CHAPTER II.

UNATTAINABLE OBJECTS OF SEARCH.

There's nothing situate under Heaven's eye,

But hath its bound in earth, in sea, or sky.—SHAKSPEARE.

IT is useless to search for that which cannot exist. Although we know but little of the actual limits of possible knowledge, there are signs that nature is not in, every respect infinite. It is highly probable that the number of forms of energy and of elementary substances is limited. At the present time we are only acquainted with less than a dozen of the former and six dozen of the latter. Elementary substances also do not unite together in every proportion by weight, but only in certain definite ones, and do not produce an unlimited series of compounds. There appear to be laws operating in the inmost nature of elementary bodies, which prevent the atoms uniting with each other, except in certain definite arrangements or groups, as if all other arrangements were geometrically or mechanically impossible. The number of forms in which each substance crystallises is also very limited; common salt, for example, crystallises only in cubes. But who, with a finite mind, shall set a limit to creative power, or assign bounds to the Universe? Ours is the science of this globe alone, and consequently of its limited conditions. Nearly all the instances of definite chemical compounds with which we are acquainted are observed under the limited ranges of pressure and temperature, &c., existing on this earth; and it is possible and even probable that under different ranges of pressure and

temperature, such as may now prevail in other parts of the universe, a great number of new compounds would be capable of existing. We already possess evidence of this in the fact that under the influence of great pressure or a low temperature, new compounds, such as the various cryohydrates, also ammonium, and hydrate of chlorine, may be obtained, and such additional bodies would add to the number of possible compounds. But the few additional instances of this kind with which we are at present acquainted also conform to, and therefore confirm, the law that elementary bodies only unite in certain definite atomic proportions by weight, and do not unite in the proportions of fractions of their atomic weights to form an unlimited number of compounds. The spectroscope has shown us that various substances in the elementary state, and probably some new elementary substances, exist in the more intensely heated heavenly bodies; but neither it nor any other instrument has yet supplied us with evidence of the existence of new compounds in the colder parts of the universe. Not only does it appear highly improbable that an unlimited variety of collocations of different atoms, united to form different substances, can exist; but many combinations and arrangements of forces are incompatible, and cannot co-exist. From these considerations, therefore, there is probably a limit to the number of natural existences, whether of forces, substances, or their phenomena, within reach of our observation, and consequently also to the amount of possible knowledge respecting them. The number of laws also which govern a finite number of substances or forces must themselves be finite. There are also statements in logic which are contradictory; mathematical quantities which are impossible; geometrical conditions which are inconceivable; mechanical arrangements which are self

SEARCHING FOR IMPOSSIBLE THINGS.

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destructive, and physical properties and motions which are incompatible. Many statements of fact also do not admit of degree; for instance, a substance either exists or it does not. According to the principles of geometry, there cannot exist more than five regular solids.

We do not create laws, nor can we command new effects, except those which are in harmony with the principles of nature. Scientific research or genius, therefore, cannot create1 new truths; it can only discover such as are in perfect accordance with the laws of matter and its forces. It is essentially truthful, and cannot verify our hypotheses unless they are true.

We must, however, carefully distinguish between the evidence supplied by the results of research and the observations, comparisons, and conclusions to be drawn from them. The former may be true, but the latter may be erroneous. Truth is that which is, and no matter how extraordinary truth may appear, our thought must be made to agree with it. The knowledge which we acquire by research in the physical and chemical sciences, although it may, so far as it goes, in most cases be thoroughly trusted as to matters of qualitative fact, is always incomplete and quantitatively inexact. More always remains to be known, and that which is known possesses only a finite degree of precision. This arises from the extremely limited power of our faculties and means of detection and observation, and our present incapability to appreciate absolute accuracy. As the analogies and conclusions we draw from research and experience are sometimes erroneous, we are frequently led by them to search for things which cannot exist. Every scientific investigator has his own notions of what is impossible;

1 I use this word in an absolute sense, viz. to form out of nothing.

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but there are several objects of search which are regarded as such by most men of science; amongst these may be mentioned perpetual motion, the creation or destruction of matter, energy, &c. But how are we to judge of what is absolutely impossible, and what is not? As our reasoning faculty is finite, and we have therefore no infallible guide, our best course is to consider those objects of search impossible which distinctly contradict any of what are termed the fundamental laws of thought,' or those of science. A thing either is or is not. That which is, is. That only which exists, or which is possible to exist in accordance with the essential nature of things, can be discovered. A self-contradictory statement, such as that which is is not, or the largest planets are the smallest, cannot be true. Two contradictory statements or hypotheses also cannot both be true. A whole is greater than its part. Things equal to the same are equal to each other. There can be no square root to a negative quantity. A figure which possesses three equal sides must have three equal angles. A substance cannot be and not. be at the same time in the same place. Every effect must have a cause. We cannot create or destroy either matter or energy. Action and reaction are equal and contrary. Two mutually destructive actions cannot coexist. A body cannot be moving in opposite directions. at the same time, &c. All of these are fundamental statements, the contrary of which are considered absolutely untrue and impossible by all scientific men. approximation, therefore, to a criterion of scientific truth, we may say, it is that which does not contradict any of what are termed the fundamental laws of thought' or

As an

1 See Boole's Laws of Thought; Jevons's Principles of Science, vol. i. p. 6; Thomson's Outlines of the Laws of Thought. Compare also the chapter on 'The Criteria of Scientific Truth.'

ANCIENT AXIOMS ARE NOT UNCHANGEABLE.

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principles of the sciences. There was a time when many of these truths were not known, but as science advances we become acquainted with a greater number of its axioms and laws, and uniformity of belief on fundamental points enlarges also. Neither our knowledge nor our accuracy in science is intuitive; they both are results of experience and education. In consequence of limited knowledge and instruction, the human mind can think erroneously, and often does so, but the tendency to think falsely in natural subjects diminishes as education advances. Erroneous propositions which were formerly believed, become absurd and almost unthinkable by the progress of science. There was a time when men thought that the earth was a plane, that the sun and planets revolved round it; that matter was destroyed by burning, &c.; but such propositions have become comparatively inconceivable by nearly all intelligent minds. The ancient axiom that the circle was the most perfect of figures, that natural motion must be circular, and therefore that the planets must move in circular orbits, was believed until the time of Kepler, but is now no longer an axiom. That which is inconceivable by one man, or in one age, is not necessarily so by another man, or in another period, and therefore the inconceivability of an idea or the reverse is only an incomplete test of its truth. Ideas which at one period are beyond reason, do in many cases, by the progress of knowledge, come within its domain; and some of those which were thought to be true are proved to be false. Some discoveries which are unattainable in one age or state of knowledge become. attainable in another; for instance, the laws of electro-magnetism or of electrochemical action could not have been discovered in an age when electro-currents were unknown, nor could the principle of conservation of matter and of energy have been

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