cal day, used by astronomers in dating events, begins and ends at 12 o'clock, noon. The civil year is composed of civil days. BISSEXTILE OR LEAP YEAR. 300. The period of time required by the sun to pass from one vernal equinox to another, called the vernal or tropical year, is exactly 365 da. 5 h. 48 min. 49.7 sec. This is the true year, and it exceeds the common year by 5 h. 48 min. 49.7 sec. If 365 days be reckoned as 1 year, the time lost in the calendar will be The time thus lost in 4 years will lack only 44 min. 41.2 sec. of 1 entire day. Hence, If every fourth year be reckoned as leap year, the time gained in the calender will be, In 4 yr., "100 66 44 min. 41.2 sec. 66 The time thus gained in 100 years will lack only 5 h. 22 min. 50 sec. of 1 day. Hence If every fourth year be reckoned as leap year, the centennial years excepted, the time lost in the calendar will be, The time thus lost in 400 years lacks only 2 h. 28 min. 40 sec. of 1 day. Hence If every fourth year be reckoned as leap year, 3 of every 4 centennial years excepted, the time gained in the calendar will be, The following rule for leap year will therefore render the calendar correct to within 1 day, for a period of 4000 years. I. Every year that is exactly divisible by 4 is a leap year, the centennial years excepted; the other years are common years. II. Every centennial year that is exactly divisible by 400 is a leap year; the other centennial years are common years. NOTES.1. Julius Cæsar, the Roman Emperor, decreed that the year should consist of 365 days 6 hours; that the 6 hours should be disregarded for 3 successive years, and an entire day be added to every fourth year. This day was inserted in the calendar between the 24th and 25th days of February, and is called the intercalary day. As the Romans counted the days backward from the first day of the following month, the 24th of February was called by them sexto calendas Martii, the sixth before the calends of March. The intercalary day which followed this was called bis-sexto calendas Martii; hence the name bissextile. 2. In 1582 the error in the calendar as established by Julius Cæsar had increased to 10 days; that is, too much time had been reckoned as a year, until the civil year was 10 days behind the solar year. To correct this error, Pope Gregory decreed that 10 entire days should be stricken from the calendar, and that the day following the 3d day of October, 1582, should be the 14th. This brought the vernal equinox at March 21 - the date on which it occurred in the year 325, at the time of the Council of Nice. 3. The year as established by Julius Cæsar is sometimes called the Julian year; and the period of time in which it was in force, namely from 46 years B. C. to 1582, is called the Julian Period. 4. The year as established by Pope Gregory is called the Gregorian year, and the calendar now used is the Gregorian Calendar. 5. Most Catholic countries adopted the Gregorian Calendar soon after it was established. Great Britain, however, continued to use the Julian Calendar until 1752. At this time the civil year was 11 days behind the solar year. To correct this error, the British Government decreed that 11 days should be stricken from the calendar, and that the day following the 2d day of September, 1752, should be the 14th. 6. Time before the adoption of the Gregorian Calendar is called Old Style (0. S), and since, New Style, (N. S.) In Old Style the year commenced March 25, and in New Style it commences January 1. 7. Russia still reckons time by Old Style, or the Julian Calendar; hence their dates are now 12 days behind ours. 8. The centuries are numbered from the commencement of the Christian era; the months from the commencement of the year; the days from the commencement of the month, and the hours from the commencement of the day, (12 o'clock, midnight.) Thus, May 23, 1860, 9 o'clock A. M., is the 9th hour of the 23d day of the 5th month of the 60th year of the 19th century. MEASURE OF ANGLES. 301. Circular Measure, or Circular Motion, is used principally in surveying, navigation, astronomy, and geography, for reckoning latitude and longitude, determining locations of places and vessels, and computing difference of time. Every circle, great or small, is divisible into the same number of equal parts: as quarters, called quadrants; twelfths, called signs; 360ths, called degrees, etc. Consequently the parts of different circles, although having the same names, are of different lengths. The unit is the degree, which is a part of the space about a point in any plane. The table is made up of divisors and multiples of this unit. 60 seconds (") 60 minutes TABLE. 1 12 signs, or 360°, 66 1 circle,. C. M 30 degrees SCALE ascending, 60, 60, 30, 12; descending, 12, 30, 60, 60. NOTES.1. Minutes of the earth's circumference are called geographic or nautical miles. 