ELLIPTICITY OF THE EARTH'S ORBIT. 125 that the amount of heat received by the earth is exactly proportioned to its angular velocity around the sun. Therefore since at the perihelion, the earth moves through an arc of 61' in a day, and at its aphelion through an arc of 57', the respective daily amounts of heat received by the earth at its perihelion and aphelion bear the relation of 61, to 57; a variation in temperature so small that its influence upon the climates of the two hemispheres is inappreciable, amid other more potent disturbances. ELLIPTICITY OF THE EARTH'S ORBIT--ITS EFFECT ON THE SEASONS. 224. A slight difference in the length of the seasons is found to exist on account of the ellipticity of the earth's orbit; for, in consequence of the earth moving faster in its path according as it is nearer to the sun, the time that elapses between the autumnal equinox and the vernal, is now between seven and eight days, (7 days 16h. 2m;) shorter than the period embraced between the vernal and autumnal.1 225. The relative positions of the perihelion and aphelion in regard to the solstices and equinoxes, at the commencement of the present century, are shown in Fig. 42, where E and E' represent the two equinoxes, EE' the line of the equinoxes, Sand S1 the two solstices, and SS1 the line joining the solstices, A and P are the aphelion and perihelion, and AP the line of the apsides. All these lines intersect at the sun. These positions are not invariable, for we have seen Art. 183, that the aphelion and perihelion have a slow motion from west to east. They days h. m. 1. In the year 1850, according to Hind, the time elapsed between, The vernal equinox and summer solstice was, The summer solstice and autumnal equinox was, The autumnal equinox and winter solstice was, The winter solstice and vernal equinox was, The interval between the vernal equinox and the autumnal, was therefore, equal to 186 days 10h. 57m., and that between the autumnal and vernal, 178 days, 18h. 55m. The difference between these two intervals, is therefore, seven days, sixteen hours, and two minutes. Explain why it is not? Why does the ellipticity of the earth's orbit affect the lengths of the seasons? How much does the period of time from the vernal to the autumnal equinox now exceed the period from the autumnal to the vernal? FIG. 42. POSITION OF THE PERIHELION IN THE YEAR 1800, A.D. will therefore in the course of nearly a thousand centuries Art. 185, pass round the entire orbit of the earth, and coincide at definite periods of time, with the solstices and equinoxes, slightly affecting the length of the various seasons by this motion. In the year 1250, the perihelion coincided with the winter, and the aphelion with the summer solstice, as shown in Fig. 43, the construction of which is similar to that of Fig. 42. The spring and winter were then equal in length, and the same was true of summer and fall. A glance at the figure substan POSITION OF THE PERIHELION IN THE YEAR 1250, A. D. Has the motion of the perihelion and aphelion any effect on the length of the sensons ? In what year did the perihelion coincide with the winter and the aphelion with the summer solstice? How did the seasons then compare with each other in length? ELLIPTICITY OF THE EARTH'S ORBIT. 127 226. The perihelion at the creation coincided very nearly with the vernal equinox, a point which can be proved by a simple calculation. In the year 1250, A. D., the perihelion was at the winter solstice, i.e. 90° or 324,000" distant from the vernal equinox. Now as the perihelion withdraws from the vernal equinox at the annual rate of 61,53"; it will consequently take as many years for it to move from the vernal equinox to the winter solstice as the number of times that 61,53" is contained in 324,000"; viz., 5,265. Subtracting then 1250 from 5265 we obtain 4,015 from the number of years before the Christian era, when the perihelion coincided with the vernal equinox, which is very nearly the date of the creation. 1. The vernal equinox moves from east to west at the annual rate of 50.24". The perihelion moves from west to east at the annual rate of 11.29". These two points therefore, separate from each other at the yearly rate of 61.53". Prove that the perihelion nearly coincided with the vernal equinox at the epoch of the creation? PART SECOND. SOLAR SYSTEM. CHAPTER I. THE SUN. 227. We now proceed to describe the SUN, a vast luminous and material globe; around which a train of planets and comets revolve, constituting with the sun the SOLAR SYSTEM. 228. When the sun is observed through colored glasses, which intercept a portion of its heat and lessen its dazzling brilliancy, it presents the appearance of a perfect circle, whose average angular diameter is 32'. We are not however to suppose that it is flat and round like a plate. While we revolve on the earth about the sun, the latter at the same time rotates on its axis, and yet always appears round; a fact which proves it to be a globe like our earth, for it is only a spherical body that will appear of a circular form when viewed from any direction. 229. REAL DIAMETER OF THE SUN. We have seen that the average distance of the sun from the earth is about 95,000,000, (more accurately 95,298,2601,) and that the average apparent diameter is 32. Knowing these two quantities were enabled to obtain the actual diameter of the orb, by the method explained in Art. 198. 230. In Fig. 44, we represent the sun by the circle S, half the sun's diameter by the line SB, the earth by the 1. According to the calculations of Prof. Encke of Berlin. What is the subject of PART SECOND? What of Chapter I. ? What is said of the SUN? What form does it present when viewed through colored glasses? What is its average angular diameter? Is it flat and round like a plate? What proof have we that it is a globe? What two quantities must be known in order to ascertain the real diameter of the sun? circle E, and the distance of the centre of the earth from the centre of the sun by the line ES, which is the hypothenuse of the right angled triangle SEB.' 231. We next take them from the trigonometrical tables the values of the sides of a triangle similar to SEB. Let S'E'B' Fig. 44, be such a triangle, in which the angle S'E'B' equal to SEB is 16'; S'BIE' equal to SBE is a right angle, and B'S'E' equal to BSE is 89° 44'." Now if S'E' is one mile, the value of S'B', as shown by the tables, is four thousand six hundred and fifty-four millions of a mile, (,004654ths of a mile.) We thus obtain the following proportion, S'E' (1 mile): SE (95,298,260 miles): S'B (004654ths of a mile): the length of SB in miles. Multiplying, therefore, the second and third terms together, and dividing by the first, we obtain the following expression for the value of SB, the radius of the sun viz., Thus the length of the radius is found. The entire di 1. SEB is a right angle, because when a line, as EB is drawn to the extremity of a radius of a circle as B, and also touches the circle at that extremity, it makes a right angle with the radius. 2. Since the sum of the three angles in the triangle SEB is equal to 1800 (Art. 13,) if the value of SBE and SEB are known, their sum subtracted from 1800 gives the value of the third angle BSE. Find the length in miles of the sun's diameter ? |