THEOKKM. 



THEORY, THEORY AND PRACTI' 



TICT. 



206 



old English lute very much enlarged, and used chiefly, if not only, as 

 an accompaniment to the voice. 



THEOREM (8eufTiiia) means properly a thing to be looked at or 

 seen ; and is used in mathematics to signify any proposition which 

 states its conclusion or makes any affirmation or negation ; as distin- 

 guished from a PROBLEM, which demands or requires a conclusion to 

 be arrived at, without so much as stating whether that conclusion is 

 even possible. Thus : " Required to draw a tangent to a circle at a 

 given point," is a problem ; but " If a straight line be drawn at right 

 angles to a diameter from its extremity, that straight line is a tangent 

 to the circle," is a theorem. The problem asks discovery both of 

 method and demonstration ; the theorem asks demonstration only. 



This distinction, as noticed in detail in PROBLEM, was not made by 

 the older Greek geometers. Theodosius is the first, so far as we know, 

 who uses the word theorem, but none of his propositions are problems. 

 Pappus is the first who uses both terms in the distinctive sense. 



THEORY, THEORY AND PRACTICE. If articles upon the 

 mere meaning of words be admissible, it is the consequence of the 

 manner in which the words are used. Of all the fallacies which infest 

 society, the most common is that of applying to one sense of a word 

 ideas or associations derived from another ; and of all the words in 

 use, there are few which are more often subjected to such process than 

 those which stand at the head of this article. 



By theory, properly speaking, is meant the mode of making seen and 

 known the dependence of truths upon one another : a theory is a con- 

 nected body of such truths belonging to one or more common 

 principles. The use of this word has enlarged with the boundaries of 

 the sciences. For example, before the discovery of universal gravita- 

 tion, all that was known of any one planet was the empirical formulas 

 for one or two of its inequalities. This constituted the theory of the 

 planet (then so called) : thus the theory of the moon, so far as peculiar, 

 consisted in the statement of the laws of the inequalities called the 

 equation of the centre, the evection, &c. ' In our day the point of 

 view is changed ; it is no longer the mere exhibition of these ine- 

 qualities which constitutes the theory, but the deduction of them, as 

 necessary consequences, from the principle of gravitation. The 

 theoretical astronomer now starts from this principle, and, taking only 

 one position and velocity for his numerical data, finds out every 

 inequality of the planetary motions, those which were previously known 

 from observation and more, and shows how to form them into tables. 

 The practical astronomer makes these tables, computes places from 

 them for the current year, compares these places with the results of 

 observation, and returning the comparison into the hands of the 

 theorist, enables him, if need be, to correct the original numerical 

 data to which he applied his methods, or to detect new inequalities. 

 The process is now deductive ; but before the time of Newton it was 

 the other way. The observer had the first task ; the inequalities wore 

 to be collected from comparison of observations, and their laws, reduced 

 to the simplest form, were the data for future tables. 



Again, before the introduction of the undulatory hypothesis, the 

 theory of light consisted in the exhibition of the laws of reflexion and 

 refraction, with a certain extent of explanation from the emanatory 

 hypothesis of Newton. Since that time the theory of light has 

 become, though at a distance, a resemblance of the theory of gravita- 

 tion in its character : prediction has commenced, that is to nay, the 

 phenomena which would appear under certain new circumstances have 

 been announced before any experiments were made to discover them ; 

 and correctly announced. This is the end to which theory ought to be 

 constantly tending ; namely, the discovery of laws of action in so 

 complete a manner that the necessary consequences of those laws 

 never fail to make their appearance, so that everything which is seen is 

 found to be a consequence of the laws when examined, and every con- 

 sequence of the laws is seen in phenomena when looked for. Whatever 

 fulfil* these conditions may be called a perfect theory, or a perfect 

 mathematical theory. 



The next step in the chain of discovery is one which may in most 

 cases be incapable of attainment. For example, nothing is more 

 certain than that the assumption of every particle of matter attracting 

 every other particle, according to the Newtonian law, leads to the 

 complete deduction of the celestial motions, and gives the complete 

 power of prediction just alluded to. But whether this ATTRACTION 

 does actually take place, or whether any intermediate agent is 

 employed, though it matters nothing at prttent to the mathematical 

 theory, is the next object of inquiry. Could this point be ascertained, 

 it is more than probable that the knowledge of the constitution oi 

 matter to which it would lead, would open hundreds of important 

 consequences even in the application of science to the arts. [CAUSE ; 

 Hvniiin 



Before coming to the distinction between theory and practice, we 

 must observe that theories may be divided into two classes, the more 

 perfect and the leas perfect. We cannot say that any theory, is 

 absolutely perfect ; but there are some of which the defects ar, 

 perceptible, and others in which the contrary is the case. for< 

 the theory of the statics and dynamics of riyid bodies is t 

 perfect ; but that of bodies composed of particles acted on by m< 

 forces is in its infancy. We know a great deal more of 1 1 

 of the planetary worlds with each other than we do of the particles 

 which, when connected together, form a bar of iron or of oak. Wt 



mow that the bar is not perfectly rigid ; that it bends and breaks : 

 and the degree of bending which a given force will cause, and the 

 amount of pressure necessary to produce fracture, must be sought for 

 in experiments, from which, imperfect as they are, the laws which 

 would follow from a good theory, if we had one, are to be deduced. 

