a pound, a groat, &c. (having no single piece that will represent them) are imaginary. The moneyers suppose any quantity of gold divisible into 24 equal parts, which they call carats, and each carat they divide into 24 parts, calling these grains of a carat; by this they denominate the fineness of their gold. If the gold be free from any mixture (called alloy), it is said to be 24 carats fine; but if there be 2 carats (out of the 24) of alloy in it, the gold is said to be 22 carats fine, &c. The standard for British gold coin is 22 carats, namely, 22 of pure gold, and 2 of alloy, composed of silver and copper. The standard for silver coin is 11oz. 2dwts. of pure silver, mixed with 18dwts. of copper alloy. A pound of standard gold makes 441 guineas, and a pound of standard silver 62 shillings. Sum 1. L. S. d. 35 12 83 21 52 17 6 14 34 47 13 5 69 15 4 13 4 192 0 8 227 EXAMPLES. Explanation. I begin at the bottom of the farthings, and say 2 and 3 are 5 and 1 are 6 and 2 are 8 and 3 are 11; 11 farthings reduced to pence are 2 pence three farthings; I put down and carry 2 to the pence, which added up amount to 28; this reduced to shillings is 2s. 4d. I put down 4, and carry 2 to the units line of shillings; the shillings being added (the units first, and then the tens) give 73 shillings; these reduced to pounds are 31. 138. put down 13 and carry 3 to the pounds, which are added up exactly like an example in simple Addition. The first line of the work being finished, I cut off the top line (namely, 357. 12s. 8d.) by drawing a light stroke under it. I then add up the same numbers again which I added before, all except the top line cut off, in the same manner as before, and the result is the second line of the work; I lastly add the said second line and the top line cut off together, and the sum will be the third line of the work; this third line agreeing in every particular with the first line, shews that the operation is right. Proof 227 13 4 A pennypiece, 2 new halfpence, or 3 old ones, should weigh an ounce Avoirdupois. When the Saxons first settled in Britain, they were called Easterlings, (from the circumstance of their coming from the east,) and their money, easterling money hence by a corruption frequent in language the word sterling is derived. But it is remarkable, that a term, which at that time was applied exclusively to express something foreign, should by the lapse of time completely change its signification, so as to denote exclusively that which is British. |