1848.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



357 



a wise man, and that he must have acted from precepts delivered 

 to liim by Jlinerva : — 



■ the workJ 



Twas a wise artist irt':n'd, his wisdom 

 By precepts from Minerva." 



taught 



II. Lord Bacon's definition of art — namely, "a proper disposition 

 of the tilings of nature, by human thought and experience, so as 

 to answer the several purposes of mankind," clearly expresses that 

 the success with which the mind achieves that desirable end, and 

 the means it adopts for the production of the beautiful, depends 

 upon such hifrh attainments as can be expected only after a long 

 course of observation and experience. Art will exert a beneficial 

 influence upon society, and be a realisation of beauty, according 

 to the wise and " proper disposition of the things of nature." 

 Herein is pointed out the necessity of a knowledge of first prin- 

 ciples, which, wlien systematised by reasoning and taste, form a 

 sure foundation whereon the artist may securely rest in all his 

 operations. The amassing together a variety of perceptions re- 

 quires the perfection and activity of tlie organ of vision, and the 

 power of combining and representing figures in their most natural 

 and appropriate forms, — is acquired only after a repetition of ma- 

 nual efforts, aided by the co-operation of the mind, and added to 

 much practical wisdom. Sucli representation of sensible objects — 

 not, however, strictly copied as they are, but improved to what 

 they should be — portrayed truly, yet poetically, demands a system 

 of various and well-appi'oved precepts, for instruction in which 

 man must look with the cautious and careful eye of observation 

 into the laws which have governed the works of the Divine artist. 

 The words of Paley, when arguing the existence and attributes of 

 God from his works, — "Contrivance proves design, and the pre- 

 dominant tendency of the contrivance indicates the disposition of 

 the designer," apply equally to human productions ; and we cor- 

 rectly infer from their elegant beauty or imposing grandeur, the 

 artist's endowments. 



III. The well-understanding of the sound principles of art (by 

 which only it can be learnt and appreciated) prevents the commis- 

 sion of solecisms and barbarisms. Pursued on principles contrary 

 to natui'e and just reasoning, its results are generally absurdities, 

 and sometimes those one-sided, partial, and imperfect views, which 

 are nothing less than proofs of insanity. Witness Borromini in 

 architecture ; oi-, who was worse. Father Guarini, the specimens of 

 whose architectural achievements in Turin look more like the 

 sugar-and-plaster compositions of a pastry-cook and confectioner ; 

 or Bernini, who in sculpture, imitated the style of Rubens ; and 

 surely nothing could be so bad in taste as to make the drapery of 

 his sculpture resemble that of painting, or anything it in reality is 

 not ; for in the imitative arts, as in morality, the advice e.sto quod 

 esse viderif, should be recollected. These are examples of an in- 

 dividual caprice, of a love of extravagance, and of a spirit so 

 opposed to all truth, that they deserve censure ; and the more so, 

 because they are apt to captivate the ignorant and unreflecting. 

 So necessary is it that all should be under the guidance of reason 

 and intention, that he who does not attend to what these govern- 

 ing faculties prescribe as binding and imperative, but acts only 

 from impulse or chance, forfeits all right to the title of artist. 

 But worthy of all admiration is he who exhibits a control over 

 himself and his, perhaps, too ardent imagination; who regulates 

 his enthusiasm by reason; who makes his genius conform to the 

 rules of art ; and rising above every particular and partial, repre- 

 sents only the universal truth. For in this, as most other pursuits, 

 it will be best to preserve a medium. Extremes on either side are 

 to be shunned. 



Altius egressus, ccelestia tecta cremahis ; 

 Iiiferius, terras ; medio tutissimus ibis.' 



Ovid. 



ON THE STABILITY OF FLOATING BODIES. 



The doctrine of stability is of much greater importance in the 

 constructive arts than is commonly imagined ; it is, moreover, a 

 difficult subject, and when considered in all its generality, it re- 

 quires a much more extensive knowledge of mathematical investi- 

 gations, than is possessed by the greater part of that class of 

 individuals engaged in mechanical pursuits ; hence the reason 

 why the subject, notwithstanding its importance, is so little under- 

 stood. But although the general investigation of the theory is 

 attended with considerable difficulty, yet there are cases of a 

 highly interesting and practical character, in which the difficulties 



are but slight, and which may consequently be understood by 

 every person moderately acquainted with the elementary depart- 

 ments of science ; and it is to those cases which, in the present 

 instance, we intend the more especially to direct the attention of 

 our readers. The following are the conditions on which the equi- 

 librium of flotation depends. A solid body, floating on a fluid 

 which is specifically heavier than itself, will remain in a state of 

 equilibrium or balanced rest, when it has sunk so far below the 

 surface, that the weight of the fluid displaced by the immersed 

 portion of the body, is exactly equal to its whole weight, and when 

 the centre of gravity .of the whole floating mass, and that of the 

 immersed portion of it, are situated in the same vertical line. 



