338 



THE POPULAR EDUCATOR. 



bulge or curve of the earth's surface. When the hull has just 

 begun to disappear from a person standing on the surface of the 

 ground, the whole will be visible to an observer on an elevated 

 building ; and if there be a lofty mountain near by, the vessel 

 will be seen from this after every portion of it is hidden from 

 those on the beach. This shows that the surface of the earth is 

 curved, and, in fact, a rough estimate of the size of the earth 

 may be formed in this way. We have only to fix upon two ele- 

 vations of equal height as, for instance, marked places on the 

 masts of two vessels and ascertain the exact distance at which 

 they are hidden from one another by the curvature of the earth. 

 We must know also the elevation of the places on the masts 

 above the level of the sea, and then by a simple proportion we 

 shall obtain the diameter of the earth. The question will be 

 stated thus : As the height of the station of observation is to 

 the distance of the visible horizon (which is half the distance 

 between the two stations), so this distance is to the diameter of 

 the earth. 



There are considerable difficulties attending this plan, which 

 prevent our arriving at very accurate results by it. When it is 

 tried at sea, there is great difficulty in ascertaining the exact 

 distance of the vessels, as well as in choosing a day when the 

 surface of the water is sufficiently smooth ; and on land it is 

 seldom that a large tract can be chosen sufficiently level to 

 answer the purpose, as, even in large plains, there are frequently 

 undulations or slopes which would materially interfere with the 

 accuracy of the results. In addition to this there is another 

 cause of error introduced by the action of the air on the rays of 

 light, or, as it is termed, refraction. The effect of this is, as 

 will shortly bo seen, to bend the rays out of their straight 

 course, and thus to render the object visible when in reality the 

 curvature of the earth intervenes between it and the observer. 

 It enables us, in fact, to see to a certain extent round the bend. 



From these causes, this plan of measuring the earth has not 

 been fully carried out. Roughly, however, we shall find that 

 two places elevated ten feet become hidden from one another at 

 a distance a little under eight miles ; that is, a straight line 

 drawn from one of these to the other would just touch the earth 

 midway between them. The curvature, then, may be set down 

 as ten feet in three miles and seven-eighths, and we state our 

 sum in the following way : 



As 10 feet : 3 miles : : 3J miles : diameter of the earth. 



We shall find that this gives us about 8,000 miles as the 

 diameter of the earth, which is not far from correct. The more 

 accurate mode of ascertaining its dimensions is by measuring an 

 arc of the meridian in a way that will shortly be explained. 



There is another very conclusive proof of the rotundity of the 

 earth which should just be referred to namely, that afforded 

 by the shape of its shadow. The earth is an opaque body, and 

 must therefore throw a dark shadow ; but the shape of this can 

 only be seen when there is some object on which it can be 

 thrown. Now, there is only one object which ever comes near 

 enough to us to receive this, and that is the moon. We must 

 wait, therefore, till the moon comes directly in a line with us 

 and the sun, and then we shall see the shadow. Now when this 

 happens, it is called a lunar eclipse ; and if we watch the moon 

 as it enters the shadow of the earth, and again as it leaves it, 

 wo shall find that the dark lino is always curved to an arc of a 

 circle. The earth, therefore, must either be a globe or a flat 

 circular disc ; and at first sight we might incline to the latter 

 view, and imagine, with some of the ancients, that we dwelt on 

 a flat surface like the top of a round table. When, however, we 

 notice that, in whatever position we happen to be with regard to 

 the sun at the time of an eclipse, the shadow is always circular, 

 vre soon are assured that the earth must be globular, as no other 

 figure would always cast a circular shadow. 



Having clearly realised the fact of the earth's rotundity, we 

 have next to look upon it as a body suspended freely in space 

 without any support. According to ancient ideas, Atlas bore 

 up the world on his shoulders ; and many of the Hindoos of the 

 present day assert that it is supported by a serpent and a 

 tortoise. It is clear, however, that these attempted solutions of 

 the difficulty only remove it one step further, for we should 

 have to seek some support for the man or the serpent. The 

 real difficulty arises from our not clearly understanding that the 

 reason why a body falls to the earth is simply because the earth 

 has an attraction for it. Hence, if we want to sustain any 



object some distance above its surface, a support of some kind 

 must be used to resist this attraction. 



