jects, which we must here point out. There are certain kinds of objects that agree with one another, and differ from all other things in a great and unknown number of attributes; so that their agreement with one another is very intimate, and their distinction from all other things very wide. Thus if we take human beings, we find that they have an exceedingly large and complex agreement, or they possess more features in common than we can enumerate, or than we may ever be able, after all our study of the human subject, to reckon up; for to know them all would be to attain the perfect knowledge of man. It is the same with many classes of animals. If we take the dog, we find that there is an almost inexhaustible fund of common features which mark the dog as a kind apart from all other animals and things. So iron, silver, phosphorus, are of this description: the specimens of any one agree with one another in all the properties discovered and undiscovered that attach to that one; the entire discovery of all these properties being the perfect knowledge of the species. Such objects are called 'lowest species,' or lowest kinds,' because they cannot be subdivided into others, having the same totality of differences from one another. Thus if we divide man into white, red, tawny, and black races, these cannot be called species in consequence of these distinctions alone: if all the difference between one race and another can be expressed in one single attribute, such as colour, or in two or three definite attributes, then these races are not different in kind, they are not specifically, or in toto distinguished; the subdivided classes are called varieties, and not kinds. But if it were discovered that an indefinite and unknown number of properties distinguished a Negro from a European, as in the case of a man and a monkey, or a dog and a horse, European and Negro would be different kinds. The classes that are not separate kinds may be exemplified by solids, liquids, and gases, of the same substance; for these differ only by a limited and assignable difference, all traceable to the one agency of heat. So houses, lands, rivers, are true classes, but they are not true kinds; for the extent of their agreement with one another, and of their difference from other things, is limited and assignable; very unlike the differences between iron and gold, which affect all the senses, and which ramify and show themselves in a boundless number of ways. All the names of kinds are nouns; and although adjectives and abstract terms are formed from them, it is always a limited and imperfect derivation. Thus the adjective manly,' and the abstract noun manliness,' are very far from expressing all that is common to man; they only point out some one property which conspicuously attracts attention for some reason or another. But the names of classes that are not kinds readily take on the adjective and abstract form-as liquid,' 'liquidity;' 'circle,' 'circular,'' circularity.' These derivations are perfectly strict and proper; and it is only such names as are formed from classes, not kinds, or limited and ascertained in their common features, that can properly yield adjectives and abstract nouns with a strictly logical application. Nameable Things. It is of importance, as a preliminary to explaining the nature of affirmations or assertions, to have a general view of the things presented to us for receiving names, and for becoming the subjects of such affirmations or assertions; in other words, it is convenient to possess a comprehensive classification of the whole of the things that can become part and parcel of the thoughts, conceptions, or knowledge of men. Mr John Stuart Mill, in his great work on Logic, has devised a classification of the universe of knowable and nameable existences as follows: This is the most immediately ascertained class of t universe of things coming under our cognisance. 2d, The minds themselves which experience tie feelings. We require to distinguish the mind from its susceptibilities, and to define it as the thing in which all these reside. 3d, The bodies or external objects that are the cause of those feelings, or states, or consciousness, and all the special powers or distinguishable properties of these bodies. We have already explained that it has pleased Nature to provide substances which have a manifold effect upon the human susceptibilities, leading to dis tinct conceptions, and the imposition of separate names for the various powers or properties thus made known. The world of outward objects-these objects being taken as wholes, and also as possessing each a numerous assemblage of powers, which must be named and described, as well as the total masses—makes one large class of our nameable and knowable things, and ss such must be recognised in Logic. We can only be aware of these by their action on our minds; and hence it is necessary to class them subsequently to the states of consciousness or feelings which make them known, and which alone are properly present to the mind. The external universe does not require for our present par pose to be more minutely classified; the chief point re garding it being the point now stated as to the complex power of its individual objects upon the mind, upon which the whole of the abstractive process is founded. 