46 A MANUAL OF TOPOGEAPHIC METHODS. 



proportion to the correction as obtained by comparison with the standard. 

 If the tape be longer than the standard, the correction will be positive, if 

 shorter, negative. 



Second. The correction for inclination, the data for which are obtained 

 by running a line of levels over the base line. This line of levels gives the 

 rise or fall, in feet and decimals of a foot, between the points of change in 

 inclination. From this and the measured distance the angle of inclination 



is computed from the formula, sin = ^ • R being the distance and h the 



difference in height, both given in feet. The correction in feet to the dis- 

 tance is then computed by the equation, 



Corr — !HLl 6 2 R or 0.00000004231 6 2 R, 9 being expressed in minutes. 



(See Lee's Tables, p 83.) 



Third. The correction for temperature. Steel expands for each degree 

 of temperature .0000063596 of its length. This fraction multiplied by the 

 average number of degrees of temperature at the time the base line was 

 measured above or below sixty-two degrees, which is taken as the normal 

 temperature, gives the proportion in which the base line is to be diminished 

 or extended on account of this factor. Care must be taken to obtain cor- 

 rectly this average temperature. It must be the mean of all the thermo- 

 metric readings, taken at uniform intervals of distance during the measure- 

 ment. If the temperature be above the normal, the correction is jjositive, 

 and vice versa. 



Fourth. The reduction to sea level. The base line is measured on a 

 circle parallel to the sea surface and raised above it, at an elevation which 

 is known at least approximately. This circle with radii drawn therefrom to 

 the center of the earth forms approximately a triangle similar to that formed 

 by the radii of the earth with the sea surface. The length at sea level is 

 derived with a sufficient approximation to correctness by the proportion: 

 R: h\: K: correction. 



I! being the radius of the earth, h the mean height of the base line 

 above sea level, and K its measured length. (See Report U. S. Coast and 

 Geodetic Survey, 1882, Appendix 9, p. 196.) 



