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ascertained. The calculations of mathematics on the motiQn ~ w a t e r through pipes, &c. are useful for several purposes: I mi~h~ enume~ rate other arts and sciences whicla depend on rnathematicaYprinciples~ thus perspective depends upon the rules of~eometrv and ootics,i. The athematlcs have reduced music to a regular systenb by inventing its scales ; and there is hardly any part of mathematics which is not sub~ servient io architecture. ~I might descend to the animal fraine' The eye, the only organ of sense w~ich the geometers have¢onsidered, is the only one whose structure and manner of operatinn are understood. Every anatomist who wnuld wish to understand the action of the bones and muscles, would need the knowledge of mechanics. ..... The usefulness of mathematics in several sciences and practical arts, is abundantly evident. They were reckoned by some of the ancient philosophers the key to all knowledge. Thus 151ato had written above the door of his school. " I , e t no one ignorant of geometry enter here." It is not meant, however, that a knowledge of mathematics will enable any person lo practise in any of the arts I have mentioned. Thus he who would attempt to compose music merely by his knowledge of harmonical numbers, could not be expected t() [produce very excellent pieces. To excel in several of those arts, bestdes the accuracy of rules, a person must be possessed of genius and fancy, and practice is necessary fi)r them all. Yet still they owe their bein~ to mathematics, which" lays the tbundatiou of their theory, and afl~'rds them precepts, which being once invented, are depended upon securely by practitioners. Thus, though many design who do not know the reas~ons of the rules by which they practise--though many compose music better, perhaps, than the inventor of the scale could t~ave done, and know nothing of the numbers on which their harmony is founded, yet as the mathematics Show the fou~latioa nf these a~rts~ they must be necessary for their improvement; and surely it Will be granted, that he who knows the fundamental principles of what he professe% has the best chance of excelling.
ttints to Paviers. tly C0r~oxr.L MACXaO.~L [Continued from page 58.] The next kinds of pavement that it may be necessary-to mention, are those of Florence, nf Sienna, of Milan, and some other cities of Northern Italy. These may, indeed, be assimilated to a kind of stone rail-road, as there are partlcu~a, tracku allotted for the wheels~ and others for the horses. [he track~ for tl~e wheels are composed of stones nf very large dimensions; they are of marble, lumacelar limestone, or of a very hard sand stone ; most of them, particularly at Florence, weighing several tons. They are laid wi~h much precision, in lines of about three feet broad. The spades for the horses, between these lines, are paved with small stones, and are, as well as I can recollect, about four feet wide. In some of the squares, the small pavement predominate~; while the lines of large stone-way VOL, I I I o ~ N o . ~,~FEm~vAr~v, 18~7. 15
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cross it in every necessa,;y direction. Nothing can be more easy or agreeable than this pavement, which is suitable to carriages of every description, without the li,hitation or confinement of an iron rail-roa.d, but w~th nearly the same smoothness. Among the causes which appear to me to have contributed to the extraordinary duration ot" these ancient Roman pavements~ the g e o logical nature of the surface over which they are constructed is not tl~e least prominent. With the exception of the Pontine Marshes, and some ~racts about Brindisi (Brundusium), Taranto, and Peruggia, nearly the whole of them have been carri6g over a surface of volcanic tufa, of greatly compressed Puzzolana, or of calcareous, or basaltic rock; all 'wlfieh fu~nisll the best possible foundation. I, ~ countries where chalk, clay, gravel, or sand, are frequent at the surface, as in England~ France, Alsace, part of Lombardy, &c., even these Roman pavements, when not kept in repair, have.speedily be come impracticable for carriages. The siZe and weight of th'e stones composing the ancient Roman pavements, certainly do, when once well laid on a compressed substra turn, oppose much vis inertia to the weights which rotl over them, While their polyangular shape prevents any acute, or even rigl~t an~ o.les, beino_' l~resented to partial p ressur~ This polyangular shane, and the excellent juxta-posmnn of their s~des, prevent any continu ous line of junction being presented to the course of the wheels, which would so much tend to create ruts, an d other irregularities; more° over, the stones being slightly pyramidical, produces a tendency to conduct the shocks towards the inferior centre of each, or laterally to the superior~edges, which are well supported by the surrounding ones.