4th, The Successions and Co-existences, the Likenesses and Unlikenesses, between feelings or states of consciousness, and between the outward objects that produce them. In addition to the individual feelings of the mind, and the individual objects of the world, we are led to take notice of their positions, movements, and similarities, or want of similarity. If thought and nature were dead and still, there would be nothing to mark but position; but as both are incessantly moving and changing, we must take cognisance of the movements, and see how one thing follows another. If no two things were ever alike, perception of Likeness would be impossible; but as the world has been con stituted on the principle of repeating the same objects in innumerable circumstances, the examples of this must force themselves on our attention, and we must signify, by appropriate names or descriptions, that such likenesses occur, so far as we descry them. Our conceptions are at the mercy of the outward universe, and ought to follow it as closely as possible; hence our processes of naming, with the view of communicating our knowledge, ought to correspond to the same common source of sensation and thought. We must therefore, in addition to feelings, objects, and their properties, possess a means of describing the co-exist ences of these, their successions, their likeness, and unlikenesses; and beyond these there is nothing that we can take a hold of. We exhaust all that passes in our minds, and all that we suppose to pass in nature, in the comprehensive grouping of Feelings, Minds, External Causes of Feeling, and the Co-Existences, and Successions, Likenesses, and Unlikeness of these Feelings, and their external causes. The entire action of the universe on the mind of man presents nothing that is not included in these four heads. Nature of Assertions or Propositions. In our exposition of names, we made no reference to matters of belief or disbelief. We spoke of objects and of their properties, conjunct and single, and of the conceptions formed of these, and of the names and descriptions given of those conceptions; but a mere notion or conception is not a matter of belief. We must now, however, proceed to state the nature of assertions, affirmations, or propositions, which all mean things to be 1st, Feelings, or states of consciousness, or every- believed or disbelieved, and therefore to be proved or thing which the mind is said to be aware of, or which disproved. A matter of belief means something we can produces an influence upon it. These include all sensa- act upon; something that will enable us to do one thing tions, thoughts, emotions, activities, volitions, and what- for the sake of attaining some other thing. When we ever is said to be felt or entertained by the human mind. I say 'bread is nourishing,' we do more than announce an object, bread,' and a property, nourishing: we | is situated on the Thames; the battle of Hastings was tie these two things together with a bond of union which rouses the activity of the human mind, and causes it to set to work in some given course. Assertions are not idle notions, but things of power and might; they are the intellectual machinery that rules the greater part of human life. When a man feels the want of nourishment, and is reminded of the assertion that bread is nourishing,' he applies his active energies to procure the bread, in the full assurance that he will thereby have something more than meets his eye in a loaf: that he will have his bodily strength renewed, and his appetite gratified. Belief is the state preliminary to action, or the state disposing to action when some given emergency arises; and assertions or propositions are what call forth this faith or belief. fought in 1066; the sun is in the sign Aries.' And the assertions of the properties of things belong to the same class-as when we say 'silver is precious,' tigers are ferocious,' ' man walks upright.' We have remarked that nature produces objects that have a manifold action on the human susceptibilities; each separate action being commonly called one of the properties of the entire object. Now when we assert that certain properties of a thing accompany certain others, we make affirmations of co-existence. Gold does not rust,' is a proposition which may be interpreted to mean that a certain substance recognised by us as yellow, heavy, and of high marketable value (the popular and obvious characteristics of gold), has also the property of not rusting, like iron or lead. ་ An assertion requires, in the first place, that there should be two things mentioned: it is not possible so to mention a single object as that it shall be a matter of belief or disbelief. Thus 'fire burns,' 'gold is yel-ration are propositions of this kind. The distinction low,'' bread is nourishing,' 'the sun is the centre of the planetary motions,' each contains at least two things or notions coupled together. Fire is one thing, burning is a different thing, if there be any meaning or anything to believe in the assertion. But the mention of two things is not enough: the two names of 'gold,'' yellow colour,' do not make an assertion of themselves; the asserting power is conferred by the verb 'is;' and we shall find that every assertion requires a verb, or that the verb is the part of speech which completes the force of an assertion, or has the power of causing belief or disbelief in the human mind. The question, then, arises what is the import of those verbs which are the bonds of union between the things coupled together in assertions? As assertions can relate only to the actual facts and appearances of the world, they must refer to some of the great classes of things above enumerated, as constituting the entire universe of the knowable. Accordingly, Mr Mill has shown that all possible assertions may be reduced to five general heads, determined by the fourth class of nameable things, or the class comprehending Successions, Co-Existences, Likenesses, and Unlikenesses. If we add to these four things the idea of mere Existence, we shall possess a summary of everything that can ever come to be asserted in any affirmation or proposition. We may, however, premise, before illustrating this statement of the meanings of assertions, that propositions may be either