Observation of a Winter Solstice. 3(5.'} 



It may perhaps be interesting to examine how far this 

 observation agrees with the formula founded on the Theory of 

 Universal Gravitation for the diminution of the obliquity of the 

 ecliptic. If we take the constants as given by Poisson, Con. des 

 Temps. 1830, Additions, p. 29, we shall have the obliquity of 

 the ecliptic at any number of years t from the year 1750, ex- 

 pressed by this formula 



23". 28'. 18"- ^.0". 45692 - <-.0". 000002242. 



Taking for t, - 1750, which will bring us to the age of Strabo, 

 this gives us for the calculated obliquity 



= 23°. 41'. 30" 

 Observed obliquity = 23 .31 .51 



Difference = . 9 . 39 



Though this difference of nearly 10' may not perhaps appear 

 very great, considering the instrument employed : yet it seems to 

 exceed the probable error of these observations. The observation 

 of Pytheas in Strabo, gives the latitude of Marseilles within four 

 minutes : that of Eratosthenes given by Cleomedes, gives the 

 latitude of Alexandria, within five minutes. In this case it is 

 not improbable that finding the ratio of the gnomon to the 

 solsticial .shadow very nearly equal to 5 : 7, the Greeks have 

 voluntarily neglected the trifling difference, in order to express 

 this ratio in the simplest terms. 



R. W. ROTHMAN. 



Thinity College, 

 Nov. 27, 1829. 



VoL III. Part II. 3 A 



