t simply increase, they increase in a geometrical
ratio. Anyone who has worked out one of these geometrical ratios knows
how wondrously they mount up. There is an old familiar story of the
blacksmith who asked the price at which the stranger would sell the
horse he was shoeing. The owner of the horse replied that, if the
blacksmith would give him one penny for the first nail he drove into
the shoe, two for the second, four for the third, and so on, he might
have the horse. No hundred horses in the world taken together have
ever brought such a price as the blacksmith would have had to pay for
the animal on which he was working. This is no circumstance to the
awful story of what would happen to the earth if any animal could
multiply unrestricted. The usual number of eggs laid by a mother robin
for a single brood is four, and she may produce two broods in one
season. This would mean that the original pair had produced eight
offspring, four times their own number. If we can imagine these mating
the next year and producing their kind in the same proportion; and, if
we further suppose that each robin needs a space one hundred feet
square from which to gather his food, we realize the astonishing fact
that in fifteen years every patch one hundred feet square in
Pennsylvania and New York would each have its resident robin, while
the following season would find a robin on every similar patch from
Maine to the Carolinas. Of course this could never happen, this is
simply what would happen if all the robins could grow to maturity and
reproduce at the normal ratio. But the robin is a comparatively slow
producer.

Our turtles are more prolific. Twenty eggs would probably not be an
unusual number. If we could imagine a turtle to live in the sea and to
produce at this rate; and, if each turtle should need as much room
each way as the robin, and a depth of water equal to its width, before
the robins had spread over New York and Pennsylvania the turtles would
have filled all the seas of the globe. Frogs are even more remarkable
in this respect. Two hundred eggs is not an uncommon number. If each
frog required a space twenty-five feet square on which to subsist, the
entire earth would be more than covered with them within six years. It
is ludicrous to think of such numbers, especially when we realize the
hundreds of thousands of kinds of animals there are in the world, each
of which is also multiplying, and it becomes evident at once that