144 U. S. COAST AND GEODETIC SURVEY. 



With these conditions we have 

 a cot (p 



^"(l-e^sinV)^^ 



dip , a c 



sin^<^)^ 



/I 2\ C'^ dip , « cot (p 



, .^ p(l-€^sinV)^ be_^ 

 ^ a cos (p b\ 



on 



5^=sin^. 



be 



By intergration 



d=^\ sin (p, 



no constant of integration being added, since 6 and X vanish 

 simultaneously. Since the parallels are represented by 

 circles and since the scale along the parallels is to be main- 

 tained constant, the last relation can be obtained by 

 equating an arc of the projection to an arc of the parallel; 

 hence 



a\ cos (p 



pd 



(1— €^ sin^ cp)^ 



a cot (p ^ a\ cos (p 



(1 — e^ sin^ <p)^ ~(1— e^ sin^ <p)^ 



or 



d=XsiQ^. 