2. The denomination, signs, is confined exclusively to Astronomy. 3. A degree has no fixed linear extent. When applied to any circle it is always part of the circumference. But, strictly speaking, it is not any part of a circle. 4. 90° make a quadrant or right-angle; 60° 66 The terms folio, quarto, octavo, duodecimo, etc., indicate the number of leaves into which a sheet of paper is folded. A sheet folded in 2 leaves is called a folio. A sheet folded in 4 leaves 66 a quarto, or 4to. an octavo, or 8vo. 66 a 12mo. a 16mo. 66 an 18mo. a 24mo. 66 a 32mo. 305. COPYING. 72 words make 1 folio or sheet of common law. 66 1 " GOVERNMENT STANDARDS OF MEASURES AND WEIGHTS. 306. In early times, almost every province and chief city had its own measures and weights; but these were neither definite nor uniform. This variety in the weights and measures of different countries has always proved a serious embarrassment to commerce; hence the many attempts that have been made in modern times to establish uniformity. The English, American, and French Governments, in establishing their standards of measures and weights, founded them upon unalterable principles or laws of nature, as will be seen by examining the several standards. UNITED STATES STANDARDS. 307. In the year 1834 the U. S. Government adopted a uniform standard of weights and measures, for the use of the custom houses, and the other branches of business connected with the General Government. Most of the States which have adopted any standards have taken those of the General Government. 308. The invariable standard unit from which the standard units of measure and weight are derived is the day. Astronomers have proved that the diurnal revolution of the earth is entirely uniform, always performing equal parts of a revolution on its axis in equal periods of duration. Having decided upon the invariable standard unit, a measure of this unit was sought that should in some manner be connected with extension as well as with this unit. A clock pendulum whose rod is of any given length, is found always to vibrate the same number of times in the same period of duration. Having now the day and the pendulum, the different standards hereafter given have been determined and adopted. STANDARD OF EXTENSION. 309. The U. S. standard unit of measures of extension, whether linear, superficial, or solid, is the yard of 3 feet, or 36 inches, and is the same as the Imperial standard yard of Great Britain. It is determined as follows: The rod of a pendulum vibrating seconds of mean time, in the latitude of London, in a vacuum, at the level of the sea, is divided into 391393 equal parts, and 360000 of these parts are 36 inches, or 1 standard yard. Hence, such a pendulum rod is 39.1393 inches long, and the standard yard is 360000 of the length of the pendulum rod. 391393 STANDARDS OF CAPACITY. 310. The U. S. standard unit of liquid measure is the old English wine gallon, of 231 cubic inches, which is equal to 8.33888 pounds avoirdupois of distilled water at its maximum density; that is, at the temperature of 39.83° Fahrenheit, the barometer at 30 inches. 311. The U. S. standard unit of dry measure is the British Winchester bushel, which is 18 inches in diameter and 8 inches deep, and contains 2150.42 cubic inches, equal to 77.6274 pounds avoirdupois of distilled water, at its maximum density. A gallon, dry measure, contains 268.8 cubic inches. NOTES.-1. Grain and some other commodities are sold by stricken measure, and in such cases the "measure is to be stricken with a round stick or roller, straight, and of the same diameter from end to end." 2. Coal, ashes, marl, manure, corn in the ear, fruit and roots are sold by heap measure. The bushel, heap measure, is the Winchester bushel heaped in the form of a cone, which cone must be 194 inches in diameter (= to the outside diameter of the standard bushel measure,) and at least 6 inches high. A bushel, heap measure, contains 2747.7167 cubic inches, or 597.2967 cubic inches more than a bushel stricken measure. Since I peck contains 7150.4 537.605 cubic inches, the bushel, heap measure, contains 59.6917 cubic inches more than 5 pecks. As this is about 1 bu. 1 pk. 12 pt., it is sufficiently accurate in practice, to call 5 pecks stricken measure a heap bushel. 3. A standard bushel, stricken measure, is commonly estimated at 2150.4 cubic inches. The old English standard bushel from which the United States standard bushel was derived, was kept at Winchester, England; hence the name. 4. The wine and dry measures of the same denomination are of different capacities. The exact and the relative size of each may be readily seen by the following NOTE. The beer gallon of 282 inches is retained in use only by custom. 573 287 732 671 333 |