L. Long Measure. Long measure is used in measuring distances, or other things where length is considered, without regard to breadth. 3 barley-corns (b.c.) make 1 inch, marked in. 12 inches make 1 foot, ft. 3 feet make 1 yard, marked yd. 53 yards or 162 feet make 1 rod, pole, or perch, rd. 40 rods make 1 furlong, fur. 8 furlongs or 320 rds. make 1 mile, M. 3 miles make 1 league, 691 statute miles make 1 degree, 360 degrees the circumference of the earth. Note. In measuring the height of horses, 4 inches make į hand. In measuring depths, 6 feet make 1 fathom. Land or Square Measure. Square measure is used in measuring land and any other xhing where length and breadth only are considered. 144 square inches make 1 square foot. 9 square feet make 1 square yard. 304 square yards or 272 square feet make 1 square rod. 40 square rods inake 1 rood or quarter of an acre. 4 roods or 160 square rods make 1 acre. 640 square acres make 1 square mile. Note. Gunter's Chain, used in measuring distances, is 4 rods in length, containing 100 links, each link being 720 inches in length. 25 links make 1 rod. Solid or Cubic Measure. Solid or cubic measure is used in measuring things that have length, breadth, and thickness. 1728 solid inches make 1 solid foot. 40 feet of round timber, or make 1 ton or load. 50 feet of hewn timber, 27 solid feet make 1 solid yard. make 1 cord of wood. x 4 high, } 128 solid feet, om bietet long} make 1 year, W. Time. Time is naturally divided into years, by the revolution of the earth round the sun ; and into days, by the revolution of the earth upon its own axis. 60 seconds (s.) make 1 minute, marked m. 60 minutes make 1 hour, h. 24 hours make 1 day, d. 365 days yr. make 1 week, mo. 13 mos. 1 d. and 6 hours make 1 Julian year. 12 Calendar months make 1 year, yr. All the rest have thirty-one. Circular Motion. Circular motion is the motion of the earth and other planets round the sụn ; and is applied to latitude and lon: gitude. 60 seconds (") make 1 minute, marked' 60 minutes make 1 degree, 30 degrees make 1 sign, S 12 signs, or 360 degrees, the whole great circle of the Zodiac. Denominations of things not included in the foregoing Tables. 12 single things make 1 dozen. 12 dozen make 1 gross. 12 gross, or 144 dozen, make 1 great gross. 20 single things make l score. 5 score make 1 hundred. 200 lbs. of Beef or Pork make 1 barrel. 112 lbs. of Fish make 1 quintal. 24 sheets of Paper make 1 quire. 20 quires make 1 ream. ARITHMETIC. 1 Arithmetic is the art, or science, of computing by numbers. It has five principal Rules for its operation, viz. : Numeration, Addition, Subtraction, Multiplication, and Division. NUMERATION. 2. Numeration teaches how to read and write numbers. 3. A single or individual thing is called a unit. 4. The following are the ten characters used in computation: A unit or one, written 1 5. The nine first of these charTwo; 2 acters are called significant figThree, 3 ures or digits ; and have each of Four, 4 them a simple and a local value. Five, 5 6. When standing separately Six, 6 or alone they express ; or repreSeven, 7 sent their simple value only; vizi Eight, 8 one, two, three, four, five, &c. Nine; 9 7. But when placed or locaCipher, O ted with other figures, they have a local value, according to the place they stand in ; counting from the right hand towards the left. For example, the number one hundred and eleven is made by repeating the figure 1 three times: Hunds. Thus, 1 1 1. The 1 on the right hand in the unit's place represents its simple value of one only. The same figure located in the second place towards the left hand, is increased in its value ten times, and now counts one ten, because stands in the place of tens : and the same figure again located or placed in the third place towards the left, is increased in its value one hundred times, and now counts one hundred, because it stands in the place of hundreds. And one hundred, one ten, and one unit, make one hundred and eleven. 8. Hence it appears that any figure in the unit's place, expresses its simple value only, or so many ones; but in the second place, or place of tens, it becomes so many tens, or ten times its simple value; and in the third place, or place of hundreds it becomes a hundred times its simple value, and so on, as in the following Numeration Table: Millions, -One unit, 3 hundreds, 2 tens and 1 unit, or three hun. dred and twenty-one. 4 3 2 1 4 thous. 3 hunds. two tens, one unit, or four thous, three hund. and twenty-one. 5 tens of thous. 4 thousands, or fifty-four 7 6 5 4 3 2 1 $ 7 millions 6 hundred and fifty-four thousand three hundred and twenty-one. 87 O O O O O O 8 tens of millions, 7 millions, or eighty-seven millions. 9 8 7 0 0 0 0 0 0 9 hund. of millions, 8 tens of millions, 7 mil. lions, or 987 millions. 1 2 3 4 5 6 7 8 9 -123 millions 456 thousand 789. 8 7 9 6 4 5 3 8 4 -879 millions 645 thousand 384. Note. There are two methods of expressing numbers shorter than writing them in words, viz: The method of expressing numbers by letters, called the Roman method of computation, which was invented and used by the Romans. But at this day it is seldom used except in numbering chapters in books, &c. The method of computing by figures, as above, was invented and used by the Arabs, and afterwards was introduced into Europe, and thence into this country, and is now in general use in all parts of the civilized world. This is called tho Arabic method of computation, because it was invented by the Arabs. 9. The cipher, when standing alone, signifies nothing ; but when' placed on the right hand of the significant figures it increases their value in a tenfold proportion. Thus 1, with a cipher annexed to it, becomes 10, ten, because 1 is thereby removed into the tens' place, and with two ciphers annexed, it becomes 100, one hundred, the 1 being now removed to the place of hundreds, &c. 10. To read numbers, or to know the value of any number of figures. RULE. i. Begin at the right hand and numerate towards the left, by saying units, tens, hundreds, thousands, &c., as in the Numeration Table. 2. Then to the simple value of each figure join the name of its place, beginning at the left hand and reading to the right. EXAMPLES. Read the following numbers: 124 One hundred and twenty-four: 365 Three hundred and sixty-five. 4628 Four thousand six hundred and twenty-eight. 54026 Fifty four thousand and twenty-six. 144321 One hundred and forty-four thousand three hun dred and twenty-one: 5684568 Five millions six hundred eighty-four thousand five hundred and sixty-eight. For convenience in reading large numbers, it is the usual method to point them off into periods of three figures each, as follows : 879 Eight hundred seventy-nine. 879 000 Eight hundred seventy-nine thousand. 879 000 000 Eight hundred seventy-nine millions. 987 854 321 Nine hundred and eighty-seven millions, eight hundred and fifty-four thousand: three hundred and twenty-one. 11. To write numbers. RULE. 1. Begin at the right hand and write the numbers according to their proper value in numeration : that is, write units in the place of units, tens in the place of tens, &c. |