Thus far in the history of Science, Mathematics, as a whole, has ranked
as the only Exact Science; being the only department of intellectual
activity, all of whose Laws or Principles are established on a basis of
_undeniable certainty_. If, however, theories of Cosmogony and
considerations of Cosmography be excluded from the field of Astronomy,
this Science consists almost wholly of the application of the Laws of
Mathematics to the movements of the celestial bodies. Restricting
Astronomy proper to this domain, where, as a _Science_, it strictly
belongs, and setting aside its merely descriptive and conjectural
features, as hardly an integral part of the Science itself, we have
another Exact Science in addition to Mathematics.

Of still another domain, that of Physics, Professor Silliman says, 'all
its phenomena are dependent on a limited number of general laws ...
which may be represented by numbers and algebraic symbols; and these
condensed _formulæ_ enable us to conduct investigations with the
certainty and precision of pure Mathematics.'

The various branches of Physics have not hitherto been ranked as Exact
Sciences, because, as in Astronomy, unsubstantiated theories and
doubtful generalizations, incapable of Mathematical Proof, have mingled
with their _Demonstrated_ Laws and Phenomena, as a component part of
the Science itself. It has consequently exhibited an ambiguous or
problematical aspect, incompatible with the rigorous requirements of
Exact Science. Even in Professor Silliman's admirable work, _formulæ_
are given as Laws, which, however correct, have yet no foundation in
axiomatic truth; while Inferences are drawn from them which are by no
means capable of _Demonstration_. Strictly speaking, however, only those
Laws which _do_ rest upon a Demonstrable basis and the Phenomena derived