TRAVEESE WORK. 85 



telescope. Pointing upon the object whose relative height is to be measured, 

 the telescope must first he brought to a horizontal position. In case the 

 vertical arc is movable, its zero must then be brought to the zero of the ver- 

 nier. In case it is not movable, the index error, with its sign, must be read. 

 The telescope is then raised or depressed to the point and the reading- 

 obtained. This adjustment of the vertical arc or reading of the index error 

 must be done for each point, as the table cannot be leveled with sufficient 

 accuracy, or cannot be expected to maintain its level, so as to dispense with 

 it. Knowing the horizontal distance to the point and the angle of elevation 

 and depression, the difference in height is obtained by the solution of a right- 

 angled triangle, thus: 



h rz d tang a, 

 h being the difference in height, rf the distance, and a the angle of elevation 

 or depression. This distance is then to be corrected for curvature of the 

 earth and for refraction by the atmosphere. The correction for the former 

 is obtained with sufficient accuracy by the following empirical rule. The 

 curvature in feet equals two-thirds the square of the distance in miles. It is 

 always positive in sign, whatever may be the sign of the difference in height. 



Refraction is an uncertain and variable quantity. It is usually greatest 

 at morning and night and least at midday. It is greater the nearer the line 

 of sight is to the ground. Often in desert regions it is excessive in amount- 

 It is usually assumed at one-seventh the curvature, and is negative. 



Tables for the solution of vertical angle work are appended to this 

 volume. These give differences in height for all angles and distances which 

 should be employed, with corrections for curvature and refraction. 



Differences of height should not be measured at greater distances than 

 10 miles, if it can be avoided. An error of 1' in the measurement of the 

 angle is at this distance about l."» feet, while the uncertainty of refraction 

 in such a length of line is necessarily great. 



TRAVERSE WORK. 



As stated above, under the head of primary traverses, a traverse line 

 consists of a series of direction and distance measurements depending upon 

 one another. These lines should be connected wherever possible with trian- 



