E When a straight line standing on another straight line makes the adjacent angles equal to one another, each of these angles is called a right angle. An acute angle is less than a right angle, as ABD, DBE. An obtuse angle is greater than a right angle, as DBC. A B LESSON II.-TABLES OF MEASUREMENT. In mensuration, we have to measure lines, surfaces, and solids, and to enable us to do this, and to express the result in words which other people will readily and accurately understand, we must learn the following tables of linear, superficial, and solid measure, or (as they are more commonly called) long, square, and cubical measure. Note. The name acre always, and the name perch nearly always, are restricted to square measure. III.-SOLID MEASURE. 1728 Cubic inches 27 Cubic feet 1 Cubic foot. 1 Cubic yard. 1 Gallon contains 277 274 cubic inches. 1 Gallon of distilled water weighs 10 lbs. 1 Cubic inch of cast-iron weighs lb., nearly. It is very important to have absolutely perfect examples of all these measurements, so that everybody can refer to them if he pleases as the standards of accuracy. Hence in every town such standards are provided by the authorities, and are used as tests in case of any dispute. But, as you all have doubtless learned already in that part of arithmetic which is called Weights and Measures, besides these standards of reference there is another method of finding whether weights and measures are correct, for all of them can be deduced by calculation from the length of a seconds' pendulum. Formerly, however, great confusion was caused by the fact that there were no invariable standards of weight or measure, and such names as pole, stone, or ell, had one meaning in one part of the country, and another meaning in another part. In some parts of England this confusion still remains; thus, although the statute pole (i.e., the measure of length called a pole which is the only one legally recognised) is equal to 5 yards, in Scotland 6 yards make one pole; and, to make matters still worse, in Ireland and the North of England a length of 7 yards, and in Cheshire of 8 yards, is called by the same name. In the same way the name ell, used in cloth measure, has at least four different meanings, according as it happens to refer to English, Flemish, French, or Scotch ells. Many of the old measures were also useless, because the standards by which they were determined are accidental and variable, e.g., nail, foot, hand, span, barley-corn, stone. The chain, which is a very important length in land measuring, will be remembered more easily if you keep in mind that in a game of cricket the wickets are pitched just one chain apart, i.e., 22 yards. This is generally called Gunter's chain, because its use was first adopted by a man named Gunter. In France they have a system of measurement called the metric system, which is much better and simpler than ours. You will find a full account of this very interesting and perfect system in most books on arithmetic, so that it is not necessary to explain it here. But you must remember that instead of the yard which we use in most English measurements of length, the French use the metre, which is a little longer than a yard, and contains 39.37,079 inches. There are two other names which are sometimes used in French mensuration, viz., are and stere. The are is a square, each side of which measures 10 metres, and which therefore contains 100 square metres. The stere is a cubic metre. Instead of using these two names, the French generally speak of square and cubic metres, which is much simpler. In order to make you acquainted with the French metric system, a few examples will be interspersed at various places among the other exercises in this book. 4. 5. 6. 7. poles in 469 ac. 3 roods 14 poles? miles in 147,852 inches 8. Reduce 78,254 Flemish ells to yards. 9. 10. 11. 12. 13. 2800 poles to acres. 489 acres 14 poles to poles, 391,256 cubical inches of cubical yards. 71 miles 1 fur. 6 po. 2 yds. to yards * The nail is used in cloth measure, and contains 24 inches. 14. Reduce 166 fur. 33 poles 3 yds. to feet. 15. 16. 17 po. 2 yds. 2 ft. 8 in. to inches. 61 miles 7 fu. 19 po. 2 yds. 7 in. to inches. 17. If I walk 2 miles 88 yards in 40 minutes, how long will it take me to walk 390 miles. 18. Multiply 399 ac. 1 ro. 18 po. 27 yds. 8 ft. 36 inches by 98. 19. Divide 76 ac. 0 ro. 4 po. 6 yds. 0 ft. 112 in. by 31. 3687 c. yds. 1684 c. in. by 264. LESSON III.-MEASUREMENT OF ANGLES. It has been already explained that a right angle is greater than an acute angle, and less than an obtuse angle. It must be carefully remembered that the size of an angle is not at all dependent upon the length of the two lines which make it, but upon the sharpness or bluntness (i.e., the acuteness or obtuseness) of the points they make at meeting. Thus, all the right angles marked A are of the same size, and all the angles marked B; while the angle C is much greater than that marked D. All angles are measured by the number of degrees which The right angle is so called because it is the standard angle by which we measure other angles, just as the straight line is often called a right line because it is the standard by which we measure and test all other lines. Again, it is usual to divide every degree (°) into sixty equal parts called minutes ('); and each minute into sixty equal parts called seconds ("). In writing, instead of the names we use the symbols, which are marked above in brackets, so that 27° 42′ 23′′ is only a short way of writing down 27 degrees, 42 minutes, 23 seconds. |