28 On Practical Geodesy. 



The expressions for e^ and -gin 115, 116, 117, 118, assume 



the form % when the latitudes of the stations are equal. If 

 the latitudes and mutual azimuths of numerous pairs of 

 suitable stations be carefully found from actual observation 

 with good instruments, &c., it is obvious that 117 and 118 

 will enable us to find the most probably correct or suitable 

 value for the earth's eccentricity in the locality of the 

 survey. And the great importance of having such a value 

 of e will be obvious from the examples worked out in the 

 sequel. 



We can easily find other expressions for e^ from 78 and 



79, by substituting in (79) the values of -p-" and ^' given 



in 51. 



34. It may be seen, from a glance at the figure, that when 

 the two stations have not the same latitude, a difference in 

 the heights of the stations (with respect to the earth's 

 spheroidal surface) will introduce errors into the observed 

 values of the azimuths A^, A^^ and other azimuthal readings. 



1°. It is evident that accordinn^ as the station S is higher 



o oo ^ o 



or lower than the station S^ by the length h, so will the 

 observed azimuth A^ be too great or too small by an angle ^u, 

 which the length expressed by Z^, X sin a subtends at the 

 distance s. And according as the station S^ is higher or 

 lower than the station S^^ by the length h, so will the 

 observed azimuth A^^ be too small or too great by an angle /x 

 which the length expressed hjhx sin a subtends at the 

 distance s. 



2°. It is .*. obvious that when the station S^ is higher than 

 the station S^^ then will the azimuths A^ and A^^, as found 

 by direct observation, be too small ; and when the station 

 S^^ is higher than the station S^ then will the azimuths A^ 

 and A^^, as found by direct observation, be too large. 



I^p° To find the error of correction [x, we have — 



w, = - • A 



s 



Now, in an example given in the sequel, we have s = 513,906 

 feet, and a = 10'^'85. And according as we suppose the 

 station S to be higher or lower than the station S by the 



O O 00 «/ 



length h — 10,000 feet, so will each of the azimuths A^, A^, 

 be too small or too great by 



[X = 0" -211 



