A Text-Book of Astronomy

Appendix 383

INDEX 387

LIST OF LITHOGRAPHIC PLATES

FACING PAGE I.--Northern Constellations 124 II.--Equatorial Constellations 190 III.--Map of Mars 246 IV.--The Pleiades 344 Protractor In pocket at back of book

LIST OF FULL-PAGE ILLUSTRATIONS

FACING PAGE A Total Solar Eclipse Frontispiece The Harvard College Observatory, Cambridge, Mass. 24 Isaac Newton 46 Galileo Galilei 52 The Lick Observatory, Mount Hamilton, Cal. 60 The Yerkes Observatory, Williams Bay, Wis. 100 The Moon, one day after First Quarter 150 William Herschel 234 Pierre Simon Laplace 364

ASTRONOMY

CHAPTER I. Different Kinds of Measurement

DIFFERENT KINDS OF MEASUREMENT

1. ACCURATE MEASUREMENT.--Accurate measurement is the foundation of exact science, and at the very beginning of his study in astronomy the student should learn something of the astronomer's kind of measurement. He should practice measuring the stars with all possible care, and should seek to attain the most accurate results of which his instruments and apparatus are capable. The ordinary affairs of life furnish abundant illustration of some of these measurements, such as finding the length of a board in inches or the weight of a load of coal in pounds and measurements of both length and weight are of importance in astronomy, but of far greater astronomical importance than these are the measurement of angles and the measurement of time. A kitchen clock or a cheap watch is usually thought of as a machine to tell the "time of day," but it may be used to time a horse or a bicycler upon a race course, and then it becomes an instrument to measure the amount of time required for covering the length of the course. Astronomers use a clock in both of these ways--to tell the time at which something happens or is done, and to measure the amount of time required for something; and in using a clock for either purpose the student should learn to take the time from it to the nearest second or better, if it has a seconds hand, or to a small fraction of a minute, by estimating the position of the minute hand between the minute marks on the dial. Estimate the fraction in tenths of a minute, not in halves or quarters.

EXERCISE 1.--If several watches are available, let one person tap sharply upon a desk with a pencil and let each of the others note the time by the minute hand to the nearest tenth of a minute and record the observations as follows:

2h. 44.5m. First tap. 2h. 46.4m. 1.9m. 2h. 44.9m. Second tap. 2h. 46.7m. 1.8m. 2h. 46.6m. Third tap. 2h. 48.6m. 2.0m.

The letters h and m are used as abbreviations for hour and minute. The first and second columns of the table are the record made by one student, and second and third the record made by another. After all the observations have been made and recorded they should be brought together and compared by taking the differences between the times recorded for each tap, as is shown in the last column. This difference shows how much faster one watch is than the other, and the agreement or disagreement of these differences shows the degree of accuracy of the observations. Keep up this practice until tenths of a minute can be estimated with fair precision.

2. ANGLES AND THEIR USE.--An angle is the amount of opening or difference of direction between two lines that cross each other. At twelve o'clock the hour and minute hand of a watch point in the same direction and the angle between them is zero. At one o'clock the minute hand is again at XII, but the hour hand has moved to I, one twelfth part of the circumference of the dial, and the angle between the hands is one twelfth of a circumference. It is customary to imagine the circumference of a dial to be cut up into 360 equal parts--i. e., each minute space of an ordinary dial to be subdivided into six equal parts, each of which is called a degree, and the measurement of an angle consists in finding how many of these degrees are included in the opening between its sides. At one o'clock the angle between the hands of a watch is thirty degrees, which is usually written 30°, at three o'clock it is 90°, at six o'clock 180°, etc.

A watch may be used to measure angles. How? But a more convenient instrument is the protractor, which is shown in Fig. 1, applied to the angle A B C and showing that A B C = 85° as nearly as the protractor scale can be read.

The student should have and use a protractor, such as is furnished with this book, for the numerous exercises which are to follow.

EXERCISE 2.--Draw neatly a triangle with sides about 100 millimeters long, measure each of its angles and take their sum. No matter what may be the shape of the triangle, this sum should be very nearly 180°--exactly 180° if the work were perfect--but perfection can seldom be attained and one of the first lessons to be learned in any science which deals with measurement is, that however careful we may be in our work some minute error will cling to it and our results can be only approximately correct. This, however, should not be taken as an excuse for careless work, but rather as a stimulus to extra effort in order that the unavoidable errors may be made as small as possible. In the present case the measured angles may be improved a little by adding (algebraically) to each of them one third of the amount by which their sum falls short of 180°, as in the following example:

Measured angles. Correction. Corrected angles. ° ° ° A 73.4 + 0.1 73.5 B 49.3 + 0.1 49.4 C 57.0 + 0.1 57.1 ----- ----- Sum 179.7 180.0 Defect + 0.3

This process is in very common use among astronomers, and is called "adjusting" the observations.

3. TRIANGLES.--The instruments used by astronomers for the measurement of angles are usually provided with a telescope, which may be pointed at different objects, and with a scale, like that of the protractor, to measure the angle through which the telescope is turned in passing from one object to another. In this way it is possible to measure the angle between lines drawn from the instrument to two distant objects, such as two church steeples or the sun and moon, and this is usually called the angle between the objects. By measuring angles in this way it is possible to determine the distance to an inaccessible point, as shown in Fig. 2. A surveyor at A desires to know the distance to C, on the opposite side of a river which he can not cross. He measures with a tape line along his own side of the stream the distance A B = 100 yards and then, with a suitable instrument, measures the angle at A between the points C and B, and the angle at B between C and A, finding B A C = 73.4°, A B C = 49.3°. To determine the distance A C he draws upon paper a line 100 millimeters long, and marks the ends a and b; with a protractor he constructs at a the angle b a c = 73.4°, and at b the angle a b c = 49.3°, and marks by c the point where the two lines thus drawn meet. With the millimeter scale he now measures the distance a c = 90.2 millimeters, which determines the distance A C across the river to be 90.2 yards, since the triangle on paper has been made similar to the one across the river, and millimeters on the one correspond to yards on the other. What is the proposition of geometry upon which this depends? The measured distance A B in the surveyor's problem is called a base line.

EXERCISE 3.--With a foot rule and a protractor measure a base line and the angles necessary to determine the length of the schoolroom. After the length has been thus found, measure it directly with the foot rule and compare the measured length with the one found from the angles. If any part of the work has been carelessly done, the student need not expect the results to agree.

In the same manner, by sighting at the moon from widely different parts of the earth, as in Fig. 3, the moon's distance from us is found to be about a quarter of a million miles. What is the base line in this case?

4. THE HORIZON--ALTITUDES.--In their observations astronomers and sailors make much use of the plane of the horizon, and practically any flat and level surface, such as that of a smooth pond, may be regarded as a part of this plane and used as such. A very common observation relating to the plane of the horizon is called "taking the sun's altitude," and consists in measuring the angle between the sun's rays and the plane of the horizon upon which they fall. This angle between a line and a plane appears slightly different from the angle between two lines, but is really the same thing, since it means the angle between the sun's rays and a line drawn in the plane of the horizon toward the point directly under the sun. Compare this with the definition given in the geographies, "The latitude of a point on the earth's surface is its angular distance north or south of the equator," and note that the latitude is the angle between the plane of the equator and a line drawn from the earth's center to the given point on its surface.

Continue reading A Text-Book of Astronomy free in the Wunder reader →