upon the Antique Dials. 



Ill 



we obtain the values of x, I for the four vertical dials of PH^EDRUS in Lord 

 ELGIN'S Collection *. These are, 



XXV. 



We come now to the case which Mr CADELL has so well illustrated by 

 his accurate drawings f . This is, in every point of view, the simplest case 

 that can be taken, and was well adapted to a first inquiry into the general 

 character of the curves. Mr CADELL has also given an equation of the pro- 

 jected curves upon the polar tangent plane, and deduced from it some gene- 

 ral inferences, which are abundantly justified by our general investigation. 



In this case, the expression is reduced to 



a sec 6 cosec 90 sec 90 





fl) + 1 



' sec 90 sec < tan I cos n cos" 1 cos (I 

 = a cot I sec n (I " 0). 



Keeping in mind that the general equation was referred to the axis of of 

 as the origin of 6, it will be at once obvious, that if we write 8' instead of 

 (/ > 0) we shall refer the equation to the meridian of the place as the origin 

 of polar co-ordinates, and the expression will be transformed into 

 r = a cot I sec n f . . . . . (A r ^) 



* Erroneously stated in the " Memoranda of Lord ELGIN'S pursuits in Greece," to 

 be from the Temple of Bacchus. Mr KINNAIRD saw the dial in the Temple of Bacchus 

 in its original position in 1818. See his Notes to the new edition of STUART'S Athens. 

 In the present arrangement of the Elgin Gallery, in the British Museum, this dial 

 stands opposite the stairs, in the angle of the room. 



f Edinburgh Transactions, vol. viii. p. 79, and the corresponding plates. 



P2 



