'All the Phenomena of Physics,' says Professor Silliman, in his _First Principles of Philosophy_, 'are dependent on a limited number of general laws, _of which they are the necessary consequences_. However various and complex may be the phenomena, their laws are few, and distinguished for their exceeding simplicity. All of them 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_. As in geometry, all the properties of figures are deduced from a few axioms and definitions; so _when the general laws of Physics are known, we may deduce from them, by a series of rigorous reasonings, all the phenomena to which they give rise_.'
Auguste Comte, in his elaborate and encyclopædic _Course of Positive Philosophy_, tells us that 'these _three_ laws [the Law of Inertia, the Law of the Equality of action and reaction, and the Law of the Composition of forces] are the experimental basis of the Science of Mechanics. From them the mind may proceed _to the logical construction of the Science, without further reference to the external world_. * * * We cannot, however, conceive of any case which is not met by these three laws of Kepler, of Newton, and of Galileo, and their expression is so precise that they can be immediately treated in the form of analytical equations easily obtained.' While also exhibiting the small number of Principles which lie at the foundation of other domains of our intellectual accumulations, Comte remarks: 'The ultimate perfection of the Positive system would be (if such perfection could be hoped for) to represent all phenomena as particular aspects of a single general fact;--such as Gravitation, for instance.'
These are a few specimens of what may be found in the books, pointing out the gradual approach of Scientific investigation to the discovery of a Unitary Law, and the expectation among Scientists of the advent, at some period not far distant, of a new Science, the greatest among Sciences, a true Pantology or Universology. Upon the apprehension of this Law, which must establish the true basis of every domain of thought or activity, and show it to be identical or analogous in the several domains, we shall be placed, _in relation to the whole universe_, precisely where we now stand in relation to Mathematics, Mechanics, and Physics; that is, the General Law or Laws of every domain of investigation will become known, as we now know those of these Sciences, and, to adopt the words of the French writer, 'from them the mind may proceed to the logical construction of the Science [being now the Science of the whole Universe], without further reference to the external world;' or to use the language of Professor Silliman, 'when the general laws of [the Universe] are known, we may _deduce_ from them, by a series of rigorous reasonings, _all the phenomena to which they give rise_.' Thus, upon the discovery of a Unitary Law, linking the Sciences together, and showing the identity of their starting points or bases, the Deductive Principle, considered either as a Method or a Process, must once more take the lead, and the Inductive occupy its legitimate position as a subordinate and corroborative auxiliary. Under the guidance of this new adjustment of the Deductive and Inductive Principles, a full, exact, complete, definite, _Scientific_ Classification of our knowledge will become possible, and the true boundaries of every domain of intellectual examination may be critically and clearly established. In the absence of such a Classification, it is only by viewing departments of the Universe with reference to the Method or Process employed in the investigation of their Phenomena, that we are able to estimate their present relations to Science, and to ascertain proximately their Scientific or Unscientific character. We proceed, then, to examine the connection of History, in its present development, with Science, a task to which the foregoing brief and incomplete consideration of the subject of Method has been a necessary preliminary.