On Practical Geodesy. Sl 



oo' 



Again, since S^F , S^F^^, S^, are parallels to NS^, NS^ 

 NM, it follows that the arc F F^^ is bisected in ; and there- 

 fore (as arc 10 is a quadrant) the arc 10 is cut harmonically 

 in F^, F^^; and the spherical pencil P ' (lOF^F^J is harmonic. 



NOTATION. 

 When any number n of stations are to be simultaneously 

 considered. 



Let 1, 2, 3, . . . . y rif indicate stations on the earth's sur- 

 face. 



„ ^i, ^2J ^3» • • • • > ^«> indicate the latitudes at these 

 stations. 



„ K^jKjjjE-g, . . . . , K„, „ the normals terminating 

 in polar axis. 



„ <^i2f ^2sf ^sif 5» the differences of longi- 

 tude between the pairs of stations 1, 2 ; 2, 3 ; 



3,4;. 



Put A^ 2> -^2 1» ^^^ *^® azimuths of the stations 2, 1, as if observed 

 from 1 and 2. 



„ A 2 3, A3 2, for the azimuths of the stations 3, 2, as if observed 

 from 2 and 3. 



}) 



» 



„ a ^ 2, a 2 1, for the angles of depression of the chord 1, 2, at the 

 stations 1 and 2. 



„ a 2 3, a 3 2, for the angles of depression of the chord 2, 3, at the 

 stations 2 and 3. 



if •• • 



» •• • 



„ ^i2» ^2 3> ^3 4> ^^^ *^® chords 1, 2 j 2, 3; 3, 4; of the sphe- 

 roidal triangle 1, 2, 3. 



,j 5^2> ^i3> ^2 3> ^0^ *^® spherical measures a^^ + a^^; 



"13 + *3i5 *2 3 + "32^ 0^ *^® ^^^^^ 0^ *^® 

 spheroidal triangle 1, 2, 3. 



„ s^ 2> *i 3> ^2 3' ^^^ *^® lengths of the sides 1, 2 ; 1, 3 ; 2, 3; of 

 the spheroidal triangle 1, 2, 3. 



1. For any n stations 1, 2, 3, n — 1, n, on the 



earth's spheroidal surface, we have the rigorously accurate 

 equations 



^2 - sina,2 . ^3 - si^«23 . ^^ ^n 



R, sina2^'E2 sin 032' R^-i 



sm a 



« — 1, « 



and.*. sina^^_i 



B,^ _ sing, 2 -singes sin a,,_i;, ' ^ , 



K, sin ag^ • sin g32 sin g^^„_i 



