360 Grinten — Projection of the Whole Earth? s Surface. 



terra must be used with reserve as no exact definition of it can 

 be given ; linear, angular, and areal values being of a hetero- 

 geneous character. Here it is the simplicity of the formula or 

 construction which proves its superiority in the solution of an 

 intricate problem. 



C = 



90 TO 



c-= w 



1 



i 



l+ y 



1 

 1 





/If 



1 zd 



1 



*y 



i+d 



Vi +c +Vi -c 



; so-o'i 



y= 



c 



2.-C 



5= 



I (z + t)\Jl-c 



° V»+-c -Vl-c 



s = 



, (2_c)Vi+-c 



c )J\+C -\\ — C 



sm0 = ^=cosrj 



Vl-J-c -V«-c 



The formula for our y can easily be developed by the fol- 

 lowing reasoning (fig. 3). The proportion 



x d . 7 a; 2 + Vx\l-d 2 )+d 2 

 = = — gives y = d \ — = • 



Now in order to preserve conformity and equivalence along 



the equator (the meridians here being equidistant) we can sub- 



a 

 stitute for x the arbitrary value — , which is to be so deter- 



a 



