This country has been long and happily distinguished for the great attention which Ise been paid to application; but it is a mistake to suppose, as some do, that our supremacy in practical matters has been co-ordinate with, still less owing to, neglect of theory. It would be envy to show that though the comparative neglect of theory alone, as a pursuit, added to its diligent cultivation on the Continent, under tho encouragement of government, had given to foreign countries a decided preponderauce, now very much on the wane, of theoretical inquirers and writers, yet that there has been no country in Europe in which a Competent knowledge of the mathematics and their Lions has been spread over so large a mass, or raised to so high an average. At any time since the beginning of the 11th century the total amount of theory in Britain has been larger than in any other European country, on account of the numbers who have possessed a useful amount of knowledge : the diffusion of education in Germany may have altered our position, but of this we are not sure. For our selves we are perfectly satisfied, however little those moat concerned may know it, that this greater diffusion of theory has been the original moving cause of the practical excellence to which we have alluded. If those who have become known foe splendid achievements in the former are few, the same may also be said of the Latter ; but a country owes its excellence in either department, not to one or two of the highest, but to the mass of those who have competent knowledge, producing good habits of thought and action. It is a new thing to hear ono branch set against the other, and would make our writers of a century back think that posterity had lost its senses. The only addition wauted has been some means of systematically nurturing the growth of theory, so that, well as we have done with what we have, we may do better with more. The efforts which are making on every aide to extend effucation will, it may be hoped, do what is wanted in this particular ; they will at least have the effect of making it clear that, whatever the force of genius may do for an isolated exception, the mass of mankind must place their best hope of progress in the union of theory and practice.
There is also a mode of viewing what we may call the action of theory, which is absolutely necessary to a true conception of the value of their labours who employ their time in its advancement. Watch the arguments of a person who calls himself, distinctively, a practical man, and it will be always found that a well-established theory, fifty years old, is practical knowledge, so called. To this there cannot be the slightest objection in the non-distinctivo Reuse : a well-established theory, which has been shown to bo sufficient, is highly practical, as opposed to ono of which the investigation is more recent, and the complete nem not so well ascertained. But when the question is theory, as theory, against practice, as practice, the advocates of the latter frequently find it convenient to assume, for their own share of the matters in contest, all the best theories plus the most recent practical knowledge, leaving to the other side the onus of supporting theory upon the most imperfect part of the mass of doctrines which it contains, being that part which is not yet off the anvil Suppose a merchaut going into the bail court to prove his being worth a certain sum : be is asked whether his business, all debts and risks allowed for, would produce that sum : he replies, that his ventures must be beyond record unsuccessful, if it would not be so, over and over again. "So then," he is further
questioned, " you cannot positively swear that your business will make you worth the sum in question." " I cannot," he replies, "positively swear any such thing; but I have enough not employed in business, in land and mortgages, and in the funds, to pay twenty shillings in the pound five times over upon every risk which I am liable to." What would be thought of counsel who should retort," That is nothing to us; you aro described as a merchant, and your solvency must be tried by the state of that part of your property which is now undergoing the fluctuations of trade I" Such is and always must bo tho state of theory; the amount which is actually realised is enormously greater than the floating balance which is being worked out. Those who are engaged in producing fixed capital from the latter, have a right to the credit which arises from the interest of the former: their labours for the time being are not to produce their return at tho instant.
We have, in compliance with common notions, not adverted to the consequences of theory upon the mind and thoughts of men, but have treated it as if its solo object were to advance the mechanical arts and better the physical condition of society. But this is under protest that even if it could not be proved that rational investigation of nature had added one single atom to the physical comfort of life, there would remain such an enormous ,mass of social ameliorations which can be traced to that source as would outweigh even the triumphs of steam. This is often forgotten by the highest men of the highest and most valuable practice, meaning the boat application of the truest theory. They confound practice with application to matter as opposed to mind. On this point wo quote aomothing we have printed else where. " There is a strong impression hm tho world of physical inquiry that a mathematician is almost bound, whatever his pursuit may be, to make Ilia science the means of investigating or registering sonic facts connected with the material world. A teacher of mathematics for example, whose business it is to study the mind and its discipline, that he may make his teaching permanently useful to those who will not, in nineteen cams out of twenty, ever have any need to apply it professionally, would be thought quite in the right way if he should take to investigating the force of steam, or the strength of beams, or the orbits of binary stars : they would call him a practical man. I should give him quite another name if he took up steam or star for anything beyond relaxation, supposing his taste to turn that way. The disposition to hold material application to be always practical is one of the consequences of the want of psychological thought, and will vanish before sound logical training, with other myopisras." Cambr. Phil. Trans.,' vol. x. p. 1.) In conclusion, the word practice as opposed to theory takes an advantage from its meaning as opposed to profession. There are many persons who have so hazy a view of the two meanings as to imagine that the two antitheses are one and the same.