MODERN VIEWS OF THE EARTH'S SHAPE. 13 



can recognise the geographical features of the coimtry is steadily 

 increased, and the circular horizon becomes larger ; and this can only 

 he explained on the hypothesis that the earth is a sphere. Because 

 if a number of tangents be drawn to a circle at equal distances on 

 tfach side of a point, and the lines are prolonged so as to meet each 

 other in pairs above that point, then it will be evident that only on 

 a spheroid can the horizon be a circle, which is enlarged propor- 

 tionately as the eye is elevated above its surface. Fourthly, ships at 

 sea gradually sink farther and farther below the horizon as their 

 distance from the shore increases, until even the tops of the masts 

 disappear. This is regarded as proof of the earth's spherical form 

 because, first, it is exactly analogous to the way in which a man 

 disappears from view by walking over ground which rises in a rounded 

 form; and, secondly, because the object which has disappeared can be 

 seen again if we climb a cliff a sufficient height above the sea. 

 Fifthly, if three rods of equal length are set up on a straight canal 

 free from locks at equal distances from each other, so that the top 

 of the most distant post can be seen through a telescope fixed to the 

 top of the post at the other end of the canal, then the top of the 

 middle post will be seen to rise considerably above the straight line 

 between the two end points ; and this can only be because the surface 

 of the water is not level, but has a spherical curve, and therefore goes 

 to prove that the earth's surface is spherical. 



There was no suspicion of the polar flattening of the earth, so far 

 as is known, till the time of Sir Isaac Newton. In the year 1671, 

 Richer, at Cayenne in South America, found that the pendulum of 

 the clock which he had brought from Europe was no longer of the 

 right length to keep time, vibrating more slowly the nearer it was 

 moved to the equator, so that the clock lost 2\ minutes a day. It 

 thus became known experimentally that the force of gravity diminished 

 towards the equator, because the rapidity of the pendulum swing is 

 in proportion to the intensity of the earth's attraction. 'And so soon 

 as one of the 360 degrees into which a circle passing through the 

 centre of the earth is divided, had been accurately measured, it became 

 possible to determine the size of the earth and to calculate the figure 

 which the earth ought to assume in consequence of its rotation. This 

 rotation diminishes the force of gravity at the equator by -g^th ; and 

 the total force of gravity is now known to be -y-p-^th greater at the 

 pole than at the equator. It was hence calculated that the earth 

 must be flattened towards the poles by an amount nearly equal to 

 that afterwards found by measurement. The exact amount of flatten- 

 ing has been determined by finding the curve of the meridians in 

 different latitudes ; and the degree of a meridian has been repeatedly 

 measured, and is known to increase in length from 362,644 feet at the 

 equator to 366,489 feet at the pole. A degree is always ^-g-^th of a 

 circle, and as the circle becomes larger so the degree obviously becomes 

 longer. The lengthening of the degree then, towards the pole, is 

 evidence that the earth's outline there becomes a part of a larger 

 circle, or in other words, it becomes more flattened and more of an 



