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METEOROLOGICAL JOURNAL FOR JUNE, 1836; KEPT AT BLACKHEATH ROAD.
N.N.E. Scanty rain; day generally overcast, with cirrus
Much cloud; rain, P.M.
S.W. S.W. Light showers; cumulus, and much driving scud.
5 13:4 2 S w bw.w.sw. Wind very high; flying clouds; rainy evening.
( Windy; scanty rain at noon; clear night. Mon. 6 30.165 | 63 | 30.142 64 | 45:5 66.8 56.2 21.342 6 8 3
Much cloud; cirri and cirro-cumuli ; windy. 730.056 63 29.976 64 53.5 64.5 59.0 11.050
8 2 2
S.S.W. S.W.S. Cloudy and lowering; drizzling rain; overcast from
8 29.780 63 29.748 67 52.6 69.661:1 17.050 7 5 3 2 S.W. S.W. Fair; passing cumuli ; distant nimbi. (scud.
Very fine; heavy clouds.
Sultry; clouds; cirro-cumuli. [to nine, P.M.
Light clouds; sultry; lightning to south, from eight
Cirro-stratus ; drops of rain.
Cirro-stratus; cum.-stratus; nimbi; distant thunder
3 w.sw. S.W. Fine; few clouds.
3 Iw.n.w. N.W. Windy; cumulus and cirro-cumulus.
W. Overcast, with scanty rain.
3 Iw.sw. W.S.W. D Rain during night; windy; clear at eleven.
2 w. b s. w.s.w. Cumulo-stratus ; a shower at 8 P.M.
W. W.S.W. Much cloud ; cirr.-cumulus. and cum.-stratus.
Ditto, ditto; cirr.-cumulus. in flocks.
28 30.215 69 | 30.23074 55.0 82.1 68.6 27.1 51 5 2 2 S.S.W. W.N. Fine; warm; wind strong at intervals.
N Hazy; cirri ; clear night. [at night, to south.
A breeze; much cirrus; continuous brilliant lightning
Day of Month Barom. Ther. Barom. Ther: Thermometer Daily. Solar
052.7 8°6 44° 9 10 1
Bar. Max. 30 in.: 461 on the 26th.
Ther. Max. 82°1 on the 28th.
Lowest point of Rad. 43°, on the 30th.
ON THE STUDY OF MATHEMATICS. Our readers are aware that attention has been lately recalled to a controversy of long standing, by the appearance of Mr. Whewell's pamphlet On the Study of Mathematics, which elicited an article in the Edinburgh Review, written with a bitterness seldom excited but by personal resentment, but with that criti acumen and profound learning which has so deservedly rendered that journal a leading one in literature. The professed object of the writer is to show, that mathematics, when made a principal study, instead of being calculated to develop and mature the intellectual faculties, have a directly contrary tendency, and train the mind to a
“one-sidedness” which disqualifies it for intercourse with others, and for sound philosophical reasoning. Professor Chevallier, of the Durham University, has replied to this attack, with an eloquence which exhibits him as a powerful champion on the other side. We shall endeavour to place the merits of the question in a simple form before our readers, to the end that they may judge for themselves on a point so vitally connected with systematic education ; we will strive to be as impartial in weighing the evidence as is compatible with a very decided opinion on the subject; one requisite to candour on the question we at least possess—that of not owing our education to either of the two universities which have been implicated in the discussion; our bias is, therefore, not due to those associations of filial reverence which these almæ matres so naturally excite in their children. If in our endeavours to justify mathematical study, and defend it from the attacks of its enemies, we appear exclusively to direct our arguments against the article alluded to, it is because we consider it as embodying, in the most detailed and luminous form, all the objections that have ever been made.
