The name is absent

Rectilinear Drawing          63

⅛ r F if) dr

admits a continuous derivative, in which case we have necessarily

n∖               f(Λ ^{1 d} [^3rp^^dr

as the unique solution.

If we do not wish to restrict attention to continuous func-
tions F and f, various extensions are clearly possible. One
of the simplest of these would be that in which F is taken
integrable in the sense of Lebesgue over the given region,
while / is similarly integrable. Here we should be led to
require that the integral /(ʃ) not only exist but be absolutely
continuous.

5∙ A SPECIAL SYMMETRIC CASE

We shall apply the preceding formal work to the discussion
of a particular symmetric case which is especially interesting,

Here the function F(f) is discontinuous at r = r₀ but not in a
way such as to cause essential difficulty. In fact if we apply
the formula (2) to this case we find at once

Since the function /(ʃ) so obtained is everywhere positive
and leads to no difficulty in (1), we conclude that it is pos-
sible to set up a symmetrical distribution of lines outside of
the circle s = r₀ in such wise that the region outside of the
given circle is of a uniform gray.

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