MEASURE OF TIME. 98. Measure of Time is applied to the various divisions and sub-divisions into which time is divided. NOTE 1. The true Solar or Tropical Year is the time measured from the sun's leaving either equinox or solstice to its return to the same again, and is 365d. 5h. 48m. 49sec. nearly. The Julian Year, so called from the calendar instituted by Julius Cæsar, contains 365 days, as a medium; three years in succession containing 365 days, and the fourth year 366 days; which, as compared with the true solar year, produces a yearly error of 11m. 10 sec., or of 1 whole day in about 120 years. The Gregorian Year, or that instituted by Pope Gregory XIII., in the year 1582, and which is now the Civil or Legal Year in use among the different nations of the earth, contains 365 days for three years in succession, and 366 days for the fourth, excepting centennial years whose number cannot be exactly divided by 400. The Gregorian year gives an error of only 1 day in 3866 years. A Common Year is one of 365 days, and a Leap or Bissextile Year is one of 366 days. Any year is Leap Year whose number can be divided by 4 without a remainder, except years whose number can be divided without a remainder by 100, but not by 400. A Sidereal Year is the time in which the earth revolves round the sun, and is 365d. 6h. 9m. 9 sec. NOTE 2. The 12 calendar months, composing the civil year, are January, February, March, April, May, June, July, August, September, October, November, December, and the number of days in each may be readily remembered by the following lines : Repeat the table. How is 98. To what is the measure of time applied? the true solar year measured? How long is it? called? Who instituted the Gregorian year? A Sidereal year? Name the months in their order. "Thirty days hath September, Hath twenty-eight; and this, in fine, TABLE SHOWING THE NUMBER OF DAYS FROM ANY DAY OF ONE MONTH TO THE SAME DAY OF ANY OTHER MONTH IN THE SAME YEAR. TO THE SAME DAY OF FROM ANY DAY OF Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. 214 245 273 304 334 365 30 61 92 122 153 183 304 335 365 31 62 92 123 153 31 61 92 122 30 June For example, to find the number of days from April 4th to November 4th we look for April in the left vertical column, and November at the top, and, where the lines intersect, is 214, the number sought. Again, to find the number of days from June 10th to September 16th, we find the difference between June 10th and September 10th to be 92 days, and add 6 days for the excess of the 16th over the 10th of September, so we have 98 days as the exact difference. If the end of February be included between the points of a time, a day must be added in leap year. When the time exceeds one year, there must be added 365 days for each year. MENTAL EXERCISES. 1. In 3 minutes how many seconds? In 5 minutes? 2. In 2 hours how many minutes? In 4 hours? 3. In 4 weeks how many days? In 6 weeks? In 9 weeks? 4. In 2 days how many hours? In 3 days? In 7 days? 5. How many weeks in 21 days? In 30 days? In 50 days? 6. How many calendar months in 2 years? In 8 years? In 10 years? In 12 years? In 20 years? 98. How many days has each month? How do you find be the table the number of days from April 4th to November 4th? When the time sought for is more than one year, how many days must be added? EXERCISES FOR THE SLATE. 1. How many seconds in 365da. 5h. 48m. 49sec., or one solar year? OPERATION. 3 6 5 da. 5h. 48m. 49sec. 1465 730 2. In 31556929 seconds how many days? OPERATION. 60) 3155 69 29 60) 5 2 5 9 4 8 m. 49sec. 24) 8 7 6 5 h. 48m. 365 da. 5h. Ans. 365da. 5h. 48m. 49sec. 8 7 6 5 hours. 60 5 2 5 9 48 minutes. 60 3155 69 29 seconds, Ans. 3. Reduce 296da. 18h. 32m. to minutes. 4. In 427352 minutes how many days? 5. How many seconds in 30 solar years 262da. 17h. 28m. 42sec.? 6. In 969407592 seconds how many solar years? 7. How many weeks in 684592 minutes? 8. In 67w. 6d. 9h. 52m. how many minutes? 9. How many days from June 5th to Dec. 11th? 10. How many days from March 17th, 1856, to May 16th, 1857? Ans. 425 days. 11. How many days from December 18th, 1856, to January 30th, 1857 ? 12. How many days from August 30th, 1857, to June 1st 1858? 13. How many days from July 4th, 1859, to July 4th 1860 ? 14. How many days from April 25th, 1855, to August 20th, 1858? Ans. 1213 days.
NOTE. The last six examples are to be performed by aid of the table on page 103. 98. How do you reduce years to seconds? The reason for the operation. How do you reduce seconds to days? To years? The reason for the operation. CIRCULAR MEASURE. 99. Circular Measure is applied to the measurement of circles and angles, and is used in reckoning latitude and longitude, and the revolutions of the planets round the sun. 300 330 270 240 A 360 081 30 - 60 388 = 1800 360 = 21600 108000 1296000 NOTE 1.-A Circle is a plane figure bounded by a curve line, every part of which is equally distant from a point called its center. The Circumference of a circle is the line which bounds it, as shown by the diagram. An Arc of a circle is any part of its circumference; as AB. A Radius of a circle is a straight line drawn from its center to its circumference; as CA, CB, or CD. Every circumference is supposed to be divided into 360 equal parts, called degrees. A Quadrant is one fourth of a circumference, or an arc of 90°; as AB. An Angle, as ACB, is the inclination or opening of two lines which meet at a point, as C. The point is the vertex of the angle. If a circumference be drawn around the vertex of an angle as a center, the two sides of the angle, as radii of the circle, will include an arc, which is the measure of the angle; as the arc AD = 120° is the measure of the angle ACD, and AB 90°, the measure of the angle ACB; hence the one is an angle of 120°, and the other, of 90°. = NOTE 2. - As the earth turns on its axis from west to east every 24 hours, the sun appears to pass from east to west 4 of 360° of longitude every hour, or over 15° of longitude in 1 hour's time, or 10 in 4 minutes of time, and I' in 4 seconds of time; so that when it is noon at any place, it is 1 hour earlier for every 15° of longitude westward, and 1 hour later for every 15° of longitude eastward. Thus, Boston being 71° 4' west of Greenwich, and San Francisco 51° 17' west of Boston, when it is noon at Boston. it is 4h. 44m. 16sec. past noon at Greenwich, and wanting 3h. 25m. 8sec. of noon at San Francisco. 99. To what is circular measure applied? Recite the table. What is a circle? An angle? 3. In 27S. 19° 51' 28" how many seconds? 4. How many signs in 2987488 seconds? 11 S. 18° Ans. 11S. 18° 57'. MISCELLANEOUS TABLE. 100. This table embraces a variety of denominations frequently used in business. 99 How do you reduce signs to seconds? Give the reason of the operation. How do you reduce seconds to degrees? To signs? Give the reason for the operation. How many degrees in a circle? -100. What is embraced in the miscellaneous table? |