divided into sections such that all places in the same section use the same time, which differs by just one hour from the time used in the next section. This system has now extended throughout the world. Time reckoned according to this system is called standard time. As 15° of longitude correspond to one hour of time, the system of Standard Time is generally based upon a division of the earth into sections 15° of longitude in width, each section using the time of the meridian through its center; but it is found convenient to make the boundaries of these divisions somewhat irregular, as is shown by the map. REFERENCE TABLE STANDARD MERIDIANS AND PLACES USING THEM 0°. Great Britain, Spain, Belgium, Holland, France. 15° E. Germany, Austria, Italy, Denmark, Norway. 30° E. South Africa, Egypt, Turkey. 821° E. British India (since July 1, 1905). 971° E. Burma (since July 1, 1905). 120° E. West Australia, eastern coast of China, Phil ippine Islands. 135° E. Japan. 1421° E. South Australia. 150° E. Victoria, Queensland, New South Wales. 17210 E. New Zealand. 60° W. Newfoundland and Eastern Canada. 75° W. Eastern belt of the United States, Chile. 1. Mariners carry on board ships chronometers which keep Greenwich time. When it is noon, local time, the chronometer indicates 4 hr. 48 min. P.M. What is the longitude of the ship? 2. When it is 10 o'clock P.M., March 2, in Washington, what is the standard time in Manila? Melbourne ? Berlin? 3. When it is 2 o'clock A.M., standard time, in Denver, what is the standard time of London? Manchester? Glasgow? Tientsin? Constantinople? 4. A telegram is sent from Madrid to Washington at 9 o'clock A.M. Allowing 1 hr. for transmission, when will it reach Washington? 5. At noon, local time, a chronometer indicates 11 o'clock P.M. What is the longitude? 6. A telegram is sent from Galveston to London at 10 o'clock P.M. When will it be received, allowing 2 hr. for transmission? 7. When it is 2 o'clock A.M. in Washington, standard time, what is the time in New Zealand? Tahiti? British India? 8. The San Francisco earthquake occurred April 18, 1906, at 5 A.M. When should the news have reached London? Berlin? Tokyo? Adelaide? (allowing one hour for transmission). 9. When it is noon in Paris, France, what is the time in Denver? Natal? Calcutta? Wellington (New Zealand)? 10. When it is 9 o'clock A.M. in Madras, what is the time in St. John's, Newfoundland? Chicago? Sitka? 11. When it is noon in the Hawaiian Islands, what is the time in Cairo (Egypt)? Perth (Western Australia)? THE LANGUAGE OF MATHEMATICS, RATIO, PROPORTION, PARTNERSHIP By mathematics is understood those branches of knowledge which deal with quantity. Arithmetic, algebra, geometry, surveying, etc., are included in the term mathematics. Mathematics has a language of its own. The word eight conveys a definite idea to the mind; the figure eight conveys the same idea. The words eight squared convey a definite idea to the mind; 82 conveys the same idea. The words three fourths of sixteen convey an idea; × 16 conveys the same idea. Similarly, the words, the quotient of seventy-two divided by eight, convey an idea; 12 conveys the same idea. The language of mathematics gives abbreviated forms for stating what P would occupy much more space if expressed in words; but one must be able to express in words the meaning conveyed by mathematical language. The sum of three and four is seven. This is written in the language of mathematics as: 3+4=7, which is usually read: "Three plus four equal seven." The difference between eighteen and seven is eleven. In the language of mathematics, this is written as : 18-7=11, which is read: "Eighteen minus seven equal eleven." It is often convenient to represent a large number by · an abbreviation, or to use an abbreviation to represent an unknown number, such as the answer to a problem. Letters are usually used for this purpose. For example: Of the 24 hr. in a day, a boy spends at school, at play, & in sleep, 2 hr. at meals, and the rest at work. How many hours does he work? For convenience, let z represent the number of hours he works, and let y represent the number of hours he does not work. Then, and Therefore, As then y, y = 1 of 24, plus of 24, plus & of 24, plus 2. y=6+4+9+2 = 21. x = 24-y, and y = 21, x= 24-21 = 3. Therefore, the boy works 3 hr. In using letters to represent numbers, any letter may be used to represent any number; but in any one problem each letter represents the same number in all parts of the problem. The expression a+b means the sum of the numbers represented by a and b; but it is read simply as: a plus b. The expression x-y means the difference obtained by subtracting the number represented by y from the number represented by x; but it is read simply as: x minus y. In writing the product of numbers represented by letters, the letters are placed next each other without any sign between. Thus, instead of writing a xbxe to represent the product of the numbers represented by a, b, and c, we write merely abc, and read it as: "a, b, c." Division of numbers represented by letters may be indicated by the division sign, or by writing the letters as numerator and denominator of a fraction. Thus, the number represented by a, divided by the number represented by b, is written a÷b, or, read: "a divided by b." the same way. a The expression,, is read in b' This use of letters gives very much abbreviated forms for stating rules. Thus, the rule for computing interest is: Multiply the principal by the rate to get the interest for 1 year, and this product by the time expressed in years. If the principal is represented by p, the rate by r, the time in years by t, then i equals p times r times t. So the rule becomes i = prt. Similarly, if F represents the area of a rectangle, b the base, and a the altitude, the rule for computing the area of a rectangle becomes F= ba. A figure written before a letter indicates multiplication. Thus, 5 a means 5 times a, which means five times the number represented by a. 46 means four times b, which means four times the number represented by b. 5 a is read: five a, and 4 b is read: four b. |