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We alluded in our opening article to the low esteem in which science is often held among those who par excellence arrogate to themselves the title of the highly-educated classes. We often perceive proofs of it in the spirit occasionally manifested by those periodicals which are under the especial patronage of the more polite portion of society; not to mention the obscurity or total neglect to which real science is generally consigned by the daily press; varied only by occasional puffs of all that species of philosophy, which, from its intrinsic emptiness and levity, least requires such aid to raise it in the gross atmosphere of popular fame.

But the circumstance which has led us to these topics at the present moment, and which is intimated by the heading of this article, is the occurrence, in the recent number (cx.) of the Quarterly Review, of some matter which appears to call for our more special animadversion.

This learned and refined organ of literary exclusiveness, does now and then condescend to acknowledge that there is such a thing as science; and that it may not be utterly degraded by allowing some obscure corner of its pages to discussions connected with these subjects. Consequently in the present number, the subject of M. Agassiz and his discoveries relative to fossil fishes is selected, and very justly, as one highly interesting in itself, and susceptible of popular illustration. Of the manner in which the subject is treated it is far from our intention to say anything. We shall only observe, that towards the end of the article the writer takes occasion, very properly, to refer to the necessity for pecuniary assistance for carrying on a work so vast, and at the same time so little likely to be profitable, as that which M. Agassiz is engaged in bringing out, in successive numbers, containing beautiful plates of the different species of fossil fishes. Indeed, (by the way,) we more than surmise the whole of the short article referred to is mainly designed to lead simply to this one point, of soliciting the public to subscribe. Nor do we at all blame such a procedure: it is highly praiseworthy; and we shall be heartily glad to concur in promoting so desirable an object. We merely remark this as tending to confirm our impression that had there not been such an object in view as the support of an individual, whom the polite journal condescends to patronize, (though engaged in the extremely unworthy occupation of groping and grovelling in the earth to disinter fossil remains,) we should probably have heard little of his important discoveries ;—though perhaps not less than we actually do, of their high philosophic bearings.

To return, however, to our immediate subject: This recommendation of subscription is introduced by a mention of the circumstance that a sum was awarded for this purpose by the British Association for the Advancemence of Science, at the Dublin meeting : which is prefaced by the following remark :-(p. 444.) * We

e are not among those who are in raptures with the British Association for the Advancement of Science. It delights in greater display than becomes the modesty of philosophers: nor do we think that their mutual bepraisingstheir Amæbean eulogiesare at all likely to add to their dignity. Wherever they go,— Earth no such sons, no folks have such a town:' and we cannot view with feelings of complacency our scientific Samsons, led forth to make sport at its festivals; even though the exhibition should be hallowed by a few sprinklings from the fountain of honour, distributed through the spout of Ireland's Viceroy."

To show his laudable candour, the writer continues

“ While, however, we do not conceal our opinion of its faults, we must not be blind. to its merits,” &c. And then comes the mention of the vote of money to M. Agassiz.

We will take these charges in order :-/st. The Association is accused of greater display than becomes the modesty of philosophers. Now what sort of display does the reviewer mean? Is it the display of the results of researches, which the members have been carrying on during the year, many, if not most of which, have been undertaken at the suggestion of the Association, and of which a public statement must be made in return? We hardly suppose this can be what is meant : yet most certainly such display as this is what, in fact, constitutes the great mass of the proceedings: a display of the results of philosophic labours, made to the assembled body of cultivators of science; and that not for any purpose of display as such, but to call forth discussion, observation, very often criticism and censure. The display of science before the public, perhaps is meant; and that philosophers, in virtue of that “modesty" which ought to be so peculiarly theirs, should keep all their discoveries. to themselves, or, at least discuss them only in select coteries, but never proclaim them to the world. But if they hold such meetings among themselves, and the public desire to be admitted, would the reviewer wish to exclude them? If a mixed audience, including numbers of the fair sex, choose to be present, who would desire to prevent them? Nay, even granting as much display in the thing as may be wished, what is the object? Is it not the promotion of something like a just recognition of the claims of science, in which public opinion has generally been so notoriously deficient? and if for this it be unavoidable to run into the slight degree of display which attends a general gathering of men of science, and the public exposition of scientific truths at their assemblies, it is difficult to see how any one can blame it, unless it is on the ground that Science does not need such a stimulus; an idea which can only be entertained by those who are profoundly ignorant of its actual condition. It

