On Practical Geodesy. 47 



Pkoblevi 4. 



Given the two azimuths A,, A,„ and one of the latitudes 

 l^ ; to iind the latitude l,^, the difference of longitude w of the 

 stations, &c. 



To find the latitude l^^, we have, from (53) — 



, ., 7 (1 — e^) tan^ / sin^ A., — (sin^ A, — sin- A ,,) , 



tan- I.. = ^^ i i—- '1 — ;-\ i '±! nearly. 



(1 — e-^) sm^ A, ^ 



Then to find the difference of longitude, we have — 

 The other entities can now be found, &;c. 



Problem 5. 



Given the latitude l^, the azimuth A^, and the diflference 

 of longitude w ; to find the latitude I,,, the azimuth A,,, &c. 

 Find L'' by means of formula 78. 

 Then finding 77i, p, q, by means of — 



m = cot^ L" — -, • K^ • sin^ I, 



p = cot^ L" — -2 • E'- • sin^ Z, + (1 — e^ 

 a 



2 = 2 e^ (1 _ e^) ^^ . sin I, 

 a 



the second of the formulae 79, gives us the equation — 



m — p ' SID? l^^ = q • sin I,, J I — e^ • sin^ l^^ 



Ajid from this we immediately obtain — 



sij^2 I ^ q' + 2mp + qJq'-\-4:m{p — m^) 

 2 ip' + q^ e') 



Now, if we conceive a case in which I, is of any value we 

 wish, and that the corresponding value of I,, is such that 

 7n = 0; then it is evident l,^, p, q, have finite values ; and 

 we perceive that in such case the + sign only must precede 

 the radical. And it is .*. evident that the -|- sign must, in 

 all cases, precede the radical in the above general expression 

 for sin^ I,,. 



Or we may proceed as follows — 



From the triangle S,PD,,, we have to find L", z^, D,, 



tan i (L" + z^) = ^o« i (f . - ^) . tan i I' 

 ^ ^ ^ '' cos i (A, + i^ 2 



