S On Practical Geodesy. 



And, since a^ — a^^ is negative, it follows A is less tlian e; 

 Hence also — 



angle IS,S, + angle IS,,S, i 180° 

 angle S,S,D, t angle S,,S,D,, 

 or, Q„ 7 O, (24) 



We have also — 



A, + A, = PS,S, + PS,S, + (€ — A) 

 &.-. A, + A, 7 A, + A,, (.5) 



Now the triangle S JD, is evidently such that — 



angle IS,D, + angle ID,S, ^ 180° 

 but, angle PD,S,, + angle ID^S, = 180° 



.-., angle PD,S,, 7 angle IS,D, 



or, 1), 7 A, 



And the triangle S,,ID,, is evidently such that — 



angle IS,,D,, + angle ID,S,, 7 180 

 but, angle PD,,S, + angle ID,S,, = 180 



angle IS,D, 7 angle PD,S, 

 or, A,, 7 D,, 



10. From equation (14) or, ~ ' = ^, we have — 



^ ^ ^ sm a,, E, ' 



sin a„ — sin a, R, — K„ 



sin a^i + sin a^ K, + ^,1 

 tan J (a,, — a,) _ P-, — ^„ 



(-) 



tan J (a,, — a,) = ' " tan J 5 (27) 



From this equation it is evident that when the latitudes are 

 of constant mao^nitudes, then the oreater the circular 

 measure % of the intervening geodesic arc is, the greater 

 will be the difference of the angles of depression of the 

 chord. But although a^^ — a^ increases or decreases according 

 as ^ increases or decreases, it is nevertheless evident, from 

 (14), that both a^^ and a^ increase or decrease as a^^ + a^ or 

 ^ increases or decreases. 



Moreover, it is evident that when the latitudes are con- 

 stants — 



cos a, . ^ . / x 



increases as 5 increases (28) 



cos a 

 tan 



— decreases as 2 increases (29) 



tan a,. 

 However, it is proper to observe that even for a geodesic 