If the floating body be inclined from the position of equilibrium 

 through a very small angle, by the action of some external force 

 any how applied, the question of stability consists in determining 

 whether the body, when left to itself under such conditions, will 

 continually recede farther and farther from its position of equili- 

 brium until it finally oversets, or whether it will librate about 

 some axis, until it ultimately restores itself to the position which 

 it occupied previously to the action of the disturbing force. 



In the following inquiry we shall confine ourselves to that par- 

 ticular case of the problem, in which the first condition of equili- 

 brium is supposed to be satisfied, in whatever position the floating 

 body may be placed ; that is, when the weight of the whole floating 

 mass is exactly equal to the weight of the fluid displaced by the 

 immersed portion of it. 



Every solid which is generated by the revolution of some plane 

 about a fixed axis, and in general, every solid body having an axis 

 about which the opposite parts are symmetrically arranged, if it 

 he specifically lighter than the fluid on which it floats, and if it be 

 placed in the fluid with its axis perpendicular to the horizon, may 

 sink to a position in the fluid, where it will remain in a state of 

 quiescence or balanced rest. In all such bodies, there are two 

 opposite positions in which the equilibrium oljtains ; but there is 

 only one position in which a permanency of flotation can take 

 place. 



If the floating body be homogeneous, or uniform in density 

 throughout the whole of the mass, the centre of gravity of the 

 entire body will be situated above that of tlie part immersed, or, 

 which is the same thing, that of the displaced fluid ; but if the 

 density of that part of the body which is below the plane of flota- 

 tion* be greater than that of the part above it, the centre of 

 gravity of the whole floating mass may be lower than that of the 

 immersed part, or of the displaced fluid. Indeed, the centre of 

 gravity of the whole floating mass may always be placed below 

 that of the immersed portion of it, by increasing the density of 

 the lower, and diminishing that of the upper portions ; and in this 

 way may the stability be augmented in any ratio at pleasure. 



If a floating body be any how cut by a plane, in respect of which 

 the opposite parts are symmetrical, or similarly placed ; then, any 

 portion of the body cut oS' by a plane perpendicular to the former, 

 will also be symmetrical in regard to the same plane ; hence, 

 we infer, that if a body, symmetrical with respect to a certain 

 plane passing through it, be partially immersed in a fluid with the 

 said plane vertical, the immersed portion of the body will also be 

 symmetrical as regards that plane ; and the centre of gravity of 

 the whole floating body, and that of the part below the surface of 

 the fluid will lie in that plane ; consequently, for every such plane 

 as that here specified, which can be taken in a floating body, there 

 will be at least one position of equilibrium. These things being 

 premised, we are now in a condition to investigate some of the 

 simpler cases of the stability of flotation. 



Problem. — If a uniform prismatic body, whose transverse section 

 is a triangle, be made to float upon a fluid specifically heavier than 

 itself in a given ratio, with one of its angles downwards, it is re- 

 quired to determine the difi'erent positions in which it will float in 

 a state of quiescence. 



Let A B V, in the annexed engraving, he a transverse section of 

 the prismatic body, floating on the fluid with the angle A V B 

 downwards, and let the straight line C D be the line of common 

 intersection of the plane of the triangle with the surface of the 

 fluid, or that which, by the writers on mechanics, has been called 

 the water-line. 



Then, since the specific gravity of the fluid, as well as that of 

 the floating body is known, the area of the triangle C D V is 

 known, being to that of the triangle A B V, as the specific gravity 

 of the floating body is to that of the fluid on which it floats. 



Let the floating body be a prism of fir, of which the specific 



* The plane of flotation, is the horizontal section of the body, coincident with the 

 surface of the fluid ; or it is that horizoutal sectioQ whith .sej-arates the immersed and 

 emerged. portioDj'Of the-body. 



