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spondence between its known energy and the amount of the observed effect. All Nature is full of such cases. That selected by M. Quetelet as an example is one of much agricultural and botanical interest, viz. the inquiry into those peculiarities of season on which its character as a forward or a backward one depends. The rudest observation suggests the prevalent temperuture of the season as the element on which the difference in question mainly turns, though it may justly be inquired whether other meteorological elements, especially moisture, may not come in for their share in producing it; and should these prove to be but little influential, according to what laws, as regards the distribution of temperature over the period of vegetable activity, the arrival of a plant at any phase of its annual life is accelerated or retarded. This inquiry is not new. Reaumur, and after him Boussingault and the Abbé Cotte, taking the simplest possible view of the subject, maintained that the arrival of a plant at a definite stage of its growth is solely dependent on the total amount of temperature to which it has been subjected from the first movement of the sap in spring*, without regard to its distribution over the intervening time, or the extent of its variations. Such a law is unlikely in itself, and the experience of every one would lead him to doubt its universal applicability. It has, however, been adopted by M. Gasparin in a work (* Cours d'Agriculture') which has commanded considerable attention, an account of which, and of the arguments which may be adduced to show the inadequacy of this hypothesis, will be found in a paper by the Earl of Lovelace in the Journal of the Royal Agricultural Society, vol. ix. part 2. M. Quetelet, who has independently arrived at a similar conclusion, proposes to substitute for the total temperature (estimated by the sum of the daily mean temperatures) the sum of the squares of such daily means, reckoned from the freezing point; assigning as a reason, that 'the force exercised by the tempera'ture is of the same nature as actual force. It is by the sum
of the squares of the degrees, not by the simple sum of the .
degrees, that we must appreciate its action. Such an analogy is not calculated to produce much conviction ; but there is good reason to presume that vegetation is accelerated in a higher ratio than that of the simple temperature, from the consideration, not only of the continual increase of dilatability by equal increments of heat which aqueous liquids undergo, but also from their much greater fluidity at high than at low temperatures, the one cause rendering circulation more free, the
• Cotte assumed arbitrarily the 1st of April.
Flowering of Plants.
other producing a more rapid dilatation of the cellular tissue by the direct action of warmth. Pending the discovery of the true law of connexion between the phenomena (which cannot be that of the squares, if only for the simple reason that it would give equal efficacy to temperatures below and above the freezing point), M. Quetelet’s as a provisional one has this advantage, that it affords scope for the influence of differences in the distribution of temperature, which that of Reaumur does not, and gives a better account of the rapid burst of vegetation which a few genial days produce in spring.
M. Quetelet has selected for observation the epoch of Aowering, as more definitely observable than any other phase of vegetation; and as there are few things more agreeable to a country resident than watching and noting the commencement of flowering in the early spring flowers which adorn our gardens, fields, and hedgerows, this branch of botanical inquiry promises to become quite as popular as it is interesting in itself.
We can only afford room for his result as regards the common lilac. That beautiful ornament of our walks and shrubberies blossoms so soon as the sum of the squares of the mean daily temperatures (as indicated by the centigrade thermometer) amounts to 4264°, so that the mean time of its flowering at any given station may be at once determined from the meteorological records of its climate. At Brussels this mean date is the 27th or 28th of April. In other localities it occurs earlier or later by about three or four days for every degree of latitude south or north of Brussels, and about five or even six days later for every hundred yards of elevation above the level of that city, which is itself sixty-five yards above the sea :
• To each plant' (thus he states his general conclusion) is attached a constant, the square of a certain number of degrees of warmth necessary for the occurrence of “inflorescence." Whether a plant is found in such and such a latitude, at such and such a height, in the open air or in a greenhouse, it is the temperature' (so measured) that must be considered. Thus are explained all the anomalies that present themselves in this kind of research. Geographical causes have no influence but by the variations they cause in temperature.' (Transl. p. 172.)
Among those branches of knowledge which are most effectually advanced by the consideration of mean or average results concluded from great masses of registered facts, to the exclusion of individual instances, statistics hold beyond all question the most important rank as regards the social well-being of man. To this subject M. Quetelet devotes the fourth and last division of his work'; not, indeed, to the delivery of statistical tables or results, nor to the actual discussion of any particular class of documents, but to the points which it so much imports to have generally well understood of the methods and principles which ought to prevail in the collection and subsequent employment of such documents.
