HISTORY OF PHYSICAL ASTRONOMY.

09

; more completely developed; and it will be necessary to include in theI formula the cubes and higher powers of t, if the same epoch should bealways retained.

j Laplace compared the preceding formula with an ancient observation| recorded in the annals of the Chinese . It appears that Teheou Kong, the’ regent of China , measured the summer solstice about the year 1100, beforethe Christian era, and from the result obtained by him, combined withanother recorded measurement of the winter solstice, astronomers havededuced 23° 54' 2".5 as the obliquity’- of the ecliptic in his time. Now, ifwe substitute 2900 for t in the preceding formula, applying to it the; negative sign, because it represents the number of years by which the: recorded observation has preceded the epoch of the formula, we get 23°51' 30" for the value of the obliquity. The near agreement of thisresult with that derived from the Chinese records is very remarkable,especially when we consider that the instrument with which Teheou Kongmade his observation was a vertical gnomon only eight feet high. Theaccordance between theory and observation is still more striking when weinstitute a comparison between the results of the former and the accuratedeterminations of modern astronomers. Titus Arago and Mathieu, fromobservations on tlie solstices made in the years 1812, 1813, 1814, con-cluded that the obliquity for the year 1813" was 23° 27' 49".28. If wecompute its value for the same epoch by the above formula, we obtain23° 27' 48".69 as our result. The difference between the observed andcomputed values is, therefore, only 0".59.

The displacement of the ecliptic, caused by the action of the planets onthe earth, affects the precession of the equinoxes, and the length of thetropical year. This displacement is found to produce a very slow motionof the equinoctial points upon the plane of the ecliptic in the direction ofthe earth's motion. Its effect is, therefore, contrary to that produced bythe action of the sun and moon upon the terrestrial spheroid; but, as it isvery minute compared with the hitter, it merely occasions a small diminu-tion of the annual quantity of precession. The mean value of precession,as determined by observation for the epoch of 1800, is 50".22350. Thelunisolar precession computed for the same epoch by the theory of gravita-tion is 50".37B15; hence the effect due to the displacement of theecliptic amounts to 0".14965.

The progression of the equinoxes, caused by the action of the planets onthe earth, will manifestly affect the length of the tropical year. Theaction of the sun and moon upon the terrestrial spheroid accelerates thearrival of the earth in the equinoxes, and, therefore, shortens the year;the action of the planets on the other hand retards its arrival, andconsequently lengthens the year. The acceleration being, however, greaterthan the retardation, the tropical year will, on the whole, be shortened bythe motion of the equinoctial points. If this motion was uniform, thelength of the tropical year would be invariable; but such, in fact, is notthe case. At present it is slowly increasing, and on this account thetropical year is gradually becoming shorter. The rate of diminution isabout half a second in a century; and consequently the tropical year isnow shorter by about ten seconds tlmn it was in the time of Hipparchus .

If the position of the equator was fixed, the variation of the obliquityof the ecliptic would depend entirely on tlie displacement of the latterplane, occasioned by the action of the planets on the earth. Laplace,however, has shewn that this displacement gives rise to a corresponding