VOL. XLIX.l PHILOSOPHICAL TRANSACTIONS. 37 



From the be- To the be- Decrement of the Decrement of the Total decrement 



ginning of ginning of obliquity of the obliquity of the of the ecliptic's 



the year, the year. ecliptic by Jup. ecliptic by Sat. obliquity. 



1750 1800 1" 5 " O" AA!" 7' 50'^ 



1800 1900 14 9 1 27 15 36 



1900 2000 14 5 1 26 15 31 



Collation of the Theory with Phenomena. 

 For the proper comparing of the theory with phenomena, the observations of 

 the ancients should be consulted and compared with the moderns; but the 

 former are more imperfect than what can serve for minute considerations of this 

 kind. We can therefore only make use of those of the latter, though less fit 

 for the purpose. 



1, M. Le Monnier relates, in the Memoirs of the Paris Academy for 1738, 

 that Picart observed there the altitude of the sun's centre at the summer solstice, 

 and found it in the year 1669 to be 64*^ 39', and in 1670 to be 64° 38' 58^^; we 

 shall take the medium 64° 38' 59^. Le Monnier himself, in the same Memoirs 

 for 1743, found the altitude of the sun's centre there at the solstice to be 64° 

 38' 45''. Also the mean place of the moon's ascending node, by the corre- 

 sponding observations, was about 27° of y at the former time, and 16° of y 

 in 1 743 ; hence in the former case the nutation of the earth's axis was 8''', the 

 whole being 18'', and in the latter 6''' 15'"; which quantities being respectively 

 deducted, the altitude of the sun's centre at the former becomes 64° 38' 51^', 

 and at the latter 64° 38' 38" 45'", the difference 12" 15'^'' is the decreasing in the 

 mean obliquity of the ecliptic in the interval of 73^- years. By the proposition 

 the decrease from the force of Jupiter in the same interval of time was 10" 27''''', 

 and by that of Saturn 1" 5". Therefore the whole decrease in the obliquity ac- 

 cording to theory was 1 \" 32'". 



2. From the observations of Walther, compared among themselves. La Caille 

 (in the Paris Memoirs for 1749) collected that the obliquity of the ecliptic about 

 the year 1 4 96 was 23° 29' 32", which at present is stated at 23° 28' 30"; and 

 therefore in the 260 years the obliquity has decreased about 1'. Now by our 

 theorem that decrease by Jupiter's force would be 37" 2'", and by Saturn's 3" 50'"; 

 hence the whole decrease in the same time becomes 40" 52"", or about 41". If 

 instead of Cassini's table of refractions that of Newton be used, the obliquity 

 of the ecliptic deduced from Walther s observations, will come out a few seconds 

 less, and so come nearer to the determination by theory. But because of the 

 uncertainty of the refractions and of the latitudes of places, it seems that the 

 variation of the obliquity can be most safely determined by observations at the 

 summer solstices made at the same place. 



If the variation at length accurately derived from experiments, should, as in 

 the example above, exceed the variation assigned by this theory, that excess will 



