CHAP. XI.] 



HEIGHTS 



265 



To understand the mode of combining the data, let us 

 consider the Figs. 66 and 67. 



In Fig. 66, Avhich is the case where the angle observed is 

 of elevation, and comprises Problems 1 and 3, we may have 

 either X or Y known, and wish to obtain the other. 



Suppose X to be known (Problem 1), to fmd Y, we have 



Y = ^ + {t + 'h) 1. 



If Y is known (Problem 3), to find X, 



X = Y-(^ + ;^) 3. 



Fig. 66 



Height 

 Formulse. 



X= Height of observer's position. 

 Y = Height of observed position. 



7i=Difiference of height. 



< = Height of theodo;ite above ground. 



In Fig. 67, the case where the observed angle is one of 

 depression, and comprises Problems 2 and 4, 

 Suppose X known (Problem 2), to find Y, 



Y={X+t)-h 2. 



Suppose Y known (Problem 4), to find X, 



X = Y+h-t 4. 



These four formulae, which it is also convenient to have 

 written for reference in the Height Book, will enable us to 

 solve any of the problems. 



When we are getting the height of the Object observed, \\ e column 



shall enter in the column of "Height of theodolite," X + ^, H^i^ht of 



o ' ' Theodo- 



or the height of theodolite above the sea ; but when the nte. 



observation is used to obtain the height of Observer, only t, the 



height of the theodolite above the ground, will be inserted. 