affirmative or negative: they may either propose something for belief, or as a ground of confidence and action; or they may propose something for disbelief, forbidding us to accept such thing as a ground of action. This is the only real and permanent distinction among propositions as to the form of their making their assertion. Other divisions, as into simple and complex, and into categorical or unqualified, and hypothetical or conditional, are not fundamental divisions. Each complex proposition may be reduced to simple propositions; and the conditional or qualified assertions may also be put in a form resembling the categorical or unqualified. It may be said, then, of assertions or propositions, that they affirm or deny some one or other of these five things-Existence, Co-Existence, Succession, Causation (a peculiar and important kind of Succession), or Resemblance. No proposition can be enunciated, no piece of knowledge or information conveyed, nothing believed or disbelieved, nothing presented as a guide to human action, that does not assert or deny of some thing or things one of these five attributes. In the case of Existence, a single object or thing is sufficient material for an assertion-as when we say, 'the sun exists,' 'God is.' But in all the others, it is obvious that there must be at least two things; for the very nature of the attributes of co-existence, succession, and likeness, is to imply plurality-to co-exist, to succeed one another, or to resemble one another. Propositions of Co-Existence are such as-London Propositions of Succession will readily occur to any one. Night follows day;' 'Queen Victoria followed King William IV.; and all the affirmations of historical narbetween geography and history is a distinction between the contemporaneous and the successive: the propositions of geography express co-existence and order in place; those in history, succession and order in time. The particular case of succession entitled Causation, is one very important in respect to the order of the world, and to our knowledge of that order; and although the idea of a cause and effect is familiar and intelligible to most people, it belongs to Logic to clear it up, and to represent it with the utmost possible precision, so that there may not be any doubt hanging over it in the most obscure and perplexed instances which can possibly occur. We shall have to take this up at an after stage; and at present we need only remind the reader, that the succession of cause and effect implies a fixed and invariable bond of connection, such as is never to be interrupted at any time, or under any circumstances; we commonly recognise a sort of unfailing power in the cause to bring on the effect, which we may confide in to the very uttermost. We have compared geography with history, as exhibiting generally the contrast of the contemporaneous with the successive; and we may likewise compare natural history, which exhibits the properties conjoined in the individual objects of nature, with the sciences of physics, chemistry, &c. which are sciences of causation, in order to contrast the contemporaneous things bound together by a natural and indissoluble bond, with the successive things bound together with the same indissoluble connection. The conjunctions of geography (such as the Atlantic divides Europe from America, Africa is the country of the Negroes') are in great part loose and casual, and so are many of the successions of history; but the conjunctions described in natural history are firm and unalterable, and belong to the deep and fundamental collocations of creation; and in like manner the successions of cause and effect are nature's unalterable successions. The contrast between anatomy and physiology is a limited example of the same distinction: the delineations of anatomy refer to co-existing objects, bound together by nature's links for connecting the properties of kinds; the laws of physiology are laws of Cause and Effect. The diamond is composed of carbon,' is a proposition of fixed natural conjunction; heat liquifies solids,' is a proposition of fixed natural succession or causation. The only remaining kind of propositions are the assertions of Likeness or Resemblance, which are totally distinct from assertions of contiguity either in place or in time; but they have the same natural basis as these -that is, nature, besides presenting contiguities, both loose and fixed, presents a copious store of similarities among the objects that she reveals to our knowledge. These similarities are usually considered to be of all degrees; but, strictly speaking, this is not the case. The idea of unequal similarity arises from the fact already alluded to-that a number of natural objects are often found agreeing in some of their properties, and not in others; and, speaking of the entire objects, we say that they have only an imperfect or partial | ceived in general, that mankind could not be mistaken similarity. The most perfect similarity is what is in any conception made up of them. called Identity-that is, taking the same object at different times, no change having happened to it meanwhile, we call the two appearances identically the same. Next to this is the similarity of different specimens of the same substance or kind. The one science wholly founded on propositions of similarity is mathematics. The procedure of discovering and verifying these different classes of affirmations is different for each; and it belongs to Logic to prescribe methods for them all. It requires one style of investigation and of proof to establish propositions of causation or of fixed succession, and another set of operations to determine the propositions of fixed co-existence; while the propositions of likeness are found in a way differing from either. Each of these