104< Mr. Rudge on the Position 



Since T/, = 0. Subtracting the latter equation from the former 

 ( X, + ^ - 2 X) [.V, - |- - j/4 cos xij) 



+ {ij-2 Y) (-i/4+ (.rj- I") cos xy^ = 0, 

 which equation may be written as follows : 



—p cos xy {Y + X cos xy) 



— {y^-\-p cos xy) {y^— 2 Y -2 Xcosxy) = 0. 



By equation (9.) 



xi+ -|- - 2 +X (J/2+J/3 — 2 r) cos.rj/ = ; hence 



{(■^■-f) (i/a+i/3) + P(Y+A^cos.r3/j cos xj/ 



- (^4+ P cos xy) ( j/4— 2 Y - 2 X cos xy) = 0. 

 Also by equation (10.) 



(a-, — I") (3/2+3/3) + p( Y+X cos ^ J/) = 0; hence 



(3/4 + j9 cos xy) (3/4—2 Y— 2 Xcos xy) — 

 3/^ = — p cos xy, or 3/4 = 2 Y + 2 X cos ^-3/, 



and it is evident that the circumscribi7ig circle passes through 



the focus of the parabola. 



XXIII. On the Position of the South Magnetic Pole. By 

 Edward Rudge, Esq., F.Il.S., S.A., L.S. 4" H-S.* 



1"^HE experiments detailed by Captain James Clark Ross, 

 R.N., &c., which led to the important discovery of the 

 north magnetic pole, and which are published in the Philo- 

 sophical Transactions for the year 1834, suggested to me as 

 an object of interesting inquiry, whether any similar affection 

 of the horizontal magnetic needle had ever been noticed by 

 any former navigator of the southern hemisphere, from which 

 an approach to the magnetic south pole could be surmised. 

 No such appearances seem to have been observed by Anson, 

 or any one after him ; but prior to his circumnavigation of the 

 globe, Captain Abel Tasman, who was appointed for the dis- 

 covery of southern countries by direction of the Dutch East 

 India Company, sailed from Batavia with two vessels on the 



• Read before the Royal Society, Feb. 19, 1835; and now communi- 

 cated by tlie Author. 



