points at G, H, I, K, L, being farther from the meridian, their corresponding points at g, h, i, k, I, must come to it later ; and as both suns come at the same moment to the point , they come to the meridian at the moment of noon by the clock.
In departing from Libra through the third quadrant, the real sun going through MNOPQ towards ft at II, and the fictitious sun through mnopq towards r, the former comes to the meridian every day sooner than the latter, until the real sun comes to R, and the fictitious to r, and then they come both to the meridian at the same time.
Lastly, as the real sun moves equably through STUYW, from R towards T, and the fictitious sun through stump, from r towards T , the former comes later every day to the meridian than the latter, until they both arrive at the point T, and then they make it noon at the same time with the clock.
It is now easy to conceive the effect of taking into account the variable motion of the sun in his annual circuit of the ecliptic. The effect already explained as arising from this cause, on the supposition that the sun moved in the equator, must simply be added to that just shown to arise from the obliquity of the ecliptic.
Let us combine the two causes, starting from December 31, on the assumption (near enough to the truth for our present purpose), that the sun moves most rapidly when at tiis greatest southerly declination. The effect due to varia tion of the sun s motion may be called A, and that due to the obliquity of the ecliptic may be called B ; and each may be considered positive or negative according as, con sidered alone, it sets the real sun later or earlier than the mean sun.
We find, then, from January 1 to March 31, A and B both positive, A increasing from to its maximum, B passing from through its maximum to again. All this time, then, A + B is positive. At the beginning A + B 0. About the middle of February B has its maximum value, and A a value less than its maximum ; at March 31, B is zero and A has its maximum value.
From April 1 to June 30, A is positive and B negative, A diminishing from its maximum to zero, B passing from through its maximum negative value to again. At the beginning, then, of this quarter, A + B is positive and equal to the maximum value of A. In the middle of May, B has its maximum negative value, arid A has a value less than its maximum positive value. The maxima due to A and B being not far from equality, it follows that A + B is now negative, and therefore some time before this A + B must have passed through the value 0. At the end of the quarter A + B is again 0, because A= and B=0.
From July .1 to September 30, A is negative and B positive, A increasing from to its maximum negative value, B passing from zero through its maximum positive value to zero again. Hence, at the beginning of the quarter A+B= ; at the end A+B=the maximum negative value of A. But about the middle of August, B has its maximum positive value while A has not its maxi mum negative value ; hence at this time A + B is positive, and therefore between then and September 30, A + B vanishes.
Lastly, from October 1 to December 31, both A and B are negative, A passing from its maximum value to zero, and B from zero to its maximum value, and thence to zero again. Throughout the quarter, then, A + B is negative. About the middle of November A + B is the sum of the maximum value of B and a value of A less than the maxi mum. At the end of the quarter A + B=0.
Owing to the fact that the time when the sun moves most rapidly follows by a few days the date (December 21) when the sun is at his greatest distance from the meridian, the dates above given are not strictly correct. The equa tion of time, or A + B, is zero nearly midway between December 21 and the end of the year, or about Christmas day, and it vanishes again on or about April 1C, June 16, and September 1st. The equation of time has four maxima. On February 11, the real sun is later than the mean sun by a maximum interval of 14 min. 31 sec. ; oil May 14, the real sun is earlier than the mean sun by a maximum interval of 3 min. 53 sec. ; on July 16, the real sun is later than the mean sun by a maximum interval of 6 min. 13 sec.; and lastly, on November 3, the real sun is earlier than the mean sun by a maximum interval of 16 min. 19 sec.
The inclination of the ecliptic to the equator results necessarily, as already mentioned, in a difference of seasons. When on the equator, the sun, like an equatorial star, is above the horizon during one-half of the day, and below the horizon during the other half. When he is north of the equator he is above the horizon for more than half the day, and reaches a higher altitude at noon than when on the equator. When south of the equator he is below the horizon for more than half the day, and does not reach so great an altitude at noon as when he is on the equator. As he is perceptibly the source of light and heat, it fol lows that when he is north of the equator we receive (in our northern latitudes), more light and heat than when he is on the equator, and so much the more as his northerly declination is greater ; while when he is south of the equator we receive less light and heat than when he is on the equator, and so much the less as his southerly declina tion is greater. These results are equally accounted for whether we regard the earth as fixed, and the sun as really travelling round the heavenly sphere on his inclined path, or whether we suppose the sun to be fixed, and the earth to travel around him on a correspondingly inclined path after the manner illustrated in fig. 14. Here, while the earth
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Fig. 14.—Diagram illustrating the Seasons.
