176 SECULAR VARIATIONS OP THE ELEMENTS OF 



49 9 .27. The present length of the tropical year is 365 d 5 h 48 m 47 s .26. Whence 

 we get 



maximum length of tropical year =365" 5 h 49 m 36 3 .53; 

 and minimum length of tropical year =365 5 47 48.13. 



Lastly, if we take the sum of the coefficients of the sines in the formula for — , 



dt 



we shall find that the annual variation of the obliquity is always confined within 



the limits of 



0" and ±0".744167. 



