LAW, PHYSICAL AND MORAL.

IN Volute Duke of Argyll, the following passage

N the interesting volume entitled "The Reign of Law," for which

occurs* :

"Words, which should be the servants of Thought, are too often its masters; and there are very few words which are used more ambiguously, and therefore more injuriously, than the word Law. . . . . In its primary signification, a law is the authoritative expression of human Will enforced by Power. The instincts of mankind finding utterance in their language, have not failed to see that the phenomena of Nature are only really conceivable to us as in like manner the expressions of a Will enforcing itself by Power. But, as in many other cases, the secondary or derivative senses of the word have supplemented the primary signification; and Law is now habitually used by men who deny the analogy on which that use is founded, and to the truth of which it is an abiding witness. It becomes, therefore, all the more necessary to define the secondary senses with precision. There are at least five different senses in which Law is habitually used, and these must be carefully distinguished:

“First, We have Law as applied simply to an observed Order of facts.

"Secondly, To that Order as involving the action of some Force or Forces, of which nothing more may be known.

"Thirdly, As applied to individual Forces, the measure of whose operation has been more or less defined or ascertained.

"Fourthly, As applied to those combinations of Force which have reference to the fulfilment of Purpose, or the discharge of Function.

"Fifthly, As applied to Abstract Conceptions of the mind-not corresponding with any actual phenomena, but deduced therefrom as axioms of thought necessary to our understanding of them. Law, in this sense, is a reduction of the phenomena, not merely to an Order of Facts, but to an Order of Thought."

If it be true that the word Law is used habitually in all these senses, and probably more (as the phrase "at least" seems to imply), and I am not intending to dispute this,-it is quite certain that the previous assertion, namely, that the word Law is used ambiguously, and therefore * Chap. ii.

injuriously, must be abundantly true also. But such a loose use of an important word can scarcely fail to suggest that it may be worth while to attempt a closer examination of the idea which the word is intended to convey, and of the manner in which it ought to be used. Such an examination can scarcely fail to be interesting; I believe it may also be useful; and I am bold enough to think that the treatment of the question contained in this paper will be found to be in some measure both interesting and useful to those who care to enter upon the discussion of a subject which is essentially one of difficulty.

There is a majestic passage in the commencement of the “Ecclesiastical Polity," in which Hooker gives us a definition of Law:—

“All things that are have some operation not violent or casual. Neither doth anything ever begin to exercise the same, without some pre-conceived end for which it worketh. And the end which it worketh for is not obtained, unless the work be also fit to obtain it by. For unto every end every operation will not serve. That which doth assign unto each thing the kind, that which dǝth appoint the form and measure, of working, the same we term a Law.”*

I quote this passage because it' exhibits the conception which is exactly opposite to that placed in the forefront in the enumeration of the senses in which the word Law is used, given by the Duke of Argyll. The first sense mentioned in this enumeration is "an observed order of facts ;" and probably, so far as physical science is concerned, this is the primary conception to a modern mind. The conception which presented itself as the primary one to the mind of Hocker was not so much the order as that which causes the order—" that which doth appoint the form and measure of working—it having been already assumed that all things that are have some operation not violent er casual,” in ether words, an "order" which may conceivably be "cbserved." The man whɔ observes the enter and the man who discovers the cause of the order way equally clam the discovery of a law, and the two cry teed a defvition of the term used to prevent them from quarrelling over their

The trendle which existed between Flamsteed and Neston, and the een troversy, which was resed some years 120 concerning the ments of this great seleunte quarrel will lustrate this Newton wanted Flamsteed's observations in order, as be sell to complete his decry of the men : Flamsteed said that the theory of the moon was a'maly omplite, and grudged the use of his observations Toword Jerry, used ambiguous y, and therefore in mousy, was the cause of the trulle. Flamstood understood by a theory an observed order of facts ulte thenk's that if the order wis se comy

was new, aud Flamsteed was perhaps not to blame for not understanding it; but it is none the less true that the misconception of the term led to serious trouble.

May we not get over the difficulty with regard to the word law by introducing qualifying words to express the sense in which it is used? It seems to me that if we agree to distinguish between what I will call objective and subjective law, we shall introduce a distinction which will lead to the clearing away of much confusion. The distinction will be analogous to that which is recognized between Plane and Physical Astronomy, or between Geometrical and Physical Optics. In the one case we are concerned with orders of facts, in the other with that which lies beneath such orders. I say advisedly lies beneath; and I may add that the subjective laws which lie beneath the objective may be indefinitely numerous, one law depending upon that immediately below it, that upon another still lower down, and so on indefinitely, like geological strata. Moreover, the objective law may be the result of several co-operating subjective laws, and each of these may depend upon one or more beneath, and so on. If this view be admitted, we shall be able to take either a descending course from the objective to the subjective, or an ascending course from the latter to the former; either we can descend from the observed order to Hooker's causative and directive law, or we can ascend from this causative and directive law to the observed order.

Let me illustrate what I have now written by reference, not to science, but to an observed order in common life.

