DIVISION OF DENOMINATE NUMBERS. EXERCISES. OZ. i. Divide 76 lb. 10 oz. 14 pwt. 12 gr. by 6. Explanation. To divide a quantity by 6 is to take } 6) 76 10 14 12 of it. i of 76 lb. 12 lb. and 4 lb. re12 9 48 oz. ; 48 oz. + 10 oz. maining ; 4 lb. 58 oz. 1 of 58 oz. == 9 oz. and 4 oz. remaining; 4 oz. = 80 pwt. ; 80 pwt. + 14 pwt. 94 pwt. ; } of 94 pwt. 15 pwt. and 4 pwt. remaining; 4 pwt. 96 gr.; 96 gr. + 12 gr. - 108 gr. ; of 108 gr. - 18. Hence the quotient is 12 lb. 9 oz. 15 pwt 18 gr. 2. Divide : 1. 112 T. 16 cwt. 66 lb. by 7. Process. £1 4s. 9d. 297d. 12. 48 T. 9 cwt. 23 lb. 8 oz. by 6 T. 1 cwt. 15 lb. 7 oz. 15. 13 lb. 7 oz. 15 pwt. by 2 oz. 10 pwt. 39 min. LONGITUDE AND TIME. INDUCTIVE STEPS. 1. Does the earth revolve on its axis from west to east or from east to west ? 2. It revolves once in how many hours ? 3. Does the sun actually revolve, or only appear to revolve around the earth? 4. If the earth revolves from west to east, do Eastern or Western people behold the sun first? 5. Has a place 30° east of Philadelphia later or earlier time? 6. When it is noon in New York, is it afternoon or forenoon in Chicago ? 7. Through how many degrees does the sun appear to travel in 24 hrs. ? 8. Then how many degrees of longitude and how many hours are compassed in a day ? Time. Longitude. 24 hrs. 360°. Dividing the equation by 24, we have: 1 hr. 15°. Dividing by 60, we have: 1 min. 15'. Dividing again by 60, we have: 15/1. 1 sec. RULE. To reduce time to longitude, multiply by 15; to reduce longitude to time, divide by 15. PROBLEMS. 1. The difference of time between two places is 1 hr. 15 min. 30 sec. Find the difference of longitude. Process. Explanation. hr. min. sec. Since we are required to reduce time to longi1 15 30 tude, we multiply the given hours, minutes, and seconds by 15, and obtain 18° 52' 30''. 18° 52' 30" 2. The difference of longitude between New York and Baltimore is 2° 36'. Find the difference of time. 15 Process. Explanation. 15) 2° 36' Since we are required to reduce lon10 min. 24 sec. gitude to time, we divide the given number of degrees and minutes by 15, and obtain 10 min. 24 sec. as the difference of time. The Meridian of a place is an imaginary line running from North Pole to South Pole through that place. A meridian divides longitude into east longitude and west longitude, making 180° of each. The meridian of Greenwich, near London, or of Washington, D. C., is commonly reckoned from. 3. The longitude of Washington (from Greenwich) is 77° 2' 48" W., and of San Francisco 122° 24' 15" W. Find the difference of longitude and the difference of time. 4. If the difference of time between San Francisco and Philadelphia is 3 hr. 9 min. 7 sec., what is the longitude of Philadelphia ? 5. The difference in time between Berlin and New York is 5 hr. 49 min. 35 sec. Find the difference in longitude. 6. If Berlin is 13° 23' 43" E., find how much of the preceding difference is west longitude. 7. In travelling west my watch seemed to gain 20 min. How many degrees did I travel ? 8. Constantinople is 28° 59' E. When it is noon in Greenwich, what is the time in Constantinople? 9. When one place is in west longitude and the other in east longitude, do you add or subtract to find the difference of longitude ? 10. New York is 74° 3' west ; Paris, France, is 2° 20' east. Find the difference of time. 11. When it is noon at Boston (71° 3' 30" west), what is the time at Paris (2° 20' 22'' east)? 12. Canton in China is 113° 14' 30" east longitude and Washington is 77° west longitude. When it is midnight on July 4th, at Washington, what time will it be at Canton? Standard Time. Nov. 18, 1883, the United States was divided into four time-belts, each 15° wide, named respectively, Eastern, Central, Mountain, and Pacific. The local time of the middle meridian of each time-belt was adopted as the standard time of the whole belt. 1. Eastern time is that of the 75th meridian. All places lying within 7° 30' of the middle meridian have the time of that meridian. |