TACHEOMETER SURVEYING WITH AN ORDINARY THEODOLITE. III. 



The operation in the field is as follows : — In figure 1 let 

 AE represent any section of sloping ground. It is required 

 to find the horizontal distance AB, and the vertical 

 height BE. Set a theodolite over a peg A and measure the 

 height of the instrument AC. Then from the table of 

 tangents giving distances in feet, set the angle on the 

 vertical arc that most nearly corresponds with the slope of 

 the ground AE. Let this angle be 5° 08' 34"; it will be found 

 from the table of tangents that this angle will give a rise 

 of 9 feet in 100 feet. An ordinary levelling staff divided to 

 t.to of a foot is held on E, and a reading of the staff taken, 

 this will be the height EP, let it equal 5*21 feet. From 

 the tables the next higher angle is 5° 42' 38", which is set 

 on the vertical arc of the theodolite this angle will give a 

 rise of 10 feet in 100 feet. The staff is again read giving 

 the height EG, which equals 9*86 feet. Then the 

 difference of the staff readings 9*86 — 5*21 = 4*65 which, 

 multiplied by 100, is the horizontal distance AB. Then 

 465 x 9 = 41*85 feet, this being the vertical height, DP 

 and BE can easily be found by adding BD and subtracting 

 EP. For obtaining the height of the instrument a small 

 length of an old metallic tape was used, and so graduated 

 that the height from the ground to the top of the tripod 

 recorded the actual height of the instrumental axis. This 

 was found more convenient than holding the staff beside 

 the instrument. The shortening of the tape enabled the 

 observer to reach from the ground to the top of the 

 tripod. 



The reduction of field notes taken by the tangential 

 method can be carried on in the field, as very little more 

 calculation is required than to reduce notes taken by 

 ordinary levelling. A sample page of field notes is shewn 

 and the notation is so arranged that the notes can be 

 entered in an ordinary level book. 



