expressed by a mathematical formula, the precise point at which the proceeds of a tax upon tobacco would attain their maximum could be determined beforehand; and an immense reform, without risk of failure, could at once be effected in our fiscal system. But as we have no means of ascertaining with precision the disposition of mankind, or of any portion of them, in this respect, we are obliged to have recourse to a series of tentative experiments, and must content ourselves with a rough approximation to the required maximum, obtained perhaps at the cost of considerable loss to the revenue and of inconvenience to the public.

I have thought it well to call attention to this source of imperfection in our economic reasonings, as it appears to me desirable that we should know the weakness as well as the strength of our position as political economists, that we may not, by affecting an accuracy that is unattainable, bring suspicion and discredit on the undoubted truths of the science.

The celebrated formula of Malthus, as you are aware, asserted that population tends to increase in a geometrical, subsistence in an arithmetical ratio. In advancing this statement, Malthus really intended nothing more, as every candid and intelligent reader of his work will at once perceive, than to give definiteness to our conceptions of an important principle; the conclusions which he based upon the principle thus expressed not in the least depending for their truth on the mathematical accuracy of the formula. His opponents, however, were not in the humour for

making this allowance. The doctrine had been stated in mathematical form, and it must, therefore, be maintained in all its strictness, or the speculations of Malthus must be forthwith pronounced a delusion, and his conclusions the phantasms of a diseased imagination.

§ 2. Such, then, being the character of an economic law, analogous in all respects to those laws of physical nature which are obtained by a similar process of deductive reasoning, with the important exception that it does not admit of quantitative statement, we are now in a position to understand how far economic laws can be made available in the explanation of economic phenomena,

The explanation of a phenomenon, or the solution of a problem (the expressions being equivalent) consists in a reference of the fact to be solved or explained to some known or acknowledged principles. The velocity of a planet through space, e.g., is said to be explained when this velocity is shown to be the result of known dynamical principles. The physical phenomenon of dew is said to be explained when it is shown that the known laws of the radiation and conduction of heat, together with the laws of the condensation of watery vapour, necessarily under certain external conditions lead to the occurrence of dew; these conditions being the same as those under which, in fact, dew is observed to appear. If we admit the existence of the laws, we see that the phenomenon must be present when, in fact, it is present. In the same way the

economic phenomenon of rent is said to be explained when it is shown to be the necessary consequence of the play of human interests trafficking in an article having the peculiar physical properties which are found to reside in land. In this case, also, if we admit that human beings in their dealings with land act with a view to their own interests, and further, that the best soils in point of fertility and situation are not unlimited in supply, and that the yield to be obtained from a limited area is also not unlimited, but diminishes in proportion to the outlay, as the quantity raised is increased, we see or by reasoning on these facts we may see-that the phenomenon of rent must present itself in the progress of society, and that it will rise and fall from those causes which we find in fact to affect it. So far, the solution of an economic problem is strictly analogous to that of a physical problem; in each case the process consists in tracing back the fact to be explained to its source in the ultimate principles of the science; if it be a physical fact, to the ultimate laws of physical nature; if an economic fact, to the ultimate axioms of Political Economy-that is to say, to the mental and physical principles from which its doctrines are derived. Until this connection is clearly established, no physical or economic phenomenon can be said to be explained.

The solution of a problem may be regarded as perfect when the principles to which it is referred are shown to exist, and to lead by necessary consequence to the precise fact which constitutes the problem to

be solved.1 Supposing our reasoning to be correct, it is evident that imperfection may yet arise either from the indefiniteness of our knowledge of the laws which operate in producing the phenomenon, or from ignorance of the precise circumstances under which they come into operation. With the exception, perhaps, of astronomy, there is no science that has attained absolute perfection in both these respects. Most of the advanced physical sciences, however, satisfy the first condition, though they generally fail of complete accuracy in the latter. To revert to a former example-the formation of dew-the laws of the radiation and conduction of heat and of the condensation of watery vapour on which that phenomenon depends may be accurately ascertained and expressed in mathematical formulæ ; but the circumstances under which the phenomenon appears-the state of the atmosphere, and the condition of the various bodies on which the deposition of dew takes place during any given night-cannot be accurately ascertained. Now, while this is so, the solution of the problem is not complete; since, although we may perceive from our knowledge of the laws of heat and of aqueous vapour that dew under the actual circumstances must

1 "In such a case," says Sir John Herschel," when we reason upward till we reach an ultimate fact, we regard a phenomenon as fully explained; as we consider the branch of a tree to terminate when traced to its insertion in the trunk, or a twig to its junction in the branch; or, rather, as a rivulet retains its importance and its name till lost in some larger tributary, or in the main river which delivers it to the ocean. This, however, always supposes that, on a reconsideration of the case, we see clearly how the admission of such a fact, with all its attendant laws, will perfectly account for every particular.”—Natural Philosophy, p. 163.

appear, yet, from want of precision in our knowledge as to what the actual circumstances are, we cannot tell the precise quantity that ought, in obedience to these laws, to be deposited; and, therefore, cannot be certain that our solution may not be more or less than adequate; nor whether there may not be other causes affecting the result which we have omitted to notice.

In Political Economy we have seen that the laws which it announces do not admit of precise quantitative statement: we have now further to note that the remaining portion of the data necessary to the solution of a given problem, namely, the circumstances under which they come into operation, though generally susceptible of measurement could they be ascertained, yet in practice can seldom be ascertained so completely as to admit of being stated numerically.

Take, e.g., an economic phenomenon which has excited much speculation lately amongst economists and commercial men-the export of silver from Europe to the East, which has been proceeding on an extraordinary scale during the last year (1856). Many causes may be assigned, which, taken together, will go a certain way in accounting for this fact. There has been, in the first place, a general rise of wages in the United Kingdom-the consequence partly of our general commercial prosperity, partly of the gold discoveries-leading to an increased money demand here for the productions of eastern countries. There has been, in the next place, a failure in the silk crop on the Continent, obliging Europeans to obtain a large portion of their silk from India and