60 On Practwal Geodesy. 



To find z^ we have (from the " Account of the Principal 

 Triangulation of Great Britain and Ireland ") the formula — 



log0, = log ( ^ J^ ^,) + 0-0004862 x sin' (aI') ' sinH' 



in which (a I') represents any close approximate to the 

 difference of the given and unknown latitudes, so as to have 

 the first three or four decimal places in the expression log 

 (sin^ A r) correct. 



In the present example we know that a ^' = 1° nearly, 

 and .*. to find z — 



log (0-0004862) = 4-6868 

 sin2(A^') = 6-4837 



,24' 

 sim 



log R, = 7-3212526296 

 sin 1" = 6-6855748668 



sinW =1-7931 



2-0068274964 

 logs = 5-7108817646 



antilog = 919-6 



3-7040542682 

 919-6 



.-. ^. = r. 

 Were we to use the more 



.'Aogz, = 3-7040543601 

 ',, 18"-8798 



.pie formulae — 



s 



we evidently have — 



^r 



sinl" 



log;^, = 3-7040542682 



.-. z, = 5058"-8785 = 1°,, 24',, 18"-8785, 



which is too small by about 0"-001 only. And since the 

 O'^'OOI part of one second represents not more than an error 

 of tV of a foot in the whole length of the arc s = 97 miles ; 

 .'. it is evident that in all cases we can safely find z^ by 

 means of this formula. 



Now knowing A^, r, z^, in the spherical triangle S^PD^^, 

 we can find the angles w, D^^, and the side L" by the usual 

 forms — 