methods will be alluded to when we come to speak of Induction. Definitions. For the sake of accurate reasoning, every general attribute whatsoever should be accurately defined. Hence a book of science must be a storehouse of definitions as well as of propositions, although these last alone constitute information or truth. It is common for parties in disputes to make each other define their terms-that is, to describe in some unmistakeable way the attributes intended to be expressed by the general or abstract words made use of. But it requires a high degree of advancement in any science to furnish perfect definitions of all the properties that it is concerned with. The generalisation and the verification of a definition is as much a process of discovery, and stands as much in need of human capacity and labour, as the generalisation and verification of a law. Hence it is only in subjects which have attained a high scientific development that accurate definitions are found. In the abstruse sciences of mind and society, good definitions are not in all cases attained, any more than good propositions. Thus the perfect definitions of will,' hardly be said to be as yet completely attained. As the things which go together by the ordination of nature, or the conjunctions which, when expressed in language, form propositions, are more frequently made up of separate attributes than of complete objects, the importance of definitions as preparatory to propositions must be evident. Thus when we say, 'electrical excitement is always polar, or consists of two opposite excitements,' we state a proposition asserting the conjunction of two very abstract attributes; and the proposition could not be discovered, nor proved, far less affirmed and acted on, until a general idea was formed of electrical excitement, and likewise of polarity, by the process of generalising and defining. The magnet has opposite poles,' is an instance of the same: magnetism does not reside invariably in one concrete substance; it is a highly abstract property, sometimes found in one substance, and sometimes in another. By far the most important distinction in the whole science of Logic, or in what constitutes the essence ofvirtue,'' beauty,' 'poetry,'' genius,' 'civilisation,' can human knowledge, is the distinction between propositions and definitions; or between affirmations and conceptions, verbs and nouns. A definition we have already shown to be the accurate expression and description of some abstract quality of which we have formed a conception, after a comparison of the different objects agreeing in the possession of such a quality. We stated that the final step in the process of abstraction was the making of some accurate description of the property abstracted, whether by words, by diagrams, by models, or by some specimen that contains the quality as little mixed with others as possible. In short, the great end of a definition is to fix by some intellectual machinery the character of an abstract conception, notion, or idea. But we have just found that a proposition couples together two ideas, and cannot possibly contain less. A definition communicates a notion or idea to the mind, it gives us one conception more than we had previously, or communicates a perfect representation where perhaps we had only a vague idea before; but it gives nothing that can be called knowledge, nothing to be affirmed, or denied, or acted on; in respect of these matters, it is only one of the things that may enter into a proposition. Two abstract ideas duly connected may make a proposition; one idea never can. For the purposes of discovery and of the investigation of nature, both definitions and propositions have to be sought; but both must not be sought as if they were the same thing. A definition and a proposition usually agree in this that they are both the results of generalising from a number of instances; but the generalisation of an idea, and the generalisation of a law or a conjunction of ideas, should never be confounded. The imperfect recognition of this vital distinction is a source of much error and perplexity, both in matters of science and in questions of truth and falsehood apart from science. In seeking a definition of an abstract property, we ought to muster the individual objects in which it occurs; compare them together in order to obtain a clear picture of their common property; and finally, invent some description, designation, or representation which will so express and fix it, that other people may be able to conceive the property with the same rigid accuracy as the person who went through the labour of making the comparison. All definitions must refer to something which does not itself require to be defined, or which is plainly and clearly known to all men, and requires only to be named that it may be truly and justly conceived. Thus when the abstract property of roundness, or the circular form, is defined in geometry, reference is made to a central point and a straight line running out from, and revolving round it in the same plane. Now the idea of a point, a straight line, and a plane, although they themselves are formally attempted to be defined in geometry, are examples of things so clearly per RATIOCINATION, OR ARGUMENTATIVE INFERENCE. Having ascertained the import of affirmations or propositions, we come next to consider the nature of proof, or of the process that is gone through when an affirmation is said to be proved. In most cases of proof, one or more affirmations are put forward which are already believed or admitted to be true; and some new affirmation is derived from these, or said to be established as following or flowing from them. John has come to town: I saw him an hour ago;' is an assertion made and proved by the help of another assertion. You will