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 "." 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 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 a Babbage, 'The Exposition of 1851,' p. 1.

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, that it is 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 (vol. ii. p. 4), enter into all acts of observation, and are often a worthy subject of inquiry. But there are many instances in the history of physical science, in which much trouble and temporary error have been caused by false assertions carelessly made, and carelessly accepted without experimental verification.

The reception of the Copernican theory was much impeded by the objection, that if the earth were perpetually 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, that of showing by trial that the asserted facts are not correct ones. In the first place, if a stone had been dropped with suitable precautions from the mast-head 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 As the anti-Copernicans had assumed the contrary result as certain to ensue, their argument would of course have fallen through at once. Had the Copernicans next

mast.

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 support the anti-Copernican views; but, with very accurate observation, they might have discovered, as Benzenberg subsequently did, a very small deflection towards the west (vol. i. p. 453). At the moment when a body begins to fall freely, it begins to resemble a very small satellite moving under the force of gravity, as exerted from the earth's centre of attraction, and it therefore describes, like other satellites, a portion of an elliptic orbit". Had the Copernicans then been able to detect and interpret the meaning of this small divergence, they would have found in it a conclusive proof 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 entirely arises from a misapprehension of the facts 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 again careful examination shows that the supposed faces are not bCambridge and Dublin Mathematical Journal' (1848), vol. iii.

P. 206.

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 purely mistaken character of the supposed exception.

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 crystallized in a form distinctly different 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 crystallization. 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 d.

In the science of crystallography many other apparent exceptions present themselves, and sometimes cause considerable perplexity. Four of the faces of a regular octahedron may become so enlarged in the crystallization of iron pyrites and some other substances, that the other four faces become altogether imperceptible and a regular tetrahedron appears to be produced, contrary to the laws of crystallographic symmetry. Many other crystalline e Daubeny's Atomic Theory,' p. 76.

C

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

forms are similarly modified, so as to produce a series of what are called hemihedral forms.

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 all 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 and learned an inquirer as Aristotle entirely failed to perceive the true nature of buoyancy or apparent lightness, and the doctrine of intrinsic lightness, being expounded in his works, became the accepted view for many centuries. It is true that Lucretius was fully aware why flame tends to rise, holding that

The flame has weight, though highly rare,

Nor mounts but when compelled by heavier air.'

Archimedes also was so perfectly acquainted with the buoyancy of bodies immersed in water, that he could not fail to perceive the existence of a parallel effect in air. Yet throughout the early middle ages the light of true science, clear though feeble, could not contend with the powerful but confused glare of the false Peripatetic doctrine. The genius of Galileo and Newton was required to convince people of the simple truth that all matter is heavy, but that the gravity of one substance may be overborne by that of another, as one scale of a balance is carried up by the preponderating weight in the opposite scale. It is curious to find Newton gravely explaining