exceptional events are commonly the points from which we start to explore new regions of knowledge. It has been beautifully said that Wonder is the daughter of Ignorance, but the mother of Invention; and though the most familiar and slight events, if fully examined, will afford endless food for wonder and for wisdom, yet it is the few peculiar and unlooked-for events which most often lead to a course of discovery. It is true, indeed, that it requires much philosophy to observe things which are too near to us.

The high scientific importance attaching, then, to exceptions, renders it desirable that we should carefully consider the various modes in which an exception may be disposed of; while some new facts will be found to confirm the very laws to which they seem at first sight clearly opposed, others will cause us to limit the generality of our previous statements. In some cases the exception may be proved to be no exception; occasionally it will prove fatal to our previous most confident speculations; and there are some new phenomena which, without really destroying any of our former theories, open to us wholly new fields of scientific investigation. The study of this subject is especially interesting and important, because, as I have before said (p. 587), no important theory can be built up complete and perfect all at once. When unexplained phenomena present themselves as objections to the theory, it will often demand the utmost judgment and sagacity to assign to them their proper place and force. The acceptance or rejection of a theory will depend upon discriminating the one insuperable contradictory fact from many, which, however singular and inexplicable at first sight, may afterwards be shown to be results of different causes, or possibly the most striking results of the very law with which they stand in apparent conflict.

I can enumerate at least eight classes or kinds of exceptional phenomena, to one or other of which any supposed exception to the known laws of nature can usually be referred; they may be briefly described as below, and will be sufficiently illustrated in the succeeding sections.

(1) Imaginary, or false exceptions, that is, facts, objects, or events which are not really what they are supposed to be.

(2) Apparent, but congruent exceptions, which, though apparently in conflict with a law of nature, are really in agreement with it.

(3) Singular exceptions, which really agree with a law of nature, but exhibit remarkable and unique results of it. (4) Divergent exceptions, which really proceed from the ordinary action of known processes of nature, but which are excessive in amount or monstrous in character.

(5) Accidental exceptions, arising from the interference of some entirely distinct but known law of nature.

(6) Novel and unexplained exceptions, which lead to the discovery of a new series of laws and phenomena, modifying or disguising the effects of previously known laws, without being inconsistent with them.

(7) Limiting exceptions showing the falsity of a supposed law in some cases to which it had been extended, but not affecting its truth in other cases.

(8) Contradictory or real exceptions which lead us to the conclusion that a supposed hypothesis or theory is in opposition to the phenomena of nature, and must therefore be abandoned.

It ought to be clearly understood that in no case is a law of nature really thwarted or prevented from being fulfilled. The effects of a law may be disguised and hidden from our view in some instances: in others the law itself may be rendered inapplicable altogether; but if a law is applicable it must be carried out. Every law of nature must therefore be stated with the utmost generality of all the instances really coming under it. Babbage proposed to distinguish between universal principles, which do not admit of a single exception, such as that every number ending in 5 is divisible by five, and general principles which are more frequently obeyed than violated, as that "men will be governed by what they believe to be their interest."1 But in a scientific point of view general principles must be universal as regards some distinct class of objects, or they are not principles at all. If a law to which exceptions exist is stated without allusion to those exceptions, the statement is erroneous. I have no right to say that "All liquids

1 Babbage, The Exposition of 1851, p. 1.

expand by heat," if I know that water below 4° C. does not; I ought to say, "All liquids, except water below 4° C., expand by heat;" and every new exception discovered will falsify the statement until inserted in it. To speak of some laws as being generally true, meaning not universally but in the majority of cases, is a hurtful abuse of the word, but is quite usual. General should mean that which is true of a whole genus or class, and every true statement must be true of some assigned or assignable class.

Imaginary or False Exceptions.

When a supposed exception to a law of nature is brought to our notice, the first inquiry ought properly to be-Is there any breach of the law at all? It may be that the supposed exceptional fact is not a fact at all, but a mere figment of the imagination. When King Charles requested the Royal Society to investigate the curious fact that a live fish put into a bucket of water does not increase the weight of the bucket and its contents, the Royal Society wisely commenced their deliberations by inquiring whether the fact was so or not. Every statement, however false, must have some cause or prior condition, and the real question for the Royal Society to investigate was, how the King came to think that the fact was so. Mental conditions, as we have seen, enter into all acts of observation, and are often a worthy subject of inquiry. But there are many instances in the history of science, in which trouble and error have been caused by false assertions carelessly made, and carelessly accepted without verification.

