intimate relation between the velocity of the variation from the spherical form. reason that the mathematician would c since the earth is in rotation, it must circular perfection, even if the true shape found by observation. A poet has writte The very law that moulds a tear, And he is right in so far as he expresses the law of gravitation tends to make all of matter assume the spherical form. C tending all the while to pull the par spherical shape. But other influences te the particles from their proper positi result is that a tear, like a dewdrop or a never truly spherical, and that the earth bodies in rotation vary considerably from conception. SYNOPSIS OF CHAPTER II The form of the earth.-Proofs of the earth's (1) The shadow of the earth, into which th during an eclipse, has a circular outline; (2) horizon is everywhere the same; (3) the alt regularly increase in travelling to higher latitudes; and (4) the times at which the sun and stars are due south are different at different places. The earth spins or rotates like a top, taking 23 hours 56 minutes to perform one rotation. The axis of rotation coincides with the shortest diameter, and the poles are at its extremities. The apparent motion of the heavens from east to west, in consequence of which celestial bodies rise, south, and set, is a reflection of the earth's real motion in an opposite direction. The reason why stars are invisible during the day, except a telescope is employed, is that the glare of sunlight in the earth's atmosphere overpowers their faint rays. Dawn and twilight are caused by the sun illuminating the upper regions of our atmosphere. The phenomena would not occur if the earth were without an atmosphere and would last longer if the atmosphere were increased in height. The earth is a cooling globe.—It was once a ball of molten matter; at the present time the interior is hot; in the distant future it will have cooled down to the condition of the moon. The effects of rotation upon a ball of melted rock, such as that in which the earth at one time existed, would be to cause polar compression and equatorial bulging. The amount of compression exhibited by a solid celestial body furnishes a means of calculating the period of rotation at the time of solidification. Polar compression and rotational velocity are intimately connected. If the latter is increased the former is increased also. The sun is an example of a body having a low velocity of rotation. Saturn and Jupiter exhibit effects of high velocity. CHAPTER III THE SIZE AND MASS OF THE EARTH In the previous chapter a general idea has been given of the figure of the earth, and we have now to show how the exact size and shape have been determined. But, before going into the subject, it is necessary to have a clear idea as to the method of measuring angles. To say that an angle is so many yards or feet wide is, of course, meaningless; it is just as absurd as expressing the time of day in miles. We use inches, feet, yards, and miles to measure linear dimensions; the flow of time is measured in seconds, minutes, and hours; and to properly express the sizes of angles, certain definite units of reference must be employed. The first thing necessary, then, is to determine the unit employed in angular measurement. If circles of any size are drawn, and the circumference of each is divided into, say, a dozen parts, the angle between two lines drawn from two adjoining parts to the centre always remains the same. In a similar manner, when the circumference is divided into 360 parts, the angle between two lines drawn from two adjoining parts is constant, whatever the size of the circle. This angle is termed a "degree." We can illustrate the principle of angular measurement by means of a watch (Fig. 17). The dial of a watch or clock has sixty points marked upon it, each representing one minute of time. On a small watch the points are rather close together; on the dial of a large clock XII XII JA FIG. 17.-To show that the angle contained between two lines does not depend upon the size of a circle. they are very clearly separated. But whether the minutes on the dial of the clock at Westminster are taken, or those of the smallest ladies' timekeeper, two lines drawn from two successive points to the centre. include precisely the same angle in each case. The minute hand of a clock or watch moves through 360 degrees in going completely round the face. In pass ing from XII. to VI. the hand moves through 180 degrees, and from XII. to III. it moves through 90 degrees. Hence it is easily calculated that, in moving from one minute to the next, the hand travels through 6 degrees. Degrees of angular measurement are divided into sixty equal parts, known as minutes, and these in turn are divided into sixty equal parts termed seconds. Degrees (°), minutes ('), and seconds (") of arc must not, of course, be confused with hours (h.), minutes (m.), and seconds (s.) of time. With this preliminary information, the methods of determining the exact size and shape of the earth can be understood. In the first place, it is evident that if we have only a portion, or an "arc," of the circumference of a circle, and we know the angle between two lines drawn from the ends of the arc to the centre, we can calculate the length of the complete circumference. Thus, suppose a certain arc measured two inches, and that the lines from the ends of the arc were inclined to each other at an angle of 12 degrees, then the length of the circumference would be thirty times two inches, that is, 60 inches, for 12 degrees represent one-thirtieth of the whole 360 degrees. Applying similar reasoning to the case of the earth, it will be seen that if we know the exact length of a comparatively small part of the circumference, and the angle between two lines drawn from the centre of the earth to the ends of the arc, the distance round the earth can be found. The first thing to be done, then, is to accurately determine the length of a line a few hundreds of miles long. A more or less level plain is chosen. To it are conveyed a half dozen bars, each about ten feet long, |