140 



Remarks on the use of 



[July 



a function the error is given of the difference of longitude, by changing 

 the formula. 



In the diagram (PI. 4 fig. 3) let AD be the meridian of the first sta- 

 tion, B C the perpendicular of any other station, then A being the pole, 

 D C will be the parallel of latitude of C, and A D will be the co- 

 latitude of E, and not A B, and B D will be the error or the differ- 

 ence of latitude between the foot of perpendicular and the parallel. 



Take A B = 90 — X 



B C = 7T 



AC = 90 — (X - so) 



D B = oo. then by right angled spherics 



we have 



sin {X — x) = sin X cos ir 

 sin X. cos x — sin oo. cos X = 



dividing by sin X we have 

 cos x — sin x. cot X — cos 7r 

 and the cos x being nearly = 1 , and substituting the value of cos tt 



1 — sin x. cot X — I — 2 sin § tt 



2 



sin x. = 2 sin i tt tang A, 

 and taking x" and w' f for the sines 

 X n = i 7r" 2 . tang X. sin 1" which is the formu- 

 la before given, — but the angle B A C is the difference of longitude 

 between B and C, and in the right angled triangle ABC 

 Tang A = tang tt. sec X, 



A" = tt. sec X and transposing 



7r" = COS X. A" 



= cos A,, diff. longitude 

 substituting this in the last formula 



x" = \ 3" 2 . cos X- Tang X. sin 1'' 

 = \ 8" 2. cos A. sin X. sin 1" 

 or become cos X. sin X = I sin 2 X 



2 



x" = I S"' sin. 2 X. sin 1" from this for- 

 mula the following table is computed x always subtractive :— 



