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HISTORY OF PHYSICAL ASTRONOMY.

it was constantly diminishing. The earliest measurement of it, if weexclude the records of Eastern nations, is due to Eratosthenes , whonourished about the year 870 a.c. This astronomer found the anglebetween the tropics to amount to 47° 42' 27", whence the obliquity of theecliptic was equal to 23° 51/ 13". A1 Batani, in the ninth century, fixed itat 23° 35'. Waltlierus, the German astronomer, made it 23° 29' 47" aboutthe close of the fifteenth century; and Tycho Brahe made it 23° 29'about the year 1581. Iticcioli, Gassendi , and Flamstead maintained thatthe obliquity was invariable, ascribing the discordances of astronomerswholly to errors of observation. On the other hand, Bouillaud andWendelin contended that it was continually diminishing; and this opinionwas urged with great ability by Louville, in the Memoirs of the Academyof Sciences for 1710. About the middle of the last century, Bradley,Lacaille, and Mayer found the obliquity to be 23° 28' 18", and in 1800,Delambre, Mechain , and Lefrancius made it 23° 28'. Thus it appearsthat, although the earlier observations are not entitled to much confidencewhen considered by themselves, the aggregate of the results indicatesbeyond all question a constant diminution of the obliquity.

Euler first explained the variation of the obliquity of the ecliptic by thetheory of gravitation. In his memoir of 1748, he showed that the actionof Jupiter on the earth would occasion a displacement in the plane of theecliptic; tending to bring it nearer to the equator. He investigated thesame subject more completely in the Berlin Memoirs for 1754, and also inhis memoir on the perturbations of the Planets , which was crowned bythe Academy of Sciences of Paris in 1756. On the last-mentionedoccasion he made the secular diminution equal to 48", a quantity whichdiffers only about 2"from the most recent determinations of astronomers*.

Lagrange computed the diminution of the obliquity in the BerlinMemoirs for 1782, and obtained 61". 5 for the amount of the secularvariation. This result is universally allowed to be too great. The sourceof Lagrange's error doubtless lay in the erroneous value which he assumedfor the mass of Venus , the planet which exercises the greatest influence onthe position of the ecliptic.

An interesting question arises; will the obliquity continually diminishuntil the equator and ecliptic coincide ? If this should happen, the sunwilLdnily attain the same meridional altitude as at the equinoxes, and aneternal spring will reign over the whole earth. Lagrange first shewedthat such a condition cannot possibly exist; the mutual action of theplanets occasioning only small oscillations in the positions of their orbits.The ecliptic will, therefore, continue to approach the equator until itreach the limit assigned by the action of the perturbing forces, after whichit will gradually recede front that plane according to the same law asthat which determined its previous approach. The diminution of theobliquity is not uniform; but the law of variation can only be ascertainedby theory. The formula for computing the obliquity corresponding to anyassigned time may be thus expressed :—6 = 23° 27' 54".8—0". 488566t—0". 000005 t denoting the number of years before or after 1800. Thisformula will be accurate enough for all the purposes of astronomy, whenthe value of t does not exceed ten or twelve centuries; it will even servefor all the ancient observations, when we take into account the uncertaintythat hangs over them. In the lapse of ages the law of variation will be

* Bessel in his Tabulae Regiomontanse, 1830, makes it 45". 7.