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Barry Rein wrote,
 
 > A few years ago on public television there was a series called "Pole to
 > Pole with Michael Palin", an entertaining travelogue in which Mr. Palin
 > travelled from the North Pole to the South Pole by a variety of means.
 > What caught my attention was this: the route he followed approximated the
 > particular longitude line that covers more land between the poles than any
 > other longitude.  I forget which one it was exactly, but it went through
 > Scandinavia, Russia, Turkey, and much of Africa.
 >
 > Anyway, that got me to thinking about similar questions, and these are the
 > ones I'd like to find answers to. For example, what pole-to-pole longitude
 > covers the LEAST land?  I imagine it would run through the Pacific.  Then
 > you might ask, what great circle going through both poles covers the most
 > land?  The least land?  And what great circle anywhere covers the most
 > land? The least?  And so on. You could think up a lot more questions like
 > this.
 >
 
I thought this was an interesting trivia question so I decided to write some
code and find out the answer when I had free time over the past two weeks.
Figuring out land lengths for paths that pass through the poles is relatively
easy. Take any unprojected digital map and count up degrees on each meridian
(I counted lakes as land). The results (+/- 1 degree):
 
Largest amount of land on a pole-to-pole meridian:
   23 degrees east longitude, land length 121 degrees --that's 67% land.
There are several other meridians nearby that have almost the same fraction
of land to total length. An interesting "also ran" is the meridian running
through 69 degrees west longitude through South America. It has only 5
degrees less land along it than 23 east.
 
Smallest amount of land on a pole-to-pole meridian:
   167 degrees west longitude, land length only 5 degrees (it hits just a
small portion of Antarctica and no other land).
 
Largest amount of land on a pole-to-pole-to-pole great circle (all the way
around the Earth passing through both poles):
   69 degrees west longitude connecting with 111 east longitude is the big
winner this time, land length 203 degrees (56% land). It passes through the
state of Maine, the Dominican Republic, the longest axis of South America, a
large path through Antarctica, across the Indian Ocean, through Java and
Borneo, right through the middle of China, and on to the pole through Siberia
just east of Lake Baikal.
 
Smallest amount of land on a pole-to-pole-to-pole great circle:
   17 degrees west longitude connecting with 163 east, land length just 50
degrees (less than 14% land). This great circle hits only Iceland, a tiny
slice of Africa near Dakar, makes a fairly long run through Antarctica, just
misses a few small Pacific islands, and then finally slices through a narrow
section of Siberia including part of Kamchatka.
 
   To find the longest paths on great circles that do NOT pass through the
poles is a little more difficult computationally. You have to rotate the
coordinates and treat each point along one given meridian as a new "pole".
The results:
 
Largest amount of land on any great circle:
   The great circle that reaches its most northerly point at 88 degrees north
latitude around 20 degrees east longitude, land length 207 degrees (58%
land). This is almost exactly the same great circle as the longest land
circle that passes through both poles. By tilting just a couple of degrees
away from the earlier circle, this one passes through western Australia and
ends up a few degrees longer.
 
Smallest amount of land on any great circle:
   The great circle that reaches its most northerly point at about 84 degrees
north latitude near 70 east longitude, land length 24 degrees (only 7% land).
This is close to the great circle with least land that passes through the
poles. By tilting six degrees, this one skips Iceland, passes through a
shorter section of Antarctica, and misses Kamchatka.
 
-Frank E. Reed
http://www.clockwk.com/fer