108 



Astronomical and Nautical Collections. 



Example IV. 

 July 6, in N. latitude at ll*", A.M., the true altitude of the sun's 

 centre was 74°, and his azimuth 63° ; at 6"* 40"" P.M. his altitude 

 was 10° 30', and his azimuth 70°, the mean declination being 

 22° 41' ; required the latitude. 



To find arc I. 

 1. cos. D' = 9.96.5037 



1. sin. i E = 9.884254 



44° 58' 28" 9.849291 1. s. 



I = 89 56 56 



To find arc II 



1. sin. E = 9.993351 



1. COS. d — 9.965080 



1. cosec. I = 0.000000 



65° 19' 45" 9.958431 1, s. 



11= 32 39 52 



To find arc III. 

 1. cosec. I = 0.000000 



1. sec. A =: 0.559662 



l.cos.jS + a= 8.685056 



l.sin. JS^= 9.988237 



2) 19.232955 



III = 24° 25' 30" 9.616474 1. s. 



II = 32 39 52 



To find arc V. 

 1. cos. A = 9.440338 



1. cos. D = 9.964994 



2 . 1. sin. IV = 9.848062 



const, log. 0.301030 



N = 358446 9.555424 



n. cos. A-D = 625200 



- N = 358446 



Lat. = 15° 28' 16 266754n.s. 



I = 89 56 55 

 A = 74 

 S 



S + a = 87 13 28 

 'W~a = 76 43 28 



IV = 57 5 22 



In this example the first observation is taken in the forenoon, and 

 the second in the afternoon ; and the sum of the azimuths is less 

 than 180°, therefore the fourth arc is equal to the sum of the second 

 and third arcs, by Riile II. 



In applying the Rule to successive altitudes of the same Jixed 

 star, the interval between the observations must be measured by 

 a sidereal chronometer. Or, if this be not at hand, the interval mea- 

 sured by a common chronometer may be increased at the rate of 

 2' 28" for every 15°. 