 In such a subject our theory, instead of being an all-sufficient guide, is 

 only a help, the services of which are to be used to an extent which 

 discrimination derived from practice and experience must point out. 

 Many a person who thinks he is proceeding upon experience only is 

 really making use of a mixture in which there is theory, though his 

 own knowledge of the process he uses, and of its history, may not be 

 sufficient to inform him of it. 



A person who uses an imperfect theory with the confidence due 

 only to a perfect one will naturally fall into abundance of mistakes ; 

 ais predictions will be crossed by disturbing circumstances of which 

 liis theory is not able to take account, and his credit will be lowered by 

 the failure. And inasmuch as more theories are imperfect than are 

 perfect, and of those who attend to anything, those who acquire very 

 sound habits of judging are few compared with those who do not get 

 eo far, it must have happened, as it has happened, that a great quantity 

 of mistake has been made by those who do not understand the true use 

 of an imperfect theory. Hence much discredit has been brought upon 

 theory in general ; and the schism of theoretical and practical men has 

 arisen. Fortunately there are many of the former who attend 

 properly to the improvement of imperfect theory by practice; and 

 many calling themselves practical who seize with avidity all that 

 theory can do for them, and who know that step by step theory has 

 been making her way with giant strides into the territory of practice 

 for the last century and a half. 



By practice, as distinguished from theory, is meant (not by us, but 

 by those who contend for the distinction) the application of that 

 knowledge which comes from .experience only, and is not sufficiently 

 connected with any general principles to be entitled to the name of a 

 theory. The distinction of labourers in the field of science or art into 

 theoretical and practical is not strictly a just one, for there is no 

 theorist whose knowledge is all theory, and there is uo practical man 

 whose skill is all derived from experience. But the terms will do well 

 enough to distinguish two classes whose peculiarities it might be 

 difficult to define exactly. 



The practical man, when he is really nothing . more, is one who can 

 just do what he has been taught to do, and who has acquired skill and 

 judgment in a small range of occupations. All who pride themselves 

 upon the title would be displeased at this definition, and we readily 

 admit that many of them are entitled to a higher character ; but only 

 because the title by which they delight to describe themselves is a 

 wrong one. They desire, under the name of a workman, to claim the 

 qualities of a master. The term theoretical serves, as one of contempt, 

 to designate any thing of which they disapprove ; and as there never is 

 any fallacy which is not carried to a fool's-cap extent by the lower 

 order of users, it would not be difficult to make a most amusing selec- 

 tion of instances of the manner in which the distinction has been 

 worked by the large number who are at the bottom of the class, and in 

 whose heads it runs that their own ignorance is practical and others' 

 i-niacledge theoretical. Our attention was called to this class in early 

 youth by hearing an educated person state that he was a " practical 

 man," by way of declining a question which involved knowledge of 

 fractioul ; it was then extracted from him, to the delight of bystanders, 

 that all above inteyert is theory. And from that time whenever we 

 wish, in a delicate way, to find out how much a person knows of his 

 subject, we manage to ascertain to what extent he considers it practi- 

 cal/!/ uicful. And we have thus discovered that what happens to 

 ourselves happens to others, namely, that all knowledge which is 

 possessed is practically useful, and all which it nut possessed is not. 

 It is very often noticed that men are unduly given to puff and vaunt 

 their own professions ; whereby they provoke the retort of " nothing 

 like leather," being the words the currier used when he was asked 

 what the city walls should be made of. The sarcasm is often unjust. 

 The exaggerator is frequently giving a true account of the effects of 

 Unouledye : his mistake lies only in restricting those effects to the 

 knowledge of things in his own line, the only knowledge he has ever 

 sufficiently cultivated. 



We say nothing about those to whom theory is but a name under 

 which they may safely sneer at knowledge, except this : two small 

 commercial companies sometimes prolong their existence by amalga- 

 mating, as they call it ; would it not be desirable that they should join 

 those who use the word itijiilrliiii instead of theory? We givo a passing 

 word to the many who blind themselves to the difference between truth 

 and falsehood by disguising the latter under the name of practice. It 

 chanced to us long ago to advise a very worthy man of busiuess,now dead, 

 up in the terms of an advertisement. On one of our alterations he re- 

 marked " Don't you think that, practically, it would read better ruy 

 way .' " " It would," Haiti we, " the objection is, that it would not be 

 true." Our friend stared ax if a light had broken in upon him, and 

 said, " Well, Sir, there it something in that." We remember seeing a 

 theorist, as he was called, endeavour to make the managers of a certain 

 undertaking comprehend that their profits could not exceed the excess 

 of the gross returns over the outlay, after they had been trying to 

 cheat the equation by inventing names for what they would have liked 