The question at issue has been simplified by excluding all consideration of the utility of the sciences brought into contrast during the argument; they have been considered solely “ as the means of a liberal education—that is, an education in which the individual is cultivated, not as an instrument towards some ulterior end, but as an end unto himself alone; in other words, in which his absolute perfection as a man, not his relative dexterity as a professional man, is the scope immediately in view.” We confess, however, that this distinction appears to us more specious than necessary, every man has an ulterior end in view, though it may not be the acquisition of wealth, or even the means of subsistence; emancipation from these cares not only does not enable the mind to attain universal knowledge, but by removing a powerful incentive to exertion generally renders it less active; it is the opposite tendencies of very general and comprehensive divisions of studies which are to be canvassed, the comparison, as will appear,
is virtually instituted between abstract and physical science, and literature in the most comprehensive sense of that term; now the student becomes devoted to one or the other of these divisions from causes quite independent of, and long anterior to the choice of a profession, which choice is greatly influenced by the inclination manifested towards one of these branches of study in preference to the other, and professional success
8 VOL. II.
must subsequently, in a great measure, depend on the general intellectual cultivation of the candidate.
The essential preliminary to such a controversy ought, we conceive, to have been a definition of what constitutes a liberal education, and of the tests by which we may estimate the degree of success in its attainment; we presume the one generally received may be adopted here-- which defines the most efficient education to be that which secures the greatest quantity of happiness to the individual, happiness being previously shown to depend on moral conduct, and that this again is fostered by mental discipline as conducing to the subjugation of our passions. If that command over our passions be obtained, it must be comparatively unimportant what may be the subjects with which the intellect is occupied; but since variety must be presented to it in order to keep the mind in constant activity, no one study exclusively pursued can be adequate to the object; all parties, accordingly, insist on diversity of pursuits, as a mean of intellectual cultivation, and the question becomes -Which ought to have the preference as the more engrossing occupation? Surely that which involves the greatest number of others, or that which cannot be successfully prosecuted independently of others.
Without entering into any metaphysical discussions, we may primarily refer the intellectual faculties which it is the object of education to develop, to those of judgment and imagination; the studies by which the former is chiefly matured are such as exercise the reasoning powers, and “ enable us to trace securely and readily the necessary consequences of assumed principles.”
“ In a great part of mankind such a power requires to be confirmed and strengthened by education, since by nature it exists in a low degree and confused form only; men's minds are full of convictions which they cannot justify by connected reasoning, however reasonable they may be... There prevails very widely an obscurity or perplexity of thought, which prevents men from seeing clearly the necessary connexion of their principles with their conclusions.
“ Now though there is this chance of being practically right and speculatively wrong, it will probably be allowed that this is not a state of mind in which those can acquiesce contentedly, whose object is the mental culture of man. ..... The object of a liberal education is to develop the whole mental system of man, and thus to bring it into consistency with itself;—to make his speculative inferences coincide with his practical convictions;—to enable him to render a reason for the belief that is in him, and not to leave him in the condition of Solomon's sluggard, who is wiser in his own conceit than seven men that can render a reason.
“ This complete mental culture must, no doubt, consist of many elements; but it is certain that an indispensable portion of it is such a discipline of the reasoning power as will enable persons to proceed with certainty and facility from fundamental principles to their consequences. ....
• There are two principal means which have been used for this purpose in our universities ;—the study of mathematics and the study of logic. These may be considered respectively as the teaching of reasoning by practice and by rule. In the former study, the student is rendered familiar with the most perfect examples of strict inference; compelled habitually to fix his attention on those conditions on which the cogency of the demonstration depends; and in the mistaken and imperfect attempts at demonstration made
by himself or others, he is presented with examples of the most natural fallacies, which he sees exposed and corrected. În studying logic, on the other hand, a person finds the conditions formally stated under which an inference is legitimate; he is enjoined to see that in any given case these conditions are satisfied; and if a fallacy exists, he is provided with rules by which it may be condemned and made more glaringly wrong. ...
“ Mathematics familiarize the student with the usual forms of inference, till they find a ready passage through his mind, while anything which is fallacious and logically wrong at once shocks bis habits of thought, and is rejected. He is accustomed to a chain of deduction, where each link hangs from the preceding; and thus he learns continuity of attention and coherency of thought. His notice is steadily fixed upon those circumstances only in the subject on which the demonstrativeness depends; and thus that mixture of various grounds of conviction, which is so common in other men's minds, is rigorously excluded from his. He knows that all depends upon his first principles, and flows inevitably from them; that however far he may have travelled, he can at will go over any portion of his path, and satisfy himself that it is legitimate; and thus he acquires a just persuasion of the importance of principles, on the one hand, and, on the other, of the necessary and constant identity of the conclusions legitimately deduced from them. Logic, on the contrary, forcing upon our notice the rules which we follow when we reason well, hardly allows them to become so habitual as to escape our consciousness; nor does she familiarize us with long trains of strict reasoning, since she generally gives special deductions only as examples of forms of argument. And thus the continuity and concentration of thought, and the quick sense of demonstration which it is our aim to educe, are not taught so well by this study as by that of mathematics."—(Whewell on the Study of Mathematics, fc., pp. 4—7.)
