On Practical Geodesy. 59 



formulae would intimate that D,, is greater than A,,, which 

 we know to be erroneous. And when A, = 90° it intimates 

 that D,, = A,,, which is also erroneous. 



In order to shew the extent to which a change in 

 the assumed values of the earth's polar and equatorial radii 

 can effect the results of geodetic computations, I give the 

 following columns of results, worked out with 7 place 

 logs.— 



FOR THE LATEST CONSTANTS. FOR CONSTANTS FORMERLY USED. 



f 



a = 20926348 ) 

 b = 20855233 j 



{ 



a 



= 20923713 ) 

 = 20853810 f 





1 



b 





K == 



134°, 51',, 25"-225 



A. 



= 



same as before 





Aoo = 



44, 22, 55-177 



Ko 



= 



j> » » 





A, = 



134°, 44, 03-683 



A, 



= 



134°, 44', 10" 



•647 



K ^ 



44, 30, 16-718 



A, 



= 



44°, 30, 09 - 



754 



o = 



0, 07, 21-541 



O 



= 



0, 07, 14- 



577 



V = 



1, 24, 29-956 



V 



= 



same as before 





2 = 



\, 24, 29-945 



2 



= 



>j » )> 





«/ = 



0, 42, 14-900 



«/ 



= 



0°,42', 14- 



901 



O-n = 



0, 42, 15-045 



«// 



= 



0, 42', 15- 



045 



A = 



0, 00, 10-852 



A 



= 



0, 00, 10- 



681 



s = 



513905-8 feet 



s 



= 



513847-7 feet 





The increase in A^ is equal to the decrease in A^^, and the 

 whole amount Q"'^ of such increase or decrease is owing to 

 the change in the ratio of a to b, and not to their absolute 



magnitudes. This shews that if the assumed value r be not 



suitable to the locality of the survey, there must of necessity 

 be discrepancies between the azimuths as found by direct 

 observation and computations, in closing work carried on by 

 means of two series of stations. We see also that the values 

 of s differ by about 58 feet in an arc of 97 miles, owing to 

 the change in the values of a and b. 



Example (Problem 2). 

 Case 1. 



Given the latitude l^ = 38°; the azimuth A, = 134°^, 44^^ 

 02"-72393 ; and the length of the geodesic arc s = 513903 

 •7237 feet ; to find the difference of longitude (a^ the latitude 

 l^^ the azimuth A^^, &;c. 