get better by taking rest: I myself got round by that means;' is another example. It is a part of Logic to ascertain the nature of the connection between one proposition and another, that will justify the belief of the one on the faith of the other. It has been shown by logicians, that when one assertion is proved by the help of others, there are always at least two previous assertions necessary to make the proof. These two assertions have been technically called premises, and the one that they prove is called the conclusion. In ordinary cases, one of the premises is a general proposition of any of the five kindsnamely, Existence, Co-Existence, Succession, Causation, or Resemblance; and the other premise is a proposition of resemblance. For example, the planets are round; Neptune is a planet, therefore Neptune is round.' Here the first assertion is a general proposition of coexistence, or an affirmation that certain bodies that circle round the sun have the attribute of roundness; or that the attribute of describing circles round the sun coincides with the attribute of roundness of form. The second assertion is, that Neptune is one of the planets, or is a body circling about the sun; or that he resembles the bodies called planets, or that his peculiarity of movement is like their peculiarity. The conclusion or inference is, that Neptune is a round body. It is obvious that if we have obtained proof, or acquired certainty in respect to the two assertions or premises in this case, there can be no doubt about the third; for when it is shown that Neptune is entitled to be called a planet, that body is included in the sweep of the general proposition that all planets are round. There are, therefore, always two things necessary in a step of argumentative proof: in the first place, a general proposition has to be established; and in the second place, an identification has to be made out between the subject of the general proposition and the subject of the affirmation that is to be proved. This last point is merely the practical application of a general affirmation to a special instance. The other step-the establishment of a general proposition-is the business of a scientific inquiry, and has to be done once for all by the proper machinery. The case we have now given of a step of deductive inference is an example of what is called a syllogism; and it used to be reckoned the chief business of Logic to lay down rules for the correct performance of this deductive inference, or for the shaping of valid syllogisms, the two assertions or premises being supposed to be proved, or to have been previously ascertained to be true.* But it is now considered that the most serious and difficult part of the process of arriving at true conclusions, is the establishment of the general propositions which include them. By what process do we come to be sure that all the planets are round-that all men are mortal-that all matter gravitates-that all chemical combinations take place in fixed proportions? We must not merely provide for the correct application of propositions which have once been proved, we must also provide for the proof of these fundamental propositions themselves. INDUCTION. Induction is the term applied to the process of forming and establishing general propositions, principles, laws, truths, or affirmations-that is, propositions which are applicable not to one case only, but to all cases that have a certain definable peculiarity; as when we say, gold is heavy,' in which case we affirm that all substances having a certain colour and lustre are also of great specific gravity. The first question that occurs to us respecting these general affirmations is-how and when are we entitled to make such very broad assertions? We have no means of ascertaining the laws and coincidences established in nature, except the observation of what the world presents to us. If we see that the qualities of yellowness and a peculiar lustre are combined with heaviness, we are entitled to assert the fact in as many instances as we have verified by examination. In like manner, if we see that water quenches fire, we may assert that it is so in the cases noticed. But there remains the grand difficulty-namely, why are we entitled to say that these coincidences and successions take place not only in the cases where they have been observed, but also in the cases where they have not been observed, and in all cases whatever? For this is implied in every general proposition. This question is answered by the fact, that nature is uniform. There is a certain class of coincidences or co-existences which we have already alluded to as tight co-existences, which are everlasting and unvaried, and need only one observation to tell how they will be in every variety of times and places; and there is a certain class of successions called Successions of Cause and Effect, that are of the like unchanging kind, being the same yesterday, to-day, and for ever. Hence, in these cases, one observation is as good as a million; we are entitled to express or affirm infinitely more than we actually find. It is from nature's repeating herself in endless ways that human labour is shortened to such an extraordinary degree, that a few years of the short life of man suffices for obtaining a very extensive mastery of the vast and varied appearances of the world. We have asserted that nature is uniform in her coincidences of the properties of kinds, and in her successions of cause and effect. But, it may be asked, what proof have we to offer in support of this assertion, which is of such magnitude and importance as to be the foundation of our proof of all other assertions, and the means of enabling us to convert a single case of observation into an infinite belief? There is no other proof to be offered for