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places on the sheet we may choose. So far
I have called the sheet a photograph, so
as not to overwhelm you with all the
difficulties of the conception at once. But
let us rather call it a map,— a map of
such a photograph if you like. A
map of the simplest kind represents all the
points of one surface by corresponding
points of another surface in such a manner
as to preserve the continuity unbroken,
however great may be the distortion. A
Mercator's chart, however, represents all the
surface of the earth by a strip, infinitely
long, both north and south poles being
at infinite distances,