LESSONS IN OKOO UA I ' 1 1 V . 



planes passing through the contro of the aun ; the sun itself 

 being placed in one of tlio foci of the ellipse. 



_'. That tho radius vector, or straight line drawn from the 

 centre of tho son to tho centre of tho planet, passes over equal 

 areas in equal times in every part of tho orbit ; that is, whether 

 the planet bo in its aphelion, or farthest from the sun, in its 

 perihelion, or nearest to the sun, or at its mean distance from 

 tho sun. 



3. That the squares of the periodic times of tho planets that 

 is, of the times of a complete revolution in their orbits are pro- 

 portional to the cubes of their mean distances from tho sun ; in 

 other words, that the square of tho periodic time of one planet is 

 to the square of the periodic timo of another planet, as the cube 

 of the mean distance of the former from the sun is to tho cube of 

 tho mean distance of tho latter from it. 



Into the full explanation of these laws we cannot enter until 

 we treat of astronomy ; in the meantime it is necessary to give 

 some explanation of the law which wo have marked first, though 

 it is generally accounted tho second, in order to clear up some 

 points connected with phenomena relating to tho earth, and the 

 circles drawn on the globe, which is the only true representation 

 of the earth's surface. Supposing, then, the ellipse in Fig. 1 to 

 represent the earth's annual orbit round the sun, and tho focus 

 r' the place of tho sun's centre ; then the point A will represent 

 the position of the earth's centre at mid-winter, when it is 

 nearest the sun, or in its perilielion ; B will represent its posi- 

 tion at mid-summer when it is farthest from tho sun, or in its 

 aphelion ; c will represent its position at the spring or vernal 

 equinox, when it is at its mean distance from the sun f and D its 

 position at the harvest or autumnal equinox, when it is also at 

 its mean distance from the sun. 



We t.Hinlf we hoar some of our readers exclaiming, notwith- 

 standing the elevated position in which we have supposed them 

 to be placed, " What ! Will you tell us that the sun is the cause 

 of light and heat on the earth's surface, and yet you assert that 

 the earth is nearer to the sun in winter than in summer ? How 

 can this be ?" Paradoxical as this may seem, it is nevertheless 

 tmio ; and the reason we shall now give. As you are supposed 

 to be looking from a great distance, and to be able to discern 

 all the motions of the planets, if you look narrowly at the earth, 

 you will perceive that besides its orbitual or annual motion round 

 the sun, it has a revolving or diurnal motion on its own axis. 

 By axis here is meant that imaginary straight line passing 

 through the globe of the earth, on which its rotation is supposed 

 to take place, and which is aptly represented in artificial globes 

 by tho strong wire passing from one side to the other, at the 

 points called the poles (that is, pivots), which are the extremities 

 of the axis. 



This revolving motion on its own axis may be likened to the 

 spinning of a top, a motion which continues while tho top ia 

 driven forward in any direction from one place to another. In 

 fact, the analogy would be so far complete independently of the 

 causes of the motion, if the top, while it is spinning or revolving 

 as it were on its own axis, were made to run regularly round in 

 an oval ring on the ground, under the lash of the whip. Thus, 

 the earth has two motions ; one on its own axis, performed once 

 every twenty -four hours ; and one in its orbit, performed once 

 every 365 days 6 hours. We have stated these periods in round 

 numbers, in order that they may be easily remembered ; but 

 the exact period of tho earth's daily revolution on its axis is 

 23 hours, 56 minutes, 4 seconds, and 9 hundredth parts of a 

 second ; and tho exact period of the earth's annual revolution in 

 its orbit is 365 days, 5 hours, 48 minutes, 49 seconds. 



Tho analogy of the motions of the top, however, to the mo- 

 tions of the earth, as thus described, is incomplete in respect of 

 the position of their axes. The axis of the spinning top is in 

 general upright or perpendicular to the ground, which may be 

 called the plane of its orbit, that is, of the oval ring in which it 

 is supposed to move ; but the axis of the earth in its daily motion 

 is not perpendicular to the plane of its orbit, or the ellipse in which 

 its annual motion is performed. In speaking of the plane of the 

 earth's orbit our analogy fails, for there is nothing to represent 

 the ground on which the motion of tho spinning top takes place. 

