xxxii INTRODUCTION TO ASTRONOMY. 



will not revolve round the sun in a circle for the following reason. The 

 centrifugal force increases with the velocity of the body, or in other words, 

 the quicker it moves the stronger is its tendency to fly off in a right line. 

 When the earth arrives at E, its accelerated motion will have so far 

 increased its velocity and consequently its centrifugal force, that the latter 

 will prevail over the force of attraction, and drag the earth away from 

 the sun till it reaches G. It is thus that we escape from the dangerous 

 vicinity of the sun ; and as we recede from it, both the force of its attrac- 

 tion, and the velocity of the earth's motion diminish. From G the direc- 

 tion of projection is towards H, that of attraction towards S, and the 

 earth proceeds between them with a retarded motion, till it has com- 

 pleted its revolution. Thus the earth travels round the sun, not in a 

 circle, but an ellipsis, of which the sun occupies one of the foci ; and in 

 its course the earth alternately approaches and recedes from it, so that 

 what at first appeared to be a dangerous irregularity, is the means by 

 which the most perfect order and harmony are produced. The earth 

 then travels on at a very unequal rate, its velocity being accelerated as it 

 approaches the sun, and retarded as it recedes from it. 



Now it is mathematically demonstrable, that when a body moves round 

 Fig. 4. a P omt towards which it is attracted, the areas 



included between the line it describes and the 

 lines joining its place at different instants to 

 the attracting point, are equal in equal times. 

 The whole of the space contained within the 

 earth's orbit is (Jig. 4), divided into a number 

 of areas, or spaces, 1, 2, 3, 4, &c., all of which 

 are of equal dimensions, though of very differ- 

 ent forms ; some of them are long and nar- 

 row, others broad and short ; but they each 

 of them contain an equal quantity of space. 

 An imaginary line drawn from the centre of 

 the earth to that of the sun, and keeping pace 

 with the earth in its revolution, passes over 

 equal areas in equal times : that is to say, if it 

 is a month going from A to B, it will be a month going from B to C, 

 and another from C to E, and so on. 



The inequality is not in fact so considerable as appears in figure 4 ; for 

 the earth's orbit is not so eccentric as it is there described ; and, in reality, 

 differs but little from a circle. That part of the earth's orbit nearest the 

 sun is called its perihelion, that part most distant from the sun its aphelion ; 

 and the earth is about three millions of miles nearer the sun at its peri- 

 helion than at its aphelion. You will learn with surprise that during the 

 height of our summer, the earth is in that part of its orbit which is most 

 distant from the sun, and it is during the severity of winter that it 

 approaches nearest to it. The difference, however, of the earth's distance 

 from the sun in summer and winter, when compared with its total distance 

 from the sun, is but inconsiderable, for three millions of miles sinks into 

 insignificance in comparison of 95 millions of miles, which is our mean 

 distance from the sun. The change of temperature, arising from this 

 difference, would in itself scarcely be sensible, and it is completely over- 

 powered by other causes which produce the variations of the seasons ; but 

 the explanation of these must be deferred till we have made some further 

 observations on the heavenly bodies. Since the earth moves with greatest 

 velocity in that part of its orbit nearest the sun, it must complete its 



