LEA 



This method is commonly used at sea, but as the sun must be on the 

 meridian, clouds may prevent its being used. A subsidiary method there- 

 fore is provided, in which the latitude may be computed from two ob- 

 served altitudes of the sun, and the interval of time between the obser- 

 vations. 



Let Z be the zenith, P the pole, S, j? two 

 positions of the sun ; then the following 

 are the steps in this process. 



(1.) Find Ssj let t interval of time, 

 p - P S then 



S s f 



2 sin. 8 -y ^in.2p. 2. sin.2 ; 



/. log. sin. ^- log. sin. p + log. sin. 



. 10. 



tan. SsP- 



cos. p ' 



,*. log. tan. S s P 10 -f. log. cot. ^- log. cos. p. 



(3.) Find / Z s S ; 



Let a and a' be the observed altitudes, then sin.s | Z * S 



- cos, f (S * + a' -f- *) sin. * (S s -|- a' - a)_ . 2 lo* sin 4 Z S = 



sin. S s X tos. a 



20 + log. cos. | (S s + a' -f a] 4. log. sin. | (S s + a> a] log. sin. 

 S * log. cos. a. 

 Hence Z*P S*P ZsSis known. 



(4.) Find Z P ; 

 Assume 9 such that 



. cos. a', ein. p. ver. sin. Z s P 

 tan " *= ver. sin. (900- a'- J9) ; 



ZP , 90 a' p 

 then sin. ^- = sm. ^ x sec. & ; 



:. log. sin. ^j~ 10 + log. sin. % (90 a' p} log. cos. 0. 



},KAP Vear.See Calendar. 

 LEMNISCATA, equation to. 

 160 