It is necessary a l ~ to remark, that the carriages used in Italy, both anciently and at the present time. are what wouhl be deemed in England, very light. Besides which, the wheels of the modern Roman and Neapolitan carts are of a larger diameter than anff used in England. It would appear that the carts of tile ancient Romans were generally two-wheeled, drawn by two, or four Oxen. T r a v e l ling-was for the most part performed on horseback, or in litters cartied by tw(~ mulds. Chariots for travelling do not appear to have been used at' all, much before the close of the republic. They were both two and four-wheeled, but not made to carr~ more than two persons, besides the driver. They do not appear to have had any sprino~s; the wheels were very low, and not-~hore than thirty-two or three inches apart. So that, altogether, it may be presumed they were more calculated to bruise the bones of the riders, than injure the pavements over which they bounced. Such, in a v e r y few words, are the best pavements I have had o,1 opportunity of o~serving, and'.there is reas~)n to believe there are no better existing. It does not. however, follow, because they are good, and perfectly well adapt(d to their respective t~urposes anti localities, that any of them might be applied with advar~tage to the streets of London. [ think it may be easily, shown; that neither the ancienl
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r~or modern Roman, the Tuscan, nor Nea olitan, :wOuld, ~)Ssess file qualities required for such an application. P P ' To pave I,o~ldon after the ancient Roman plan, would, in t~ifirst place, be aitended wiih eno,'mous expense, and entirely new'~tbnes wouhl be re~mirod fbr the whole uudertakinz. Stones of so iari% a surfitce w¢~ald also become most dangerous'-}br horses, at any ~i~e faster than a walk. or when drawing "fieavy weights, or upon an acclivity. In London. wagons and (:arts are in'~general ~tse,'of far greater burthen than ;my Which were anciently, or are at present, used in l I,d3 . Some of our sta~es and van% to a very conmderable welght~ m.'weover, add great velocity. [ shall ~ toht, perhaps, that in proportion to this tiorizontal velocity, the vertical ~ravitation is dimin~.bed ; but these c a r n a g e s have vcr~ small tore-wheels, upon which the drivers, with exh'ao(i'finavy smpiility, contrive to place the greater part of the load.* Such small wheels, so overloaded, descend with great viote,ce inlo ~he least depression of the pavement, and are thrown up (to IMI ap;ain) b), lhe slightest protuberance. I very much do(ibt whether, even in point of durability~ either the R,):n~.n (n' N~.al)~)|itan pavements wouhl succeed in London. Considerin;~ the friable nature . f most descriptions of mortar, I suspect, i;hat (he rel~oated s h o c k s o f ver~," h e a v y carriages would pulverize and detach i~ from the inferior su~'titce of the stones, part of it would work out, and the storm become loose.t A fiwther,great objection to any such .solid masonry pavements is, the fi'equent necessity of partiatly mkin~ it up to lay gas and water pipes, and to repair out" trdmpery, crnnal)lin~, brick~sewers.2 The foregoi,k~ objections witl equally apply to the modern Neapo!itan pavements. The modern Roman has not the defect of being too sm(~oth, but it has that of homo~'eneous solidity, which wilFnot admit of its being perpetuall'¢ displac~ed tbr the temporary purposes above mentioned'~ Moreove{', where are we to get a suff[cient'quan~:~ty'of ~uch Pnzzolat~a moriar as is employed in Italy, witli whicli the pavement becomes as one rock ?§ With regard to the pavements, or, as I have ventured to call them, the stone rail-ways of Florence, Sienne, Milan, &c. &c. the. objecThe pertl naclty with whMI this custom is fi)llowed, is somewhat surprising in this scientific conntry. W h a t are we to say to the riders too? W e ti'equent{y see five or six in fi'ont on a stage coach, without ~ single person behind, or even inside ! j- I have seen portions of ancient Iloman road broken up by the passag'e of heavy artillery. A very few such large stones displaced, will render the road impassable for carriages. ~; Our sewers are admirably planned and levelled, but the materials mid t h e r.onstruction are very short of the necessary solldity. § I have fi.equentty seen portions of such pavements undermined, and displaeed by torrents, without a sing'le stone being" detached fi'om the masses of aevcr:d square yarcts' surface, [ntu which the pavement was broken. On one occasion I remember the water having undermined the whole breadth of pavement, so as ~o admit of my crawling m~der it from one side to the other. .I im~nediately aft.or passed over it in my carriage, as safely as over a bridge.
