To find Difference of Time between Dates. Example.-1. How many years, months, and days from June 12, 1868 to May 7, 1879 ? Yr. mo. d. 1879 5 1868 6 12 10, 10, 25, Solution.-May 7, 1879, is the 7th day of the 5th month of 1879, and June 12 is the 12th day of the 6th month of 1868. Hence, by subtracting 1868 years 6 months and 12 days from 1879 years 5 months and 7 days, we find the time elapsed from the earlier to the later date. We consider 30 days a month, irrespective of what calendar months may intervene between the two dates. 248. This method, though usually employed in business, does not obtain the exact time elapsing from one date to another. A more accurate method is to find first the number of entire years between the dates, then of entire months, and lastly of the days. The difference between the results of these methods may be seen from solutions of the following problem: 2. A sum of money was borrowed Sept. 18, 1867, and paid March 16, 1870. How long was it in the hands of the borrower? 5 mo. 28 d. Second Method. From Sept. 18, 1867, to Sept. 18, 1869 = 2 yr. 66 Sept. 18, 1869, to Feb. 18, 1870 = 5 mo. 249. The first method is based on the supposition that there are 360 days in the year, and 30 days in each month. The second method takes no account of the number of days in the several years nor in the entire month, but reckons a year from a given day of one year to the corresponding day of the next, and a month from a given day of one month to the same day of the next. In reckoning the odd days, however, it takes into account the number of days in the month preceding the last. 4. I start from Cincinnati, and, on arriving at another city, compare my watch with a well-regulated clock, and find it faster than my watch; have I traveled east or west? I find it 20 minutes faster; how many degrees have I traveled? 5. When it is 12 o'clock noon at Omaha, what is the time at places lying 15, 72, 334 degrees west? East ? 6. What difference in longitude makes a difference of 1 hour 30 min. in time? Of 1 min.? Of 12 sec.? 7. Suppose the sun is rising at 4 o'clock A. M. on the first meridian (Greenwich), on what meridian is it noon? 8. What is the difference of time between Greenwich (on the first meridian) and a place lying under the 74th meridian? SLATE EXERCISES. 9. What is the difference of longitude between Washington and Cleveland, the difference in time being 18 min. 32 sec.? Note. Let it be kept in mind that, inasmuch as there are 360° in the circumference of the earth, and only 24 h. in the day, there are more degrees in any difference of longitude than hours in difference of time; more minutes of longitude than minutes in time, and more seconds of longitude than seconds in time. (How many times as many?) 10. When it is noon at Washington, it is only 11 o'clock, 17 min. and 44 sec. A. M. at Chicago. Find (a) the difference in time; (b) the difference in longitude. 252. The names of a few important cities are given below, with the longitude of each from Greenwich (see Haswell, ed. 1885): Cities. Longitude. Chicago, Ill. 87° 37' 47" W. St. Petersburg, Russ. 30° 19′ 0′′ E. 11. When it is noon at St. Louis, is it before or after noon at Washington? At San Francisco ? 12. When it is noon at San Francisco, is it before or after noon at St. Louis? At Washington ? 13. When noon in St. Louis, about what time in Calcutta? 14. When it is midnight at Paris, what is the local time at Cleveland? Explanation.-First step.-To find the difference of longitude we add the longitude of Paris to that of Cleveland, since Paris lies east and Cleveland west of Greenwich. Second step.--Since 15° of longitude produce a difference of 1 hour in time, 84° produce a difference of 5 hours in time and something more, for there are 9° more than 5 times 15° in 84°. The remainder, 9° = = 9 × 60′ 540′, which being added to the 2' in the next term, we have 542', etc. (The pupil should be able to take the remaining steps of the analysis without aid.) Third step.-Since Cleveland is west from Paris, the time of Cleveland is earlier than that of Paris, hence we subtract 5 h. 36 m. 2 sec. from 12 h. Rules for Computations in Longitude and Time. I. For finding difference of longitude, difference in time being given : 253. Rule.-Multiply the difference in time by 15, and the hours, minutes, and seconds of time will give respectively 's, 's, and 's of longitude. II. For finding difference in time, difference of longitude being given: 254. Rule.-Divide the difference of longitude by 15, and the °s, 's, "s of longitude will give respectively hours, minutes, and seconds of time. SLATE EXERCISES. Examples. Using the longitudes given in the above table, Find the difference in time between 1. Albany and Chicago. 6. St. Louis and San 10. New York and New 2. Berlin and Paris. 3. Greenwich and St. Petersburg. 4. Boston and Cleve land. 5. Boston and St. Louis. Francisco. Orleans. 11. Washington and 7. Rome and Paris. 9. Cincinnati and San 12. San Francisco and Calcutta. For oral exercises, let the differences in time be estimated. Rough estimates are as frequently required as exact computations. 13. When it is 12 o'clock noon at Greenwich, what is the time at each of the cities mentioned in the table (Art. 252) ? 14. Suppose it to be 8 o'clock P. M. (Post meridian or after noon) at Berlin, what time is it at the other cities? 15. Suppose it to be 7 o'clock A. M. (Ante meridian or before noon) at New York, what time is it at the other cities? 16. The difference in time between two places is 1 h. 15 min. 26 sec.; what is their difference of longitude? 17. Find the distance in geographical miles between two places on the equator that are 3 h. 2 min. 12 sec. apart. (1o – 60 geo. mi.) = Applications and Review. 1. If 1 cwt. costs $16.16, $18.25, $19.50, $25.25, $36.36, what is the cost of 328 lb.? 2. If 1 gallon costs $25, $3.50, $13⁄4, $3.30, $42, $23⁄4%, what is the cost of 51⁄4 gallons? 3. If 1 pound costs 71% francs, what is the cost of 35, 2.5, 13 4.6, 5% pounds? 4. If 1 cwt. costs $127.64, what is the cost of 32, 63, 95, 17 lb. avoirdupois ? 5. What will a lot, measuring 5712X100 feet, cost, if the price of 1 foot is $252, $373/4, $4815, $571/2? 6. What will be the cost of 52, 84, 158, 237 oz., if 1 oz. cost 37124? 7. What does a family spend for meat in a month of 30 days, at 433 a day? In a year of 365 days? 8. If 5 gal. cost $1.15, $2.35, $4.25, $6.75, $7.45, $15.25, $20.20, what is the cost of 1/2 gallon? (One step.) 9. If 41⁄2 lb. cost $2.32, $3.48, $4.28, $5.44, $6.64, $7.22, $9.04, what is the cost of 1/2 lb.? 10. If 32 dozen cost $14.48, $28.36, $30, $16.75, $27.50, what is the cost of 1 gross? 11. If 6 reams of writing-paper cost $7.20, $18.50, $20.25, $30.75, $50.15, what is the cost of 18 quires? 12. If 9 acres cost $100.75, $140.25, $225.50, $350.40, what is the cost of 67.5 acres? 13. If 7 barrels cost $48.25, $36.70, $64.83, $94.24, what is the cost of 12 barrel ? 14. If 8 cords cost $24.25, $25.75, $26.40, $38.85, what is the cost of 14 cord? 15. If 1 cwt. costs $568.25, what will 20 lb. cost? 25 lb. ? 33 lb. ? (Pursue the shortest method.) |