Going through a street of a town, I observe that all the houses are of the same height, that they agree very closely in pattern, all have bale onies, &c. &c. This is the observed order: it constitutes, so far as the observation goes, a law: I should call it an objective law: the suspicion is raised that this outward uniformity is the result of something internal. I inquire, and I find that the property all belongs to one man, and that he has leased his land upon the condition that the houses shall be built in accordance with a certain prescribed plan and pattern: this is the subjective law, to the discovery of which my observation has led me.

It is obvious that, although the observed uniformity in the building and the conditions of building enforced by the proprietor of the land are two things different in kind, yet there is no danger of confusion, if either one or the other be described as the law of the estate. The one is the outcome of the other. The written conditions according to which. the architect works are potentially the same thing as the effect produced when the architect has done his work.

Notice, in this simple example, the passage from the barest observed fact in objective law to volition or purpose in subjective law. I have gone at once to the conditions prescribed by the owner of the soil; but the analogy with natural phenomena would be more complete if we regarded the observed uniformity of the houses as being dependent, which

For

no doubt in practice it would be, on conditions intermediate. example, if you inquired why the houses were uniform, the builder might show the contract into which he had entered to build the whole street after one pattern; and that contract might be regarded as the subjective law of the street. But you would perceive at once that there must be something underneath that contract, some subjective law of the second order, upon which the first law rested. The builder might, for example, throw you back upon the architect, and the architect's instructions might be regarded as the subjective law of the second order in question. But you would not rest here, and you would come ultimately to the volition or choice of the person who could say with authority what the order of things or the objective law should benamely, the owner of the soil.

Thus objective law points to subjective; the first subjective law to another of the second order; this, it may be, to a third; and so onshall we say, in some cases, ad infinitum. Why not?

As observed facts may thus rest upon a series of subjective laws, so there is a class of facts which may be said to rest upon no subjective laws at all, but to be complete in themselves. Let me explain what I

mean.

The facts of space and number are a good illustration.

It is a law of right-angled triangles that the squares described upon the two sides are together equal in area to that described upon the hypotenuse it is a law of circles that the tangent is at right angles to the diameter: it is a law of ellipses that the normal bisects the angle between the focal distances.

So in numbers: it is a law that all numbers are divisible by 9, the sum of whose digits is so divisible: it is a law that the difference between the square of two numbers is divisible by either their sum or their difference. Hundreds of other theorems, simple and complicated, might be quoted, which may all be regarded as laws of numbers.

All laws of space and number, however, are objective laws, and nothing else. You may make one theorem depend upon another, and so reduce the most complex to something which is axiomatic; but you come ultimately to axiom, not to volition; to something which must be because it cannot be otherwise, not to something which is because a will has ordained that so it shall be. Whenever you can reduce a law to axiom you get rid of volition; in space and number, for example, there is no volition; in physics there are, as I believe, some laws of one kind and some of another.

What is true of space and number is of course true in all departments of pure mathematics. Thus, to take the case of Taylor's theorem. If f(x) be a function of a such that f(x+h) is capable of expansion according to powers of h, then the law of the series is determinable by actual à priori demonstration. The formula which represents the series must be, and always has been, true. The objective law stands upon its

own foundation. There is no subjective law beneath it upon which it can be said to rest.

It may be well to observe that what is true in the case of geometry and numbers and algebraical formulæ, is true also of the fundamental propositions of mechanics. The parallelogram of forces, for example, is a law resting (so to speak) on its own foundations; like the truths of space, it is deducible from appropriate definitions and axioms; and, like them, it gradually assumes to reflecting minds an axiomatic or selfevident character. It occupies a kind of border-land between geometry and physics; it is the introduction to the latter, but it belongs to some extent to the former.

When we come to the consideration of physical laws, properly so called, we find ourselves in a new region altogether. Here we have always the objective law as expressed in an observed order of facts, and the subjective law or laws which lie below it.

I will take as the most familiar and most illustrative of these laws what are known as those of Kepler. The Duke of Argyll, in the chapter of the "Reign of Law" to which I have already referred, has naturally enough done the same thing, but he has not made exactly the same use of the illustration as that which I propose to make. For my pur

pose it will be well to quote Kepler's laws, because as regards my discussion of them there is an important difference between one of them and the other two.

The laws are as follows:

1. The planets move in ellipses, each having one of its foci in the sun's centre.

2. The areas swept out by each planet about the sun are, in the same orbit, proportional to the time of describing them.

3. The squares of the periodic times of the planets about the sun are proportional to the cubes of the mean distances.

It is unnecessary to explain here that these remarkable laws are not accurately true, but are laws which would be accurately true of a single planet regarded as a particle moving round the sun regarded as fixed. It is, however, much to my purpose to observe that to Kepler they were the result of the purest and most laborious observation and calculation; no chapter in the history of physical discovery is more interesting than that which records Kepler's honest and earnest struggles. He felt absolutely sure that there must be laws of some kind regulating planetary motion; he made a guess as to what they might be, and having made his guess he proceeded to test its truth: hypothesis after hypothesis was thrown aside as worthless because it failed to conform itself to hard fact, and the result was that the three laws above quoted, and which his boundless ingenuity suggested, stood the test and became part of our recognized knowledge. Great fruits have, as we know, resulted from them, but to Kepler they were complete in themselves; they were the laws which governed planetary motion, and he was