On Practical Geodesy. 65 



the mean between the known and unknown latitudes, and 

 in which — 



1 (A, - A, + = i (A, - D,) 



i (A, + A,, + = i (A, + D J. 



The value of l^ — l^^ as computed from the above is — 



I, — I,, = 3600"-0057 = 1°, 00',, 00" -0057 



.-. l, = 36°,, 59',, 59"-9943, 



which is nearly 0'''*006 in error, when by the method fol- 

 lowed in this paper the error amounts only to about 0'''0004. 



It may perhaps be proper to observe that in the example 

 under consideration we have in reahty — 



i (A, + A,, - = 4 (A, + D„) 



so that the fact of the expression for l^ — l^^, being written 

 as above shews that its author considered A^^ to be less than 

 D^^: however, we know that A^^ must be greater than D^^. 



Example (Problem 2). 



Case 2. 



Given the latitude l^^ = 37°; the azimuth A^^ = 44°^ SO'^ 

 17''-67692 ; and the length of the geodesic arc s=r 5139037237 

 feet : to find w, l^, and A^, &;c. 



To find the arc z^^^ we have- 

 log 3„ = log :^-4— J + 0-0004862 X sin^ (aI") sin^ l" 

 E,„ sm 1 ^ ^ 



in which a T is the nearest approximate which we can easily 

 find to the difierence of the known and unknown latitudes. 

 In the present case we know that a T is nearly 1°. 



log (0-0004862) = 4-6868 



log R„ 



= 7-3212277292 



logsin=^(A^") = 6-4837 



sin 1" 



= 6-6855748668 



sin^^" = 1-8047 





2-0068025960 



2-9752 



logs 



= 5-7108817646 



antilog = 944*5 





3-7040791686 

 944 



.• 



• log z,, 



= 3-7040792630 



.-. ^„ = 5059"-16988 = 



= 1°. 24' 



,, 19'''-16988 



