ally conceded to be less liable to error than any other form of
scientific analysis. This line, then, is too short to fathom the ocean
of destiny; too weak to bear inferences from even the facts of common
life.

Attempts have indeed been made to apply mathematics to the facts of life
in what is called the doctrine of chances. By this kind of calculation
it can be shown, that the chances were a thousand millions to one that
you and I should never have been born. Yet here we are.

But when we begin to apply mathematics to the affairs of every-day life,
we immediately multiply our chances of error by the number and
complexity of these facts. The proper field of mathematics is that of
magnitude and numbers. But very few subjects are capable of a
mathematical demonstration. _No fact_ whatever which depends on the will
of God or man can be so proved. For mathematical demonstration is
founded on necessary and eternal relations, and admits of no
contingencies in its premises. The mathematician may demonstrate the
size and properties of a triangle, but he can not demonstrate the
continuance of any actual triangle for one hour, or one minute, after
his demonstration. And if he could, how many of my most important
affairs can I submit to the multiplication table, or lay off in squares
and triangles? It deals with purely ideal figures, which never did or
could exist. There is not a mathematical line--length without
breadth--in the universe. When we come to the application of
mathematics, we are met at once by the fact that there are no
mathematical figures in nature. It is true we speak of the orbits of the
planets as elliptical or circular, but it is only in a general way, as
we speak of a circular saw, the outline of its teeth being regularity
itself compared with the perturbations of the planets. We speak of the
earth as a spheroid, but it is a spheroid pitted with hollows as deep as
the ocean, and crusted with irregular protuberances as vast as the
Himalaya and the Andes, in every conceivable irregularity of form. Its
seas, coasts, and rivers follow no straight lines nor geometrical
curves. There is not an acre of absolutely level ground on the face of
the earth; and even its waters will pile themselves up in waves, or dash
into breakers, rather than remain perfectly level for a single hour. Its
minuter formations present the same regular irregularity of form. Even
the crystals, which approach the nearest of any natural produc