ON THE CLASSIFICATION OF THE SCIENCES. 271 the motions of simple molecules to the motions of compound molecules, from molecular motions to the motions of masses, and from the motions of smaller masses to the motions of larger masses. 1 ' There may be compared with this extract Biology, p. 109, and Cla.^i'n>:ation of the. Sciences, passim. But we shall seek to trace this principle as helpful in a classification of the sciences. The units which are, no doubt, fundamental to all others are the units of number and form of which mathematics treats. From the integer one all numbers arise, and by the motion of a point all forms arise. Mathematical units and aggregates are ideal, or rather are imperfectly actualised. In a classification according to the principle adopted we should best regard Mathematics, not as constitutive, but as concomitant with the other sciences, as pre- senting an ascending series of increasingly complex units con- comitant with the sciences ; and in the scheme subjoined to this explanation we have so placed it. The mathematics of a mole- cule is more |Complex than that of an atom ; and we know that the highest forms of matter present the most complex curves. Clifford and others have speculated as to what order of curves an investigation of the phenomena of life requires. The most refined piece of matter in existence is the human brain, and it presents, no doubt, mathematical complexities of a very high order. At each increasingly complex stage in nature there is, then, a corresponding mathematical stage, whose complexity is measured by the combination of simpler elements. The atom is confessedly the lowest unit which science has yet revealed, but it is quite conceivable that we may yet find an atomecule which shall bear the same relation to the atom which the molecule does to the mass. It is the unit of chemical forces, and Chemistry may be defined as the science of the atom. Mole- cules are aggregates of atoms, and are the units of physical forces ; hence we have Molecular Physics as a branch of science. Molecules are aggregated into masses, which act under molecular forces as units, as when the piston is moved by the molecular energy of the steam in the cylinder. Masses are rendered possible by the dissipation of molecular energy, and even gravitation may pos- sibly be considered as the tendency to massing inevitably arising from the dissipation of energy. As dissipation is continually in- creasing, gravitative tendency is continually increasing, although restrained by the original projectile force. We would divide masses into orbital and non-orbital, the orbital being those which perform an orbit in the heavens, and the non-orbital those which rest on the orbital, and have been differentiated from them. As- tronomy and Geology treat of the first class of masses. The dis- tinction between these sciences is, as Mr. Spencer remarks, non-essential and relative : Geology, as the science of the earth, treats of that heavenly body with which we happen to be best acquainted. Xon-orbital masses are subject to Molar Physics. Viewing a mass as an aggregate of molecules bound together by
