minute and second hand of all timepieces will remain the same. The correct time is distributed by telegraph throughout the United States from the Naval Observatory at Washington each day. 149. The Eastern time belt lies approximately 71° each side of the 75th meridian, and has throughout the local time of the 75th meridian. Similarly, the Central, Mountain and Pacific time belts lie approximately 71° each side of the 90th, 105th and 120th meridians, and the time throughout in each belt is determined by the local time of the 90th, 105th and 120th meridians. 150. These divisions are not by any means equal or uniform, since railroads change their time at important junctions and termini. Consequently, variations are made from the straight line to include such places. Thus, while most roads change from Eastern to Central time at Buffalo, the Canadian roads extend the Eastern belt much farther west. 151. Standard time has more recently been adopted by most of the leading governments of the world. With few exceptions the standard meridian chosen represents a whole number of hours from the prime meridian through Greenwich. Great Britain, Belgium and Holland use the time of the meridian through Greenwich. France uses the time of the meridian (2° 20′ E.) through Paris. Cape Colony uses the time of the meridian 22° 30′ E. Germany, Italy, Austria, Denmark, Norway and Sweden use the time of the 15th meridian east. Roumania, Bulgaria and Natal use the time of the 30th meridian Western Australia uses the time of Southern Australia and Japan use the time Eastern Australia, Victoria and Queens the 120th meridian east. of the 135th meridian east. east. land and Tasmania use the time of the 150th meridian east. New Zealand uses the time of 170° 30′ E. EXERCISES 24 1. When it is 7 P.M. at Philadelphia, what time is it at London? at Paris? at Berlin? 2. What is the difference in time between Boston and Rome? Melbourne and Tokyo? 3. It is 7 A.M. March 1 at St. Louis. What is the time and date at Tokyo? 4. When it is 1.30 P.M. at Buffalo, what time is it at Cleveland? 5. What is the difference between the local and standard time of Boston? of Chicago? of St. Louis? of New York? 6. The local time of Detroit is 27.658 min. faster than the standard time. Find the longitude of Detroit. 7. When it is noon local time at Boston, what is the standard time at Ogden, Utah ? THE EQUATION 152. An equation is a statement of equality of two numbers or expressions. Thus, 5 = 3 + 2 and 3 × 5 = 15 are equations. 153. The equation is one of the most powerful instruments used in mathematics and can be used to decided advantage in the solution of many arithmetical problems. 154. The book written by the Egyptian priest Ahmes, and referred to elsewhere, is one of the very oldest records of the extent of mathematical knowledge among the ancients. In this book we find a very close relation between arithmetic and algebra. A number of problems are given leading to the simple equation. Here the unknown quantity is called hau or "heap," and the equation is given in the following form: heap its , its, its, its whole, gives 33, or 3x + x +4x+x=33. (Cajori, "History of Elementary Mathematics," p. 23.) Ex. 1. Find a number such that, if 30 is subtracted, of the original number will remain. The given relation may be expressed as follows: The number diminished by 30 equals of the number. Let x = the number. = Then x 30 the number diminished by 30, and x = of the number. .. x − 30 = 3 x is the equation expressing the relation between the number given in the conditions of the problem and the letter representing the number to be found. Solution. Since we wish to obtain an equation with x alone on the left side and only numerical quantities on the right side, we proceed as follows: Subtracting 3 x from both sides of the equation, we have or or or Adding 30 to both sides of the equation, we have To check the result, substitute 90 for x in the original equation. This gives us 90 - 30 = } of 90, 60 = 60. .. x 90 is the correct result. Ex. 2. The sum of two numbers is 20 and their difference is 4. What are the numbers? EXERCISE 25 1. The sum of two numbers is 31 and their difference is 11. What are the numbers? 2. The difference of two numbers is 60, and if both numbers are increased by 5 the greater becomes four times as large as the smaller. What are the numbers? 3. Find two numbers such that their difference is 95 and the smaller divided by the greater is 4. 4. After spending of his money a man pays bills of $25, $40 and $14, and finds that he has $132 left. How much money had he at first? 5. Find a number such that its half, third and fourth parts shall exceed its fifth part by 106. 6. A father wishes to divide $28,000 among his two sons and a daughter so that the elder son shall receive twice as much as the younger, and the younger son twice as much as the daughter. Find the share of each. |