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lions to their adaptation to the streets of London must also be obvious enough. Independently of the enormous expense of the materiaist such a system could never answer in streets where vehicles of all descriptions, going at every degree of velocity, have occasion to cro~s~ pass, and run abreast of each-ott~er, over the entire breadth of the street. Such large stones, whether of granite or limestone, would soon becon)e dangerously smooth, their longitudinal edges would wear, and ru~s continually be formed along them. '~ It remains for me to observe a n e w method of paving, which has been lately attempted in Piccadilly, but which I am confident will not be found to possess any advantages over the old plan in general * In that delectable imitation of the I.'rench, which is exhibited on the Hammersmith road, ofwhlch one portion is paved and tile other not, the high ridge, which must perpetually exist at the edge of t h e paved portion, has afforded many good jobs to the surF eons and wheelwrights, d/propos of French r o a d s ~ I will venture to dig'ress so far as to observe, that with the exception of the-lr straightness, their construction in other points is very bad. T h e y are in ffe~ neral three times too w l d e - - t h e y are too much arched or elevated in the midrile, and when this part of t h e m is paved, nothing" is done to t h e l~teral pot'lions, which are not. From being too wide, so m u c h care cannot be bestowed on their construction, at the same expense as would suffice were they narrower. Secondly, the carriages and carts not being' obliged to g'et out of each other's way, tbrm reg'ular tracks and ruts for those going and those coming-, out o f which they never dream of movln~. T h e s e French carts and wagons are o f quite as barbarous aud rude a construction as t h e y could have b e e n in the days of Clovis or Charlemagne, save and except, perad~,enture,that very ingenious in. vention of the modern French, for t h e express purpose of cnabllng the said carts to keep exactly and madeviatingly in the same rots. For whereas in diffcre~t districts the carts vary more or less in wklth, so that cart A would not be able to g'o exaclly in the rut of cart P;, it is contrived~ that their axletrees shonld have six or seven inches to spare, over and above the portion confined in ~h: ~ave of each wheel. T h e linch pin is affixed to t h e extremity of t h e axle, so that the wheels are at liberty to wash to and fro fi'om side to side, and adapt themselves exactly to the ruts, whlcb the French road-makers so highly appreciate. In passing by a Frencheart you must therefore be carefulto allow for, at least, six inches of concealed axle, which ever and anon darts out fi'0m the nave, like tile tongue fl'om the mouth of a snake. The middle portion of a F r e n c h road, which is generally paved, is so m u c h arched, that carts arc naturally induced, if not compelled, to take the centre o f it; so that those g-oinff in opposite directions invariably use the same track, o u t of which they only momentarily move at the instant of meeting'. Deep ruts a r e thus soma worn even in the most substantial p a v e m e n t - - t h e difficulty of repairing" which, unless throughout the whole extent at once, m u s t be snfficiently obvious. I hay,., here alhnted only to the two or three main roads of France. I n the others, which they regard as secondary ones, I have travelled for scores o f miles where the ruts have been so deep, that on one of nay wheels falling in~ it could not touch the bottom, b u t rested on the nave and axle. Besides the consequences of the defects of locality and of materlaJs, I have r e marked three principal causes of the speedy deterioration of highways. T h e i r being too wide--too much a r c h e d ~ o r having but little traffic upon t h e m ; ~ all which circumstances'conduce to the carriag'es k e e p i n g in one track, and to t h e consequent fi~rmation of ruts and holes. VFhe only [tefect in the English high roads, is their having so many unnecessary, and often dangerous turning~s and windings. I f : r e and there, they are even too narrow~ and buildings;have been sufi~ered to encroach u p o n them.
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use, at all commensurate to the great imonveniene~ and ~ e n s e at, tertdingitsformatiort. Aceordin~ to this method, the Oldpavemen:t is taken u p for a space of about tl~irty or forty yards at a ti6i~, and a regular road is laid with gravel an'f broken granite, ~ laM'~dam, upon which the pavinz stones are subsequently laid, and the: Ol~ra, tm i repeated for another forty yards. It, however, takes at leg~ ten clays or a fortnight to harden in succession each of these traetS~ su~ciently for the application of the paving stones, and these sue, cessive i~ar.denings are to be performed by the carts( carriages, and horses ot the public; with so much inconvenience anti annoyance as amount to a complete nuisance! After all, this pavement of such troublesome and expemive production, will not stand much longer than the ohl. When any p})rtiou of it has to be taken up, for pipe la)'ing, &c., how is that'portiou to be restored to an equal density with the rest? In tact, there is no species of pavement that 1 have ever seen or heard of, to the application of which to the streets of London, there would i~ot be many great objections. 1, however, flatter myself, that, atter much ob;~ervation and reflection, I have hit upon a method that would combine economy with dt~rabilily, and wlth~wh
ESSAYS ON BLEACHING. B y James l~ennie, ./t. M. Lecturer on Philosophy, 4"c. ~fe. Londoi~, ~To, II.~BLEACHING APPARATUS.
S~CTIO~ I I . ~ T h e apparatus for preparing the difi'e~ent combinations of chlorine with the alkalies, with lime, or with water, has also been somewhat improved since its first invention by Berthollet, but this ha~ only been the case in the materials used for its construction, anti in some of its less important parts : the principles on which it is now made, are the same as in tile earliest periods of its employment. Mr. Rupp, (Manchester Memoirs, V. p. 80l, in a note,) complains of Berthollet's apparatus as too complex for a manufactory, and recommends a range of|bur, five, or six hogsheads, or rum puncheons, connected with one another in the manner of Woulfe's apparatus, as being greatly preferable. It will be recollected that this is exactly the method which was resorted to by the Aberdeetl bleachers, when they found it inconvenient to use glass,