a display, too, not merely to the public, on the part of the philosophers, but anxiously desired by the junior and humbler cultivators of Science, from their elder and more distinguished fellow-labourers. The numerical majority attend these meetings with the view of gaining information, (we might say, with truth, all do so in some sense ;) which they cannot do unless it be publicly and formally put before them. The British Association, we affirm, does not, as the reviewer asserts, delight in display.” Some publicity is necessary for its object, and if the attendant degree of display be an evil, it is a necessary evil.

But further, “ the mutual bepraisings,” the “ Am@bean eulogies” of the philosophers,“ do not add to their dignity." We should be glad to compare the proceedings of the British Association, in this particular point, with those of any other large public institution which holds annual

meetings. We imagine the “ bepraisings” which take place in any other great meeting are not only, at least, fully as numerous, but generally far more vehement, in proportion as they usually refer to topics in which the feelings of the parties have so much more to do. We do not well see how a great meeting is to be carried on without some attention to the customary decencies of courteousness : without some such things as votes of thanks to officers, to benefactors, to supporters of the cause ; some notice shown towards persons of eminence who may be present; and the like. Nor will the customary expectations of a mixed audience allow such occasions to pass without the occurrence of many expressions of eulogy, which are well enough carried off by the excitement of the moment, however little they might bear the test of severe criticism on cool reflection afterwards. But there is one thing peculiar to the “ Amebean eulogies," in the particular case in question, which is often overlooked by those (and there are many such) who make objections on this ground; viz., that in some (and those the most marked) cases, this eulogy is not mere unmeaning flattery, but is rather the pronouncing of the judicial sentence, as it were, of a great scientific tribunal on the pretensions of some aspirant after philosophic honours, whose researches have previously formed the subject of close examination and debate : that, then, which appears, to an inconsiderate bystander, the mere effusion of flattery, is often nothing less than the united decision of the assembled Science of the country, on the labours of some retired cultivator of Science, which thus receive the stamp of public opinion from those best qualified to judge of their merits :—the highest recompense of scientific toil, and the surest stimulus to renewed and well-directed exertion.

As to the compliments paid to those whose liberal hospitality welcomes the Association wherever it goes, and even contends (often with no slight warmth, as we could witness,) for the priority of selection, we can only ask how is it possible for any individual or any body, received as the Association and all its members have been, to abstain from uttering those thanks, which they must be unfeeling indeed, not to perceive are barely an act of justice? We will merely add, on this topic, that though the reviewer is evidently glancing at the Dublin meeting, he clearly has no right to talk of subjects of which he is ignorant: the very fact of his penning the words alluded to, amounts to a positive proof that he was not among the visiters on that occasion, or he could not have written them,

The Samsons led forth to make sport at its festivals,” is, doubtless, a most humorous and right merry conceit; but we should be glad if the writer had produced a few instances of the sort of sport he alludes to. On casting a rapid glance over the report of the proceedings of the last meeting, we tried to recognise some of these Samsons who figured in the Rotunda, and to see what sort of sport they made. The grave and learned opening speech of the venerable President was, we should imagine, anything but sport. The brilliant eloquence of Sir W. R. Hamilton's address (delivered officially as secretary), we may allow so far, was indeed the production of a Samson. We do not know what exhibition of this kind could be found in the masterly exposé of Mr. Whewell on the Tides; or in the lucid, but by no means sportive, lecture of Dr. Lardner on Rail-roads. We could discover no particular comic display in the philosophic observations of Professor Babbage ; nor in the grave discussion on Light of Professor Powell. If there was anything approaching to sport, it was in the address of Professor Sedgwick; but it was not the sport afforded by a blinded and fettered Samson. For our own parts we think, if, under this ridiculous phrase, it be meant to complain that the public lectures and expositions of Science were of too popular a kind, it merely shows how little the Quarterly reviewer appreciates the value of a popular diffusion of a taste for physical knowledge, and the extreme importance of enlisting in this service the talents of really sound and eminent scientific men, instead of mere shallow declaimers and ignorant empirics. One of the grandest objects of such an Association, we are persuaded, is that of promoting, not only the abstract researches of the few, but the dissemination of a knowledge of them among


many : : to secure to Science something like the attention it ought fairly to receive, and the estimation it ought to command, in public opinion. And so far from thinking there is too much of popular display at its meetings, we are persuaded, on the contrary, there has been (at the two last meetings especially) too little opportunity given for the public exposition and enforcement of these great objects.

