Method of co)nputmg the Latitude. 389 



ii. Mr. Ivory's Method of compiding the Latitude from tico 

 Altitudes and the Time intervening. 



Mr. IvouY, after a candid examination of the various approxi- 

 mations that have been proposed for the sohition of the problem 

 of two altitudes, is disposed to tliink them seldom so eligible as 

 the direct computation, which he has somewhat abridged by a 

 method that may be thus enunciated. (Phil. Mag. Aug- p. 84.) 

 Mr, Ivory's Rule. 



Putting h the greater altitude. 



h' the lesser, 



D the mean declination, 



t the half time elapsed, reduced to angular space, 



( b the half base of the triangle A P B, 



p the perpendicular, 



y the perpendicular Z D falling from the zenith on p, 



X the portion of p between y and A B, ) 



A the latitude, 



s the horary angle of the middle time, 



A =:z ^ (sin h — sin A') 



B = \ (sin h — sin li) 



1. Sin b :=. cos D sin t 



n r~, sin D 



2. Cos p = 



cos b 



3. Sm y =: 



sin b 



A 



4. Cos X = 



cos y cos b 



5. Sin ^ = cos ?/ cos ( p ^ r) 



,. r.- sin y 

 t). Sin s = i 



cos A 



Correction for the change of declination. 

 (I the declination at B the greater altitude, 



>. — (D ~ d) lilii- will be tlio true latitude, 

 sill / 



J + (D — d) cos A' the corrected iiorary angle. 



sill t 



