PROBLEM V.

FORCE AND CAUSE.

"He that shall discourse weightily on Efficient Causes, setting forth in clear conceits the nature thereof, maketh philosophy his servant. 'Tis a noble quest, but we have wandered from the ways."-SIR THOMAS BROWNE.

"The problem of the sciences is in the first place to seek the laws by which the particular processes of nature may be referred to and deduced from general rules. These are evidently nothing more than general ideas by which the various phenomena are connected together. The finding of these is the office of experimental science. The theoretic position seeks, on the contrary, to evolve the unknown causes of the processes from the visible actions which they present; it seeks to comprehend these processes according to the laws of causality. We proceed until we at length arrive at ultimate causes which are unchangeable, and which must, therefore, in all cases where the conditions are the same, produce the same invariable effects." HELMHOLTZ.

FORCE AND CAUSE.

CHAPTER I.

THE CONCEPTION OF FORCE.

1. THE word Force is a symbol which has many meanings. It varies in different works, and often in different passages of the same work. Sometimes it stands for the Unknowable, whose manifestations are the objective universe; sometimes it is the common measure by which all phenomena are rendered intelligible; sometimes it is an imaginary entity supposed to take up its habitation in substances, passing freely from one to the other; sometimes a peculiar kind of Matter, very subtle, and endowed with qualities wholly unlike those of ordinary Matter; sometimes it is the simple synonyme of cause, sometimes of strength, sometimes of motion; now confounded with, and now distinguished from, Energy. A mathematician is contented with defining it "the differential coefficient of the quantity of movement," and the formula F = M answers all his purposes. But the physicist has his cohesive, diffusive, elastic forces, the chemist has his affinity, the biologist his vital forces, and the psychologist his moral forces, which are not so readily reducible to the mathematical formula.

dv

dt

If we consider what all these different meanings have in common, it will be found that the definition I have proposed the Activity of Matter, or the Changes in the Felt comprises them all. Every Agent, material

or spiritual, may be viewed statically, capable of acting, or dynamically, in action; and when forces are said to animate Matter, they are supposed to give life and activity to what is in itself inert. Activity is the Kraftbegriff, or conception of Force, which is common to all European thinkers; but in England the leading physicists of our day have greatly restricted the meaning of the term Force, and introduced that of Energy to express much of what elsewhere is included under Force. There is certainly great need of precision, for we meet with such tautologies as dynamic-force, motive-force, and staticforce, which are equivalent to force-force, motivemotion, and resting-motion.

2. Helmholtz has stated with precision the point of view I here adopt: "Science regards the phenomena of the external world by two processes of abstraction: in the first place it looks upon them as simple existences without reference to their action upon our organs of sense, or upon each other; in this aspect they are named matter. The existence of matter in itself is to us something passive and devoid of action: in it we distinguish merely the relations of space and of quantity (mass), which we assume to be eternally unchangeable. To matter thus regarded we must not ascribe qualitative differences, for when we speak of different kinds of matter, we refer to differences of action, that is, to differences in the forces of matter. Matter in itself can therefore partake of one change only, a change which has reference to space, that is, motion." [In other words, the abstraction Passivity can only be correlated with the abstraction Activity.] "Natural objects are not, however, passive; in fact, we come to a knowledge of their existence solely from their action upon our organs of sense, and infer from these actions a something which acts. When, therefore, we wish to make real application of our idea of

matter, we can only do it by means of a second abstraction, and ascribe to it properties which in the first case were excluded from the idea, namely, the capability of producing effects, or, in other words, of exerting force.

"It is evident that in the application of the ideas of matter and force to nature the two ideas should never be separated: a mass of pure matter would, as far as we and nature are concerned, be a nullity, inasmuch as no action could be wrought by it either on our organs of sense, or on the remaining portion of nature. A pure force would be something which must have a basis, and yet which has no basis, for the basis we name matter. It would be equally erroneous to define matter as something which has an actual existence, and force an idea which has no corresponding reality. Both, on the contrary, are abstractions from the actual, formed in precisely similar ways. Matter is only discernible by its forces, not by itself.” *

3. The aim of Science is to express all phenomena in terms of Matter and Force, so that by these means congruity may be introduced into the conceptions which systematize Experience. The phenomena are viewed alternately as causes and effects, as agents and actions. We generalize our manifold experiences, and generalize these generalities into wider generalities. Among these latter there are four of supreme importance: Matter, Force, Position, and Motion.† Although we distinguish these as symbols, they only represent different aspects of reality. It is only in abstraction that Force can be separated from Matter, or Motion from Position. The one reflects the other as a correlative. For Position there must be Matter posited, and for Motion there must be Matter in

* HELMHOLTZ, On the Conservation of Force, translated in the Scientific Memoirs edited by TAYLOR and FRANCIS, 1853, Part II. p. 115 (slightly altered).

+ See TAIT, Thermodynamics, 1868, § 3.