set term pngc font "Times,10" size 480,360 
set out "mercator.png"


unset key
unset ytics
set yrange [-3:3]
set xr [-180:180]
set xtics 30  format "" 
set grid xtic front
set label "Mercator" at 100,2.7 font ",18" 
set object rectangle from -180,-3 to 180,3  fc rgb "light-cyan" behind
do for [i = 0:2 ] {
y = atanh(sin(i*pi/6))
set arrow from -180, y to 180, y  nohead  lt 0
set arrow from -180, -y to 180, -y nohead lt 0
}

plot "world_110m.txt" u 1:(atanh(sin($2/180*pi))) w filledc \
     lc rgb "dark-green"

! display mercator.png