the uniformity of nature than the unbroken experience of the human race. Every age has found it so; and in the more recent times of human history, it has been tested in every possible variety of ways, and no valid exception has ever been recorded. There was a time when men might entertain doubts on the matter, or when the confirmation was but limited, and the apparent exceptions irreconcileable with the doctrine. But this time has now gone by, and the principle has come to be established upon a basis that seems impossible to be shaken; and all the future generations of men will rest upon it with unswerving confidence. Some have derived the proof of the principle from an instinct in human nature, which leads us to expect this uniformity; but this is to rest upon a most perilous assumption-namely, that the native instincts of men can correctly anticipate the laws of the outer world-an assumption indeed that is far from true. The very same instinct which leads us to expect uniformity in nature, also prompts us to believe that all other men are like ourselves; that our experience is the experience of the whole world; and that what is at variance with it must be false. It is the instinct that urges the inhabitants of a tropical climate to denounce as liars and impostors the people who assert that water can become solid like glass. Such an instinct is utterly untrustworthy, until corrected by the observation of the actual world; but it is extremely valuable as an impulse advancing in the same general direction with the results of our experience. The laws of causation, or the successions of events established by nature, and invariably adhered to, make the first and foremost subject of inductive investigation. In this case the great problem given for mankind to solve is to find the effects of all causes, and the causes of all effects. The general maxim of the uniformity of nature does not always apply to the outward appearances of things. A south wind brings rain one day and drought another; and in many other cases the law of strict succession fails to hold good. The reason of this is discovered by a very little examination: the superficial phenomena of the world, the things that prominently arrest our attention, are not single trains of causation, but mixtures of many different trains; and the law of uniformity does not necessarily hold good, except in the simple and indivisible sequences of phenomena and events. No doubt if a certain number of causes acting together produce a certain amount of effects, the very same combination will always produce like effects; but it is not easy to make sure that two given combinations are really the same. In order to do so, we must first become acquainted with the simple causes one by one. Induction, therefore, in such a state of things, is essentially a process of analysis, or the separation of the complex threads of causation, with the view to determine the simple threads; and when we have once possessed ourselves of all these, we will be prepared to calculate the effects of any combinations of them. Nature rarely presents us with a cause and its effect standing alone. The usual case is to have a multitude of effects flowing from a multitude of causes. It requires, therefore, the whole analytic force of the mind to be devoted to their reduction to single couples of cause and effect. This frequently involves a very difficult operation of the abstractive faculty. The great object of inductive inquiry being to ascertain among a multitude of connected things, which of them stand to each other in the relation of cause and effect, we have now to consider the methods of observa- | bodies of their heat, nor exhibit it by itself and apart tion and experiment suited to this determination. By from all other things; and hence the methods above experiment' is meant the process of altering the alluded to would entirely fail in determining what arrangements presented by nature, and shaping new things are connected with it as cause and effect. To arrangements of our own to assist us in ascertaining meet this difficulty, we have recourse to a method the simple sequences of cause and effect. Thus if na- named by Mr Mill the Method of Concomitant Variature presented to our observation a confused and com- tions—that is, in such a case as heat, we observe what plicated train, and if we contrive to remove a great effects increase as it increases, and diminish as it dimany of the circumstances, so as to reduce the train to minishes. The method is expressed in general terms a more simple sequence, we are said to proceed by as follows:-Whatever phenomenon varies in any manexperiment. If we find or observe a certain locality is ner whenever another phenomenon varies in some partiexceedingly favourable to health; and if, in our wish to cular manner, is either a cause or an effect of that pheascertain which of all the peculiarities of the place is nomenon, or is connected with it through some fact the cause of the wholesomeness, we endeavour to put of causation. We very frequently proceed upon this ourselves into situations where each circumstance is method of observing the effects of the increased or excluded in turn, we are said to proceed experimen- diminished quantity of things, in order to see what tally. Mr Mill has laid down the different ways of effects they have a tendency to produce, judging rightly arriving at cause and effect by this experimental pro- that if one event be the cause of another, the two will cedure, under the title of the Four Experimental Me- rise and fall together. thods; which he names the Methods of Agreement, of Difference, of Residues, and of Concomitant Variations. The simplest and most obvious modes of singling out from the circumstances which precede or follow a phenomenon those with