Whether statistics be an art or a science (a question to which he devotes a preliminary letter) or a scientific art, we concern ourselves little. Define it as we may, it is the basis of social and political dynamics, and affords the only secure ground on which the truth or falsehood of the theories and hypothesis of that complicated science can be brought to the test. It is not unadvisedly that we use the term Dynamics as applied to the mechanism and movements of the social body; nor is it by any loose metaphor or strained analogy that much of the language of mechanical philosophy finds a parallel meaning in the discussion of such subjects. Both involve the consideration of momentary changes proportional to acting powers,—of corresponding momentary displacements of the incidence of power, of impulse given and propagated onward, - of resistance overcome, - and of mutual reaction. Both involve the consideration of time as an essential element or independent variable; not simply delaying the final attainment of a state of equilibrium and repose, - the final adjustment of interests and relations, but, from instant to instant, pending the process of mutual accommodation, altering those relations, and, in effect, rendering any such final state unattainable. One great source of error and mistake in political economy consists in persisting to regard its problems as statical rather than dynamical in their character; confounding the propagation of impulse with a step towards equilibrium, - a state unattainable where the interests of masses of mankind are concerned. So long, indeed, as society is little developed, its movements fettered, its commercial activity sluggish, and all things go on leisurely, the distinction is one of small importance; a state of acquiescence, nearly approaching to that of equilibrium and final adjustment, being taken up from instant to instant, and following at a little distance, yet pari passu, the slow changes of the acting causes. It is otherwise under the increased facilities, excessive mobility, and excited energy which prevail under the high temperature and pressure of modern civilisation. Friction (which has an equally real existence in both mechanisms) is diminished, the intensity of the active forces increased, the scale on which movements are carried on enlarged, - a state of things which finds its expression in the over-speculations,' 'gluts,' panics,' reactions,' et hoc genus omne of mudern commerce and social change. The
same must be the case whenever efficient causes, of whatever nature, act through a train of varying circumstances, and result in effects of which it can only be securely asserted that their momentary and infinitesimal changes stand under given circumstances in given relations. It may be true, for example, that capital tends to a common level of profit in the choice among its possible employments; but endless fallacies would be involved in any reasoning which should proceed on the assumption that it finds that level. Demand may tend to increase supply by stimulating exertion, but a supply proportionate to the demand, and steadily following its variations, is what no sound political economist will ever expect to see. The Rule of Three has ceased to be the sheet anchor of the political arithmetician, nor is a problem resolved by making arbitrary and purely gratuitous assumptions to facilitate its reduction under the domain of that time-honoured canon.
Number, weight, and measure are the foundations of all exact science; neither can any branch of human knowledge be held advanced beyond its infancy which does not, in some way or other, fråme its theories or correct its practice by reference to these elements. What astronomical records or meteorological registers are to a rational explanation of the movements of the planets or of the atmosphere, statistical returns are to social and political philosophy. They assign, at determinate intervals, the numerical values of the variables which form the subject matter of its reasonings, or at least of such ‘functions' of them as are accessible to direct observation; which it is the business of sound theory so to analyse or to combine as to educe from them those deeper-seated elements which enter into the expression of general laws. We are far enough at present from the actual attainment of any such knowledge, but there are several encouraging circumstances which forbid us to despair of attaining it.
The first of these is the exceeding regularity which is found to prevail in the annual march of statistical returns and the constancy of the ratios they indicate where great masses of population are concerned, where leading features of human nature are the obviously influential elements on which the observed results depend, and where temporary or periodical causes of disturbance (evidently such) do not visibly interfere. As instances might be cited the relative proportion in the births of the sexes already spoken of; the ratio of illegitimate to legitimate births in the same country and the same section of the population ; nay, even the number of the still-born (with a distinct per-centage for town and country), which M. Quetelet has ascertained to be so uniform in Belgium that, on a total number of nearly 6000 annual cases, the yearly deviation from the mean falls short of 140; the ratio of marriages to the whole population, of second marriages to the whole number of annual marriages, and, still more minutely, of widowers with widows, widows with bachelors, and widowers with spinsters; the relative ages of parties intermarrying; and innumerable other particulars; all which, free as air in individual cases, seem to be regulated with a precision, where masses are concerned, clearly proving the existence of relations among the acting causes so determinate, that there is evidently nothing but the intricacy of their mode of action to prevent their being subjected to exact calculation, and tested by appeal to fact. Taken in the mass, and in reference both to the physical and moral laws of his existence, the boasted freedom of man disappears; and hardly an action of his life can be named which usages, conventions, and the stern necessities of his being, do not appear to enjoin on him as inevitable, rather than to leave to the free determination of his choice.
Another encouraging feature in the aspect of statistical documents, which shows them, when properly collected, to be trustworthy for the purposes to which we desire to apply them, and holds out a rational hope of their available application,- is their evident sensitiveness to the influence of real and unmistakable causes, which we are sure, à priori, ought to influence them. Thus we see the uniform march in the number of apnual marriages, corresponding to an increasing population, visibly accelerated in years of prosperity and abundance, and visibly retarded in those of scarcity and public distress. Thus, too, we see in Bavaria, laws restraining marriage result in an inereased number of illegitimate births. Wherever monthly returns, of whatever kind, are compared, the influence of season is marked by a more or less conspicuous annual maximum and minimum. Instances of this, of the most striking character, are adduced by our author in his • Essai de Physique Sociale. In these and similar cases, where we clearly perceive the existence of definite tendencies, or of a generally modifying cause pervading the whole field of their action, it is satisfactory and reassuring to find the result in correspondence with our views. For it must never be forgotten that tendencies only, not causes, emerge as the first product of statistical inquiry, and this consideration, moreover, ought to make us extremely reserved in applying to any of the crude results of such inquiries the axioms or the language of direct unimpeded causation. The proportionality of cause to effect, for instance, is a principle rather emphatically repudiated in the history of the correspondence of increase of imposts with increase of revenue, and of profits as compared with prices.