The progressive enlargement of the boundaries of our knowledge, and consequent multiplication of subjects with which the mind may be occupied, compels every one to make a selection of them for study; it is only in times when science is extremely limited and vague, that universal geniuses can exist, such as a Mirandola or a Crichton are represented to have been; in the present day men are attracted towards that branch of study for which their intellectual constitution more particularly inclines them, and they are obliged to content themselves with a general acquaintance with the others; the comparative value of each as a mean of mental culture, can only be estimated by the average result of that peculiar study on individuals, and if any one study appears steadily to decline in general estimation, it is a presumptive proof that it is found to be either inadequate to mental discipline, or is relinquished from causes over which we have no control. Now we think that this tendency to decreasing estimation has manifested itself for a considerable period, with regard to those studies denominated philosophy by the reviewer; on such matters individual must yield to general opinion; it is futile endeavouring to stigmatize the latter by attributing it to the spread of utilitarian or revolutionary principles; the doctrines thus designated could not extend themselves, unless they were found to contribute ulteriorly to general happiness, or to have become involved in our well-doing There can exist no permanent standard with which to compare the
several studies that may engage the mind, for the purpose of deciding on their relative merits; as the various relations among the great family of mankind increase in number and complexity, the general plan of intellectual cultivation must be modified, the one essential condition being kept in view—that of controlling the passions and cultivating the social virtues; in order to fulfil this condition, certain studies must always be insisted on as essential to a liberal education; the relations of man to his Creator must obviously be the first of these, and all those that tend to repress our self-sufficiency and presumption, and to increase our charity towards other beings; but the means for inculcating these feelings, and for maturing our conceptions of these relations, may vary, and have varied greatly; the increasing difficulty of providing for our physical, and of gratifying our acquired wants, has compelled us to study with greater attention the qualities of the material universe, and has, comparatively, withdrawn the mind from those reflections on its own operations, which solicited it in times when man had more leisure for speculation, and less necessity for action. Fortunately, this inevitable change in the direction of our pursuits is favourable, as we shall endeavour to show, to the paramount object we have alluded to.
In impugning the efficiency of mathematics as a means of intellectual culture, an arbitrary limit to that science has been assumed, which is not admitted by its advocates, and is grounded, as we think, on av erroneous conception of the distinction between pure and mixed mathematics. We shall first comment on the limitation alluded to.
“ In the first place, it is wholly beyond the domain of mathematics to inquire into the origin and nature of their principles. Mathematics, as Plato and Proclus observe, are founded on hypotheses of which they can render no account. The geometer (says Aristotle) can attempt no discussion of his principles; and Seneca observes that mathematical is a superficial science, it builds on a borrowed site, and the principles, by aid of which it proceeds, are not its own: philosophy begs nothing from another; it rears its own edifice from its own soil. These authorities represent the harmonious opinion of philosophers and mathematicians of ancient and modern times.”—(Edinb. Review, No. 126, p. 415.)
Now we would ask any one who does not insist on nice subtilties, whether the processes of the mind, by which we arrive at those abstractions absolutely necessary to the study of mathematics in every stage, may not be fairly considered as pertaining to its domains? The ideas of space, quantity, ratio, limit, force, motion, time, &c., require the most strenuous intellectual effort to grasp, yet they must be rightly conceived by every mathematician from an early period of his study; surely it is unfair to require that he should do so, and yet deny him the right of reasoning on them? They must certainly be regarded as forming an integral part of that science, if the notions of fate, necessity, evil, taste, beauty, &c., be.considered as belonging to the domain of ethical. It is useless, in a question of practical bearing, to insist on any strict boundary to different sciences, if one study absolutely necessitates “an inroad into the province of another,” it must be regarded as an additional recommendation of the former, by every one advocating diversity of intellectual pursuits.