where ua is. the measured  azimuth of. tne Jine. The form” of 
equation 63) would have to be altered if the field. data were 
bearings. s: [his could | easily. De done after the "second term in 
the night Side of (239. ds computed by simple data 
manipulafion/testing. to insure that the"" proper" angie" and 
quadrant are compiled. Therefore, 
G(X0) 7 87 a (for 0°< a < 90°) (4) 
6(x,) = 8 - (180 - a) (for 90°< a « 180°) (5) 
G(X,) = 8 - (a - 180°) (for 1809« a « 270?) (6) 
G(Xa) = 6 - (3609 + à) (for 270°< a < 360°) (73 
In equations (4) - (7), 8. is the measured bearing of the line. 
For an angle measured from a third point i between points j and 
k, the conventional form of the mathematical model is 
: Ae = Ay X4 7 Xy 
G(Xa) 7 80- Stan} 5j tanti A. 1-9 (8) 
Ye Xi Yj - 14 
where 8 is the measured field angle. 
in the"  U.$., a large portion of ^ land was surveyed under the 
Rectangular Survey System by the Government Land Office (now 
Bureau of Land Management). Figure 1 shows the subdivision of 
the land into townships consisting of six square miles numbered 
from a designated meridian and base line. Figure 2 depicts the 
subivision of these townships into one mile square sections 
while figure 3 shows the breakdown of the section into aliquot 
parts. Circles indicate . government corners set in the field. 
One can. see that this configuration will cause problems with 
equations (3) to (8). Therefore, ijt is recommended . that, the 
tangent function be replaced Dy the sine function for values. up 
to 45-dagress and the cosine function for angles from 45- to 
30-degrees. Thus, azimuths in a North/South direction would be 
represented by 
he Le 5 2 
G(Xa) far sm D (9) 
while azimuths in an East/West direction can be shown as 
f Y 2 Y. 
s = K 
G(X,) =.a -- cos”! p = 0 (10) 
where D is the distance between points .j and Kk, Similarly, 
equation (8) can take the following form for section corners 
    
   
     
  
  
   
    
       
   
  
  
   
  
   
     
  
  
    
   
    
      
Fic 
Fi 
sq