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ai)(j °^ s °f buildings situated in towns, and of farm-housesh aa i° ta S es in the country ; but of late years the use of themslates tnuc l l circumscribed by the extension of that ofI'Hj,’ aor tbe mode of manufacturing and using them, see

I ' e ar^- eC ^ n ° san< l> tbe ancient and modern practices agreeSh ape y * n a H that need be said ; that which is of an angularis adm'™ textui 'e, and perfectly free from earthy particles,be at - 1 , to be best. For the circumstances necessary toj n en oed to in employing it, as well as lime, see Cement. and ^ e » ar< l to metals, in modern times, the use of copperdon e d 0n ^ e has, for building purposes, been mostly aban-tvi n( j ’ tirass has been continued in locks, pulleys, sash-ay^. WS ’ handles, sliding plates, connected with bells, andtnentg °^ ler P ur poses in fitting up the interior of apart-

fortnej ^- aS ^ een applied to many purposes unthought of ine ast.; r F tlrn . es - The improvement and general introduction oftur e °? bids fair to create a totally new school of architec-P'Ua’rs r has already been extensively empkq-ed in bridges,faciiit' ro .°^ s ’ floors, chimneys, doors, and windows ; and theCor itinn2 V i. t ^ w l*'ch it is moulded into different shapes will

►... •• •••vii j.v iq moutuv^u

pUvp e to extend its application. The before-mentionedpartial 8 ’ to w bich it has already been applied, are morenoticed in the discussions of practice in thebead s n branches of architecture, under their respectiveQl'

the a || S8 ’ as a building material, was little if at all known toofco mf ents ; and ’ ts introduction alone has been productiveorts and elegances to which the most refined of the

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Pape r t an< ^ Romans were utter strangers. Their oiledever, rans parent horn, talc, shells, and linen, would now,I'd- aiJ an English peasant, appear a miserable expedient.

°f >ts manufacture, and application to archi-ll^ PUrpos es, see Glass.

a s cor 6S .^ le materials which have already been enumeratedflo 0rs P ° 8ln S the principal members, as walls, roofs, floors,also n'ocg 11 " 0 "?’ chimneys, stairs, and pavements ; hair isEfface ’ n the composition of mortar for plastering the

pa Perg f Wa lls and ceilings ; likewise various paints andMh ch ' a ° r aover >ng them and other parts of the work ; alltbeij. tn ,, re described, with the modes of applying them, in

^ATltp P laces -

S(dei 'ce wh'^^dA.TICS ( from the Greek paQ^aruo)), the'yl'ciicg if • ' treats of the ratio and comparison of quantities,ae sci en ls defined the science of ratios ; some writers call it’ties th ' e °f quantities; but this is inacurate, since quan-£ati 0tl) ^ selves are not the subject of mathematical investi-°th er _’ u the ratio which such quantities bear to eacha be i

t] 8c 'pline m f a ^ iema tics is derived from /ladrirnc, mathesis,i le hio-pj ’ SCle nee, representing with justness and precision^Medjjp ea that we ought to form of this branch of human. n fact, mathematics are a methodical concate-

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^ 0 ^ °^. P r 'nciples, reasonings, and conclusions, always!' lv ' ! 'n{!T;‘ le d by certainty, as the truth is always evident, anparticularly characterizes accurate knowledgeass °ciat rUe Science8 > with which we must be careful not to6 h tl nietaphysieal notions, conjectures, nor even the. The g friabilities.

P'tvsde a A ec ^ s °f mathematics are the comparisons of mag-^asidgp 8 Cambers, velocity, distance, &c. Thus, geometiyfbe relative magnitude and extension of bodies ;^bani relative velocities and distances of the planets;>hi' 8 > fbe relative powers and force of differenta b°h in Cl &c., some determinate quantity being fixed

‘ih all

Cases > as a standard of measure.

The study of mathematics is highly useful to the architect,particularly arithmetic, geometry, mensuration, and mechanicsGeometry enables him to take his dimensions under the mostdifficult circumstances, and to lay out the various parts of hisdesign, while it furnishes him with rules for executing thesame. Mensuration is the application of arithmetic togeometry, and shows him how to find the exact proportionof his labour, according to the difficulty of executing a certainuniform portion of a work, and to estimate the quantity ofmaterials employed therein : that branch of mathematicscalled mechanics , enables him to compute the strength andstrain of the materials he employs. In short, without the aidof mathematics, he is unfit for his profession ; and the morehe understands, the fewer difficulties he will have to encounterin the prosecution of his art.

Mathematics are naturally divided into two classes ; theone comprehending what we call pure and abstract; andthe other the compound or mixed. Pure mathematics relateto magnitudes generally, simply, and abstractedly, and aretherefore founded on the elementary ideas of quantity.Under this class are included arithmetic, or the art of com-putation ; geometry, or the science of mensuration andcomparison of extensions of every kind ; analysis, or thecomparison of magnitudes in general; to which we may addgeometrical analysis, which is a combination of the two latter.Mixed mathematics are certain parts of physics, which are,by their nature, susceptible of being submitted to mathe-matical investigation. We here borrow from incontestableexperiments, or otherwise suppose bodies to possess someprincipal and necessary quality, and then, by a methodicaland demonstrative chain of reasoning, deduce from the prin-ciples established conclusions as evident and certain as thosewhich pure mathematics draw immediately from axioms anddefinitions, observing, that these results are always givenwith reference to the experiments on which they are founded,or the hypothesis which furnished the first datum. To illus-trate this by an example : numberless experiments haveshown us, that all bodies near the earth’s surface fall with anaccelerated velocity, and that the spaces passed through areas the squares of the time they have occupied in falling.This, then, the mathematician considers as a necessary andessential quality of matter, and with this datum he proceedsto examine what will be the velocity of a body after anygiven time, in what time it will have acquired a givenvelocity, what time is necessary for it to have generated agiven space, &c., and in all these investigations his conclu-sions are as certain and indisputable as any of those whichgeometry deduces from self-evident truths and definitions.Again, in optics, having established it as a principle of light,that it is transmitted in right lines while no obstacle is opposedto the passage of the rays ; that when they become reflected,the angle of incidence is equal to the angle of reflection; thatin passing from one medium to another, of different density,they fly off from their first direction, but still follow a certaingeometrical law ; these principles, or qualities of light, beingonce admitted, whatever may be its nature, be it material orimmaterial, or whatever may be the medium through whichit passes, or the surface by which it is reflected, are matterstotally indifferent to the mathematician; he considers therays only as right lines, the surfaces on which they impingeas geometrical planes, of which the form only enters into hisinvestigation : and from this point all his inquiries are purelygeometrical, his investigation clear and perspicuous, and hisdeduction evident and satisfactory. To this class of mathe-matics belong mechanics, or the science of equilibrium andmotion of solid bodies; hydrodynamics, in which the equili-brium and motion of fluids are considered ; astronomy, which