We must be careful to distinguish the task of a Philosophy of Nature and a Philosophy of Mind from those of the experimental sciences which deal directly with the fact of the physical and psychical orders. The fundamental business of the latter is, as we have already seen, the discovery of descriptive formulæ by the aid of which the various processes which make up the physical and psychical orders may be depicted and calculated. The fewer and simpler these formulæ, the more they economise the labour of calculation, the more completely do the experimental sciences perform the work for which we look to them. And so long as our formulæ adequately accomplish this work of calculation, it is indifferent for the experimental sciences whether the language in which they are couched represents a “reality” or not. The “atoms,” “forces,” and “ethers” of our physical, the “sensations” of our psychological formulæ, might be as purely symbolic creations of our own imagination as the “imaginary quantities” of mathematics, without their unreality in any way interfering with their scientific usefulness. In the words of an eminent physicist, “the atomic theory plays a part in physics similar to that of certain auxiliary concepts in mathematics, ... although we represent vibrations by the harmonic formula, the phenomena of cooling by exponentials, falls by squares of times, etc., no one will fancy that vibrations _in themselves_ have anything to do with the circular functions, or the motion of falling bodies with squares” (Mach, _Science of Mechanics_, p. 492). When it is asserted that the usefulness of a scientific hypothesis, such as, _e.g._, the atomic theory or the hypothesis of the existence of an etherial undulating medium, of itself proves the real existence of things corresponding to the concepts employed by the hypothesis, the same fallacy is committed as when it is contended that if an algebraical calculus is generally capable of geometrical interpretation, every step in its operations must be interpretable.