 The mere attraction of the sun, coupled with the effect of an origi- 

 nal impulse in the direction of a tangent to its orbit, is sufficient 

 to preserve tho earth in its orbitual motion in emoty space. Henoo 

 the sublimity and truth of the ancient passage in the book of 

 Job : " He stretcheth out the north over the empty place, and 



hangeth the earth upon nothing " (Job xxvi. 7). Thin passage 

 ia ringularly true in regard to the fiwt neutenoe an well a* to the 

 second, for the axis of the earth is inclined to the plane of iU 

 orbit, at an angle of 66 degree* 32 minutes, that w, rather 

 more than two- thirds of a right angle; so that literally and truly 

 " the north is stretched over the empty place," and not over the 

 body of the earth iUelf, in either of its motion*, whether axial 

 or orbitual. Thin inclination in preserved during the whole of its 

 motion in its orbit, and is the cause of the variation of the 

 seasons ; the preservation of the inclination of thin axis has been 

 not inaptly called the parallelism of the earth' 8 axu. 



Before explaining the effect of this parallelism and inclination 

 of tho earth's axis in producing the seasons, it will be proper to 

 explain what is meant by tangential impulse. In Fig. 2, let A C B 

 represent the orbit of tho earth, which is nearly 

 circular ; let D represent tho place of the sun, 

 and A the place of the earth at the moment 

 when it began its revolution in its orbit. At 

 this moment the force of the sun's attraction 

 would begin to act on the earth in the direction 

 A D, and had this alone been allowed to ope- 

 rate, would have drawn it rapidly towards the 



Fig. 2. 



sun in a straight line, until it had come finally in contact with 

 the sun itself; but at the same moment an original impulse 

 was, or is supposed to have been given to the earth in the direc- 

 tion A K, which is that of a tangent, or straight line tonchinf 

 the circle at the point A ; so that the earth, which under th 

 action of the former force would in a certain time have been 

 found at some point in A D, and under that of the latter forct 

 would, in the fame time, have been found at the point F in A K, 

 would, by the combined action of both forces, be found near the 

 point c in the curvilinear orbit A c B. This original impulse, 

 the effect of which remains to this day unaltered by the action of 

 attraction (seeing it has met with no resistance iu empty space, 

 and has been so balanced against the force of attraction as to 

 retain the earth in its orbit), is called the tangential impulse or 

 force, which was imparted to it when it began its orbitual revo- 

 lution. Young, Li his " Night Thoughts," alluding to this tenet 

 of the Newtonian philosophy, asks 



" Who rounded in his palm those spacious orbs ? 



Who bowled them flamiug through the dark profound ':" 



Night II. 



Let us now consider the effect of the inclination of the earth's 

 axis to the plane of its orbit. In Fig. 1 we have supposed the 

 sun to be at the focus F', while the earth is at the point A in 

 mid-winter. Now, at this point, you would see from your sap- 

 posed elevated position, that the northern half of tho earth's 

 axis is inclined to the major axis A B at an angle of 113 degrees 

 28 minutes, the supplement of its angle of inclination to the 

 plane of the orbit ; so that the North Pole, with the space on 

 the earth's surface around it to a considerable extent, is pr 

 vented from receiving the rays of the sun, and consequently thu> 

 heat of those rays ; while the South Pole, with the space around 

 it to the same extent, is made to receive these rays and to enjoy 

 their heat. Hence, while it is winter in the northern or arctic 

 regions of the earth, it is summer in the southern or antarctic 

 regions. While the earth is still in this position, the rays of 

 tho sun fall more obliquely upon the illuminated portions of the 

 northern hemisphere than they do upon tho southern hemisphere, 

 and thus have less power to produce heat than if they fell per- 

 pendicularly ; just as a person sitting at the side of a fire-place 

 with a good fire in it, feels less heat than a person who site 

 exactly in the front of it. 



On the other hand, if yon consider the earth from your 

 elevated position, when it is at the point B in mid-cummer, the 

 reverse of all this takes place. The northern half of the earth's 

 axis is inclined to the major axis (or line of apsides, as it is 

 sometimes called ; that is, the line of junction of the two oppo- 

 site points A and B) at an angle of 66 degrees 32 minutes, which 

 is its angle of inclination to tho plane of its orbit ; so that the 

 North Pole, with the space on the earth's surface around it, 

 above-mentioned, is made to receive the sun's wye, and conse- 

 quently their heat ; while the South Pole, with tho similar space 

 around it, is prevented from receiving those rays and enjoying 

 their heat. Hence, while it is summer in the northern or arctic 

 regions, it is winter in the southern or antarctic regions. While 

 the earth remains in this position, the rays of tho sun fall more 

 directly upon the northern hemisphere than they do upon the 



