CHAP. IV.] FALSE STATION 89 



Thirdly. Required the angle D A H. 

 Here CAH = CBH+BHA 



and CAD-CBD+BDA. 



Adding, we get D A H = D B H + (B H A +B D A). 



These small angles, B D A, B E A, etc., the angles subtended 

 by the distance between true and false station at each object 

 observed, must be either calculated in each triangle, having 

 two sides and the included angle (for the rough distances 

 B D, BE, etc., will answer the purpose), or else, which is 

 simpler, have a table* made of the angles which are sub- 

 tended by different lengths at different distances, and take 

 the required angles out, thus : 



Let us suppose the theodolite angle in our book corre- Caicuia- 

 sponding to A is 60°, D 160°, and E 220°. A B is 12 feet. JStion bj 

 E B is li miles, and B D 2 miles, measured rouglily on the Table, 

 sheet. 



Required B E A by the table. 



It will be evident that the angle B E A is that subtended 

 by a chord drawn across to E A from B. This chord we get 

 near enough by considering B N as at right angles to both E B 

 and E A, and looking out in the traverse table with B A, or 

 12 feet, as a distance, and B A N or 20° (180°— 160°) as a 

 course, and taking the departure for the length of B N, which 

 in this case is 4-1 feet. 



We then turn to our table, and see that 4 feet at Ij miles 

 subtends 1' 31", which is the angle B E A. In a similar manner 

 we can deduce any of the required angles, quite near enough 

 for ordinary purposes. 



Now, this process becomes far simpler, and much time is Arrange- 

 saved if, in making a false station, a zero for the theodolite working 

 is chosen in a direction exactly opposite to the true station, ^^"^^ 

 as, for example, in our figure at Z ; for then each angle taken 

 can easily be corrected separately for the error of the false 

 station, and the true angle entered in the book. Difficulties 

 as to whether the ultimate correction is + or — will be avoided, 

 as in correcting the angles the error is subtracted from all theo- 

 dolite angles up to 180°, and added to all angles between 180^ 

 and 360°. 



* Appendix, Table 0. 