which it is really connected as an invariable law, are two in number: one is, by comparing together different instances in which the phenomenon occurs; the other is, by comparing instances in which the phenomenon does occur with instances in other respects similar, in which it does not. These two methods may respectively be denominated the Method of Agreement, and the Method of Difference. In illustrating these methods, it will be necessary to bear in mind the twofold character of inquiries into the laws of phenomena; which may be either inquiries into the cause of a given effect, or into the effects and properties of a given cause. For example, let the antecedent be the contact of an alkaline substance and an oil. This combination being tried under several varieties of circumstance resembling each other in nothing else, the results agree in the production of a greasy and detersive or saponaceous substance. It is therefore concluded that the combination of an oil and an alkali causes the production of soap.' Mr Mill states the method of Agreement in a formal canon as follows:-If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon. By the method of difference, is meant the process of comparing two sets of circumstances-one containing the effect, and the other not; and where between the two we can see no difference except in one other particular. When a man is shot through the heart, it is by this method we know that it was the gunshot that killed him; for he was in the fulness of life immediately before, all circumstances being the same, except the wound.' This method is expressed as follows:-If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance except one in common, that one occurring only in the former, the circumstance in which alone the two instances differ is the effect, or cause, or a necessary part of the cause, of the phenomenon. The method of residues will be seen to be a carrying out of the same attempt to break up complicated trains, and to fasten down the invariability of sequence upon the true particulars where cause and effect operate. It is stated thus:-Subduct from any phenomenon such part as is known by previous induction to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents. There remains a class of laws which it is impracticable to ascertain by any of the three methods which I have attempted to characterise namely, the laws of those permanent causes, or indestructible natural agents, which it is impossible either to exclude or to isolate, which we can neither hinder from being present, nor contrive that they shall be present alone.' Heat is an example of this kind of agents; we can neither divest | There are two kinds of complications that are beyond the reach of any of these four methods, and require a distinct treatment. The one is termed the case of the Plurality of Causes, the other the Intermixture of Effects. By a plurality of causes is meant, that it sometimes happens that an effect may arise equally from several causes, creating, as it were, an ambiguity of causation. Thus a motion may arise from any one of a great number of forces; happiness or misery is produced by innumerable agencies. In such cases, the methods above stated are somewhat nonplussed, inasmuch as it may be possible to exclude one cause and yet keep in another. A still greater difficulty is presented by the Intermixture of Effects-that is, when an effect is not single, but complex. Thus the course of a projectile is not a single, but a mixed effect, or two different effects combined into one different from either. The discovery of the cause or causes, under such circumstances, cannot be effected by the Experimental Methods. But this leads us to the consideration of a method different from any of these, which has a vast range of efficacy in scientific research, and becomes more and more powerful as the sciences advance, or as discovery is extended. It is called the Deductive Method. The Experimental Methods suppose that we take up a subject that is as yet fresh and unexplored, or where no great general principles have been attained. They are the methods adapted to the commencement of inquiry. But when one or two comprehensive laws have been arrived at, a great deal is to be discovered by following out the application of these laws wherever they are found to operate. Thus when the law of the perseverance of moving bodies was once discovered, it was made use of to explain many motions that would otherwise have remained inexplicable: such as the rotation of the earth, and the tendency of the planets to maintain their distance from the sun. In like manner, the discovery of the general law of reaction enabled Newton to determine the cause, and even for the first time to ascertain the existence, of the fluctuation of the sun in the centre of the planetary system. By the Deductive Method alone are we able to trace the operation of that class of causes which, by intermixture, are wholly neutralised, and produce no apparent consequences whatever-as in what are called the laws of equilibrium or counterpoise. There are three different steps in the complete working out of the Deductive Method. The first is Induction, or the determination of the general law by the Experimental Methods. The second is the carrying out of the law to the explanation of all cases where it seems to apply, and especially the tracing out of the action that would result from two or more principles acting in combination. Thus the Deductive Method applied to trace out the cause of the curved motion of a projectile, would consist in combining together the law of perseverance with the law of accelerated motion under à constantly-acting force, and in determining what would be the path that a body would describe under the two actions. The third step, which is Veri |