Obliquity of the Ecliptic, . 431, 



fVeret's calculations want a slight correction. By recti- 

 fying them, and allowing for the refraction and the parallax 

 of the sun supposed to be 8",7> J find 79° 22' 39,6 for 

 the altitude of the superior edge of the sun's disk at the 

 summer solstice, aud of 31° 35' 1",8 for thatof the said cA^a 

 in the winter solstice* By subtracting the apparent semi- 

 diameter of the sun at the two solstices, which I find to be 

 15' 47">7 and 16' 14'$3 respectively, the corresponding al- 

 titudes to the centre will be 79° 6' 5i",9, and 31° 18' 47",3, 

 which gives 23° 54' 2", 2 for the obliquity of the ecliptic, 

 and 34 J 47' 10" for the polar altitude; which, being nearly 

 a mean between the three observations of the missionaries, 

 proves the accuracy of Tcheou-Kong's determinations. 



Freret by certain and ingenious calculations had in the 

 same dissertation fixed theepochaofTcheou K^i^s regency 

 between the year 1098 and HOl, before our aera. 1 shall 

 observe that in this respect he agrees perfectly with Father 

 Gaubil. I shall then suppose that these observations were 

 made in the year 1 100 before our aera. I have given in the 

 3d vol. of my Mec. Cel. b. vi. ch. 12, a formula by which 

 the obliquity of the ecliptic may be determined for a very 

 distant period : and t expressing a number of years elapsed 

 since 1750, the value of this obliquity in decimal degrees 

 will be 



26°,0706— 3676',6l— cos(^3",0446) — 10330,4 sin (tgg\ 1 227) 

 whereby t — — - 2850, which gives in decimal degrees the 

 corresponding obliquity of the ecliptic = 26 \5 "6il, or in 

 ordinary degrees =25° 51' 53' ; which must be increased 

 about 5', because the obliquity of the ecliptic in 1750 ex- 

 ceeded to that amount the quantity used in the preceding 

 formula: thus 1100 years before our sera, the obliquity of 

 the ecliptic was 23° 51' 58', — a result which only differs 

 2' 4" from that given by die observed lengths of the gno- 

 mon shadow in the two solstices. A more perfect coinci- 

 dence cannot be wished for, if allowance be made for the 

 uncertainty attending this sort of observation, owing parti- 

 cularly to the penumbra which renders the shadow ill-de- 

 fined. 



If, together with Father Gaubil, the observation alone of 

 the summer solstice was taken into account, and the polar 

 altitude at Loyang was supposed with him to be 34° 43' 15", 

 by subtracting its complement 55° 16' 45" from the alti- 

 tude 79 3 6' 52" of the sun's centre, determined by the length 

 of the shadow in the summer solstice, the obliquity of 

 the ecliptic would be 23 2 50' f. The result of my for- 

 mula is very nearly a mean between that and the obliquity 



given 