The reception of the Copernican theory was much impeded by the objection, that if the earth were moving, a stone dropped from the top of a high tower should be left behind, and should appear to move towards the west, just as a stone dropped from the mast-head of a moving ship would fall behind, owing to the motion of the ship. The Copernicans attempted to meet this grave objection in every way but the true one, namely, showing by trial that the asserted facts are not correct. In the first place, if a stone had been dropped with suitable precautions from the masthead of a moving ship, it would have fallen close to the foot of the mast, because, by the first law of motion, it would

remain in the same state of horizontal motion communicated to it by the mast. As the anti-Copernicans had assumed the contrary result as certain to ensue, their argument would of course have fallen through. Had the Copernicans next proceeded to test with great care the other assertion involved, they would have become still better convinced of the truth of their own theory. A stone dropped from the top of a high tower, or into a deep well, would certainly not have been deflected from the vertical direction in the considerable degree required to agree with the supposed consequences of the Copernican views; but, with very accurate observation, they might have discovered, as Benzenberg subsequently did, a very small deflection. towards the east, showing that the eastward velocity is greater at the top than the bottom. Had the Copernicans then been able to detect and interpret the meaning of the small divergence thus arising, they would have found in it. corroboration of their own views.

Multitudes of cases might be cited in which laws of nature seem to be evidently broken, but in which the apparent breach arises from a misapprehension of the case. It is a general law, absolutely true of all crystals yet submitted to examination, that no crystal has a re-entrant angle, that is an angle which towards the axis of the crystal is greater than two right angles. Wherever the faces of a crystal meet they produce a projecting edge, and wherever edges meet they produce a corner. Many crystals, however, when carelessly examined, present exceptions to this law, but closer observation always shows that the apparently re-entrant angle really arises from the oblique union of two distinct crystals. Other crystals seem to possess faces contradicting all the principles of crystallography; but careful examination shows that the supposed faces are not true faces, but surfaces produced by the orderly junction of an immense number of distinct thin crystalline plates, each plate being in fact a separate crystal, in which the laws of crystallography are strictly observed. The roughness of the supposed face, the striæ detected by the microscope, or inference by continuity from other specimens where the true faces of the plates are clearly seen, prove the mistaken character of the supposed exceptions. Again, four of the faces of a regular octahedron may become so enlarged

in the crystallisation of iron pyrites and some other substances, that the other four faces become imperceptible and a regular tetrahedron appears to be produced, contrary to the laws of crystallographic symmetry. Many other crystalline forms are similarly modified, so as to produce a series of what are called hemihedral forms.

In tracing out the isomorphic relations of the elements, great perplexity has often been caused by mistaking one substance for another. It was pointed out that though arsenic was supposed to be isomorphous with phosphorus, the arseniate of soda crystallised in a form distinct from that of the corresponding phosphate. Some chemists held this to be a fatal objection to the doctrine of isomorphism; but it was afterwards pointed out by Clarke, that the arseniate and phosphate in question were not corresponding compounds, as they differed in regard to the water of crystallisation.1 Vanadium again appeared to be an exception to the laws of isomorphism, until it was proved by Professor Roscoe, that what Berzelius supposed to be metallic vanadium was really an oxide of vanadium.2

Apparent but Congruent Exceptions.

Not unfrequently a law of nature will present results in certain circumstances which appear to be entirely in conflict with the law itself. Not only may the action of the law be much complicated and disguised, but it may in various ways be reversed or inverted, so that careless observers are misled. Ancient philosophers generally believed that while some bodies were heavy by nature, others, such as flame, smoke, bubbles, clouds, &c., were essentially light, or possessed a tendency to move upwards. So acute an inquirer as Aristotle failed to perceive the true nature of buoyancy, and the doctrine of intrinsic lightness, expounded in his works, became the accepted view for many centuries. It is true that Lucretius was aware why flame tends to rise, holding that

"The flame has weight, though highly rare,

Nor mounts but when compelled by heavier air."

Daubeny's Atomic Theory, p. 76.

2 Bakerian Lecture, Philosophical Transactions (1868), vol. clviii

p. 2.