158 TJ. S. COAST AND GEODETIC SURVEY, 



R 



Fig. 44.— Tissot's indicatrix. 



smaller of the two, we see that the representation dimin- 

 ishes all the acute angles one side of which coincides with 

 the first principal tangent. Between u and u' we have, 

 moreover, the relation 



d 



tan u' =— tan u, 



c ' 



smce 



tan u = 



tan u^ = 



and, consequently, 



tan u' 



RS 

 OS 



MS 

 OS' 



r,a tan u = - tan u. 

 ES c 



Let us prolong the line RS to R^ and then join and E\ 

 The two triangles OEM' and OR'M' give 



c — d 

 sin (u—u')= -J sin {u-\-u'), 



