Vol. II. 271 soning, any of the other fundamental principles of geometry,) not a definition but a fact. According to his own principle, therefore, of which it is singular that he did not perceive the application to this case, geometrical and mechanical reasoning, as far as the original source of their evidence is con-cerned, are placed exactly on a footing. We apprehend, however, that it will be found that the parallel between these two branches of science may be carried still farther. It is true that an appeal to direct experiments can be admitted in geometry only in the way of illustration: but its application, in what Mr. Stewart has very properly styled theoretical mechanics, is of precisely the same kind. If, for instance, we attempt to illustrate the forty-seventh proposition of Euclid by the ingenious method of superposition ascribed to Mr. Ferguson, it is very probable that the squares of the two sides of our triangle, when cut into parts according to the rule laid down, will nearly but not exactly cover the square of the hypothenuse: - but what do we infer from this? That the proposition is only nearly, not exactly, true? By no means, we deduce the proper inference that the figures employed, owing to the imperfection of our senses and instruments, did not exactly answer to the definitions of the mathematical quantities concerned; — and, in precisely the same manner, when we have deduced from theoretical principles the conclusion that bodies, descending along the chords of a circle set in a vertical plane, will all reach the lowest point in the same time, we are perfectly satisfied of the validity of this reasoning. Our confidence in it is not shaken if, on trying the experiment, the result should not exactly answer our expectations; from which circumstance, the only inference that we should feel ourselves authorized to deduce would be that the experiment was not correctly performed, the circle was not perfect, the bodies did not begin their descent at the same instant, proper allowance was not made for friction, the resistance of the air, &c. The coincidences between the reasoning employed in theoretical mechanics and theoretical geometry (if we may be allowed the use of such a term in speaking of the investigations of geometricians, as distinguished from those practical operations to which the name geometry was originally applied,) multiply on us as we advance in their comparison. ideas of extension and figure, not less than those of motion and force, are derived originally from the senses. In both cases, our inquiries may be pursued in a certain vague and rude manner by an immediate and constant reference to the The evidence evidence of sense: but no exact knowlege can be obtained in this way in either of these sciences, chiefly on account of the imperfection of our knowlege and our instruments of analysis. We know little or nothing of the principles on which the effects of friction, the rigidity of cords, the flexibility of bars of wood or metal, the resistance of the air, and a variety of other particulars essential to the accurate determination of any individual case, are to be estimated. Hence it is necessary, in our theoretical investigations, to abstract from these circumstances, in order to simplify the object of our examination, and adapt it to our limited faculties; and therefore, in transferring the results of these inquiries to the actual phænomena of nature, where these circumstances are to be taken into the account, a discrepancy occurs, in consequence of which we are apt to think that we may not perfectly confide in our theoretical principles. Yet this suspicion is founded in mistake; as decidedly as if we were to deduce a similar inference with regard to geometrical reasoning from a want of exact conformity between our theoretical conclusions, and the most accurate and carefully executed practical measurements. It is probable that no perfect circle or straight line exists in nature; at least we know of none; any more than we know of rods perfectly inflexible or bodies perfectly elastic: but we abstract in this case also from these deviations or irregularities, as we call them, and for the same reason as before; viz. to simplify the object of our examination, and bring it down to the level of human conceptions. If it were not for this artifice, the theoretical investigation of the simplest theorem in geometry, or mechanics, would be too abstruse and complicated for the comprehension of the profoundest analyst. Unless we greatly mistake, it will be found, on comparing the reasoning used in geometry and mechanics with this view, that the conclusions deduced in such cases from definitions arbitrarily assumed, for the purpose already mentioned, have the same absolute and necessary truth; and that the very same lofty and imposing language, applied by Mr. Stewart to the former of these sciences, will appear to be equally applicable to the latter, considered as a mere theory in which sense alone, indeed, such language is applicable to either. [To be continued.] ART. ART. V. Prospectus and Specimen of an intended National Work. By William and Robert Whistlecraft, of Stow-Market, in Suffolk, Harness and Collar-Makers. Intended to comprise the most interesting Particulars relating to King Arthur and his Round Table. Cantos III. and IV. 8vo. pp. 61. 5s. 6d. sewed. Murray. 1818. WHEN we had read this continuation of a work of which we noticed the commencement in our Number for April, our recollection was forcibly drawn to the advice which that curiously compounded character Polonius gives to his son Laertes; "Be thou familiar, but by no means vulgar;" and we could not but speculate on the example furnished in these cantos of the difficulty of being the one without becoming the other. Though the author is evidently a man of taste and education, yet in his attempt to tell his story in conversational language, we fear that we must say that he has used common-places which come within the veto of the obsequious chamberlain; and in support of our charge we need only instance the line, 'Poor Pericles himself he went to pot. The result of a comparison with the first two cantos of this specimen is by no means favourable to the present. Instead of manifesting that increased facility both of versification and expression which is in general the effect of practice, the author does not proceed so glibly as before; fewer detached passages of any marked excellence occur; and, except in one or two instances, so great a deficiency of vivacity is observable, that the writer appears to be really incumbered with the mercenary engagement to which he alludes in the first line, and to write doggedly on as 'If every stanza brought him in a crown.' Notwithstanding these remarks, we still find much, to admire and much to entertain: we shall therefore pursue our former plan, and present our readers with a slight analysis of the work, and attended by such extracts as may give them an idea of the poetry and style. Instead of keeping the promise made at the conclusion of the former publication, 'A giant's education and his travels Will occupy the next succeeding page,' ་ Messrs. Whistlecraft, after a lively exordium in which they represent the benefits of their engagement with their book REV. JULY, 1818. T seller, 6 seller, introduce us to fifty friars, fat and good,' inhabiting an antient abbey some ten miles off:' Between the monks and giants there subsisted, A poor lame giant once the monks assisted, *This seem'd a glorious, golden opportunity, To draw them to pay tythes, and dwell in unity; And might have much enrich'd the whole community, But he relaps'd, and though all means were tried, This good understanding was increased by the friars' 'sober, cautious, and prudential' conduct, and by the love of music, which often led the giants • To listen all the livelong summer night;' and it continued without any interruption till the monks took it into their heads to indulge an ambition For bells of larger size, and louder tone; Giants abominate the sound of bells, And soon the fierce antipathy was shown, The following is a very happy playful description of the effect of the bells among the mountains: Meanwhile the solemn mountains that surrounded They scarce knew what to think, or what to say; Yet) Cader-Gibbrish from his cloudy throne The The next stanza but one is humorous: Historians are extremely to be pitied, So -"my heart sickens, and I drop my pen," The siege is then described in an excellent specimen of monkish legendary Latin: • Erant rumores et timores varii; Stabant ad necessarium præsidium, Et perduravit hoc crudele obsidium, Ad primum diem proximorum Idium; In lecto per tres menses brachio fracto, Et nihil relinquebat de intacto, Et alia multa damna atque outragia." After a sly hit at the custom of owning the obligations of friends, by one of whom a translation has been furnished, the author proceeds to notice a difference in the abbey be-tween the tintinnabularians and anti-tintinnabularians; the latter of whom, 'the wise are always few', • Were over-borne, canonicali voto.' Among the antis, is A prudent monk, their reader and librarian,' who considers himself as a marked man; and an admirable description is given of his spection of his brethren. conduct under the suspicious inOn the day of |