Now the only body which exerts a sufficiently powerful 

 influence on the earth to have much effect is the sun : to it, 

 accordingly, the earth would speedily fall were it not that its 

 own momentum in its orbit is just sufficient to overcome this 

 attraction. These two forces are so beautifully balanced that 

 under their joint influence the earth moves evenly round in its 

 elliptical orbit. At a certain part of the year namely, in the 

 middle of winter the earth is nearer the sun than at any other 

 time ; and, as we saw in our lessons on Mechanics, attraction, 

 increases inversely as the square of the distance, the attraction 

 of the sun is therefore greater at this period, and we should at 

 first expect that since this is the case, the earth would approach 

 it nearer and nearer with ever-increasing speed, till at last the 

 momentum would be quite overcome, and it would fall into the 

 sun and be consumed. 



No such result, however, happens, for as soon as the earth 

 begins to approach the sun, it is, as it were, rolling down hill ; 

 its speed, therefore, increases, and with this its momentum, 

 as to more than overcome the increased attraction ; and tilt 

 the earth, having passed the end of the ellipse, begins to recec 

 again. During the next half of its orbit it is receding frou 

 the sun, which is therefore drawing it back, and checking 

 speed ; so that gravitation again becomes the more powerfii 

 force, and the earth commences again to approach the sun. 

 this way the two forces alternately preponderate, and by the 

 joint action the earth constantly keeps to its orbit. 



Let us, then, all through our lessons bear in mind these fact 

 that the earth is an almost spherical body, rotating constant 

 on its axis, and that it is suspended freely in space, while 

 describes its journey round the sun in the course of a year. 



As we have several times spoken of the horizon, it will 

 well for us distinctly to know what we understand by it, 

 sometimes there is a little confusion on this matter. 



The rational or tri>e horizon is an imaginary plane 

 through the centre of the earth, so that the line where it cuts 

 the surface is everywhere equidistant from the observer. If we 

 take an orange or an apple, and divide it into two equal por- 

 tions, or place a ring round it as shown in Fig. 6, so that it 

 is midway between the eye and the stalk, it will represent the 

 horizon. In an ordinary celestial globe, if the pole be elevated 

 to the latitude of the place, the situation of the wooden horizon 

 will correspond with that of the rational horizon to the observer. 

 Thus it will be seen that if this plane be extended on all sides 

 to the sky, it will divide it into two exactly equal hemispheres, 

 one of which will be visible to the observer. 



There is, however, another sense in which the word horizon is 

 used. On ascending any height a line will be seen all round us, 

 where the earth and sky appear to touch, and this is called the 

 sensible or visible horizon. 



At sea, or on a level plain, this line will be seen to be a per- 

 fect circle ; on land, the elevations of the country usually inter- 

 fere with the outline : still we can perceive that it is of a circular 

 form, and that our point of observation is situated exactly in 

 the middle of it. 



The size of this circle increases with our elevation above the 

 earth. Hence, when a sailor wants to know if any vessel is in 

 sight, he ascends to the mast-head, where his view is much more 

 extensive than if he had remained on the deck of the vessel. 

 In the same way, if we ascend any lofty mountain, we gain a 

 very extensive view of the country round. If we could be 

 placed at a great distance from the earth as, for instance, on 

 the surface of the moon we should see just one-half of the 

 globe, and the rational and sensible horizons would then exactly 

 coincide. This, of course, cannot be, and the highest elevation 

 ever yet reached by man, or that in all probability ever will be 

 attained, is so small in comparison with the diameter of the 

 earth, that only a small portion of the earth has ever been 

 visible at once. The largest amount ever thus seen was by 

 Messrs. Coxwell and Glaisher, when they attained in a balloon 

 an elevation of about six and a-half miles, and then about 5^5 

 of the surface of the globe was in sight. 



The following general rule will enable us to calculate approxi- 

 mately the distance of the visible horizon when the height of 

 the station of observation is known : Express the height in 

 feet and increase it by a half, then extract the square root, and 

 this will give the distance in miles. Thus, if a tower be IS 