The miserable pun in which the Representative of the Sovereign is here insulted by the loyal Quarterly, shows clearly the feeling which dictated the attack: the writer is anxious to fix a political stigma on the Association, and this is his proof!



There are few questions in reference to which writers on elementary mathematics have been more divided, than that between the Geometrical and Algebraical methods. But though able disputants have contended strenuously on each side for the superiority of the respective systems, they have contributed very little to a clear exposition of the essential points of difference.

The question refers not merely to the comparative advantages afforded by the two systems, but even to the absolute validity of the processes of reasoning which they employ. The external characteristics of style, method, and notation, doubtless present many points of discussion and comparison : even these have been by no means well contrasted, and a very discordant variety of representations may be collected from the writings of the most eminent men who have drawn such comparisons. But these are distinct from the more important point in dispute, which relates rather to the fundamental principles assumed, and the nature of the reasonings adopted in each system, and here it is that the discussion has been most defective. From the writings of the most distinguished mathematicians, it is very difficult to derive any satisfactory or precise notion of these more essential grounds of distinction : and it may with truth be said, that though many have contested whether Algebra or Geometry be the best, but few have discussed, and none have clearly pointed out what is Geometry, and what Algebra.

The subject, indeed, has been but incidentally introduced by most of these writers, and a complete investigation of it has been long a desideratum in mathematical literature. By some it has been alleged as the distinction between Geometry and Algebra, that the demonstrations of the one are synthetical, while the processes of the other are analytical. But in any sense of the words, this is far from being universally or even extensively applicable: and did it obtain, it could in no way affect the validity of either method. But in truth, so wide has been the latitude of meaning in which the terms analysis and synthesis have been applied in these departments of Science, that it is difficult to fix upon any determinate particular in which the distinction can be understood to consist.

By others it has been made the point of comparison, that in the one system we reason independently on each particular case, by a method limited to that case, whilst in the other, we avail ourselves of general methods, applicable at once to all cases; and when the first data are established, affording the facility of an almost mechanical process for arriving at results, to which Geometry, if at all, could only conduct us by a slow and laborious advance. Thus aided, the analyst is enabled with ease to overcome difficulties, with which the Geometer might often struggle, single-handed, in vain. The methods of Geometry have been compared to manual labour, those of Algebra, to manufacture by machinery: the one to a journey performed on foot, the other to a steamcarriage on a railroad.

In all this there may be much truth of description, but nothing by which any essential distinctive principle is brought to light.

Some authors characterize Geometry as not requiring that abstraction which analysis demands, and directly addressing the senses as well as the understanding. Others represent analysis as superseding thought by mechanical processes, and thus rendering investigation easy to those who are incapable of the abstraction which Geometry requires.

Some censure an exclusive pursuit of Algebra, as tending to narrow the mind, by confining the attention to the more individual steps as they succeed one another, and to the routine of set rules, without requiring or allowing any extended and comprehensive views; while Geometry, it is alleged, expands and invigorates all the mental powers, by the healthful exercise of unfettered invention.

Others, on the contrary, select this as the very ground of commendation, that Algebra expands and generalizes our conceptions, while Geometry contracts and restricts them to the consideration of isolated


The two methods are characterized by Professor Playfair, from “ the different modes they employ to express our ideas. In Geometry, every magnitude is represented by one of the same kind; lines are represented by a line, and angles by an angle; the genus is always signified by the individual, and a general idea by one of the particulars which fall under it.

In Algebra, every magnitude is denoted by an artificial symbol, to which it has no resemblance," &c. And, again,

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