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be fixed ; the points a and k being fixed, the point b, of thetriangle A k b, will likewise be fixed. Again, the points band k being fixed, the point l will also be fixed : in the samemanner, all the remaining points, C, m, d, n, o, f, p, g, l, maybe proved to be stationary in respect of the points A, h ; andthe whole figure being kept in equilibrio by any three forces,acting in the plane of the figure at any three angles, theaction of the forces will only tend to compress or extend thetimbers in the direction of their length.

| In the construction of this truss, the triangular parts maybe constructed all in the same plane, and the pieces, bd andd f, may be halved upon the pieces c A and e g ; but theutmost care must be taken to secure the several pieces con-curring at each of the angles, by bolting, or iron straps, asno dependence can be put in any such joint without iron;but perhaps the best method of any is to halve the thick-nesses of the pieces a c, c e, e g, at the points C and e, andalso the pieces ab,bc,CD,db,ip,fg, at the points b, d, f:then bolting the ends, a and c, of the pieces b a, b c, the endc and e, of the pieces d c and d e, and the ends e and g ofthe pieces f e and f g, and then fixing double braces, b d,d f ; that is, fixing B D upon one side of the truss, andanother upon the other side of the truss, opposite to it ; also! fixing df upon one side, and another opposite to it.

I Figure 6, of the same plate, represents the manner of con-structing a centre according to the principles ofPerronet, the] celebrated French engineer; but the disposition of the[ | timbers, forming only a series of quadrilaterals, gives nothingj | but immutability of figure ; and can, therefore, only derive1 its stiffness from the resistance of the joints.

! Having thus given a general account of the principles ofcentering, as connected with the article Carpentry, we mustrefer our readers to the article Stone Bridge for its appli-cation, and other practical remarks in the construction.

MECHANICAL POWERS, such machines as are usedfor raising greater weights, or overcoming greater resis-tances, than could be effected by the natural strength withoutthem ; the power or strength being applied to one part of the; machine, and another part of the machine applied to the| weight or resistance. In treating of each of which, two' principal problems ought to be resolved.

The first is, to determine the proportion which the powerand weight ought to have to each other, that they may justsustain one another, or be in equilibrio.

The second is, to determine what ought to be the propor-tion of the power and weight to each other in a givenmachine, that it may produce the greatest effect possible, ina given time.

As to the first problem, this general rule holds in allpowers: suppose the engine to move, and reduce the velocitiesof the power and weight to the respective directions in whichthey act; find the proportions of these velocities; then, ifthe power be to the weight as the velocity of the weight is tothe velocity of the power,—or, which amounts to the samething, if the power multiplied by its velocity, gives the sameproduct as the weight multiplied by its velocity,—this is thecase wherein the power and weight sustain each other, andare in equilibrio; so that in this case the one would not pre-vail over the other, if the engine were at rest; and if inmotion, it would continue to proceed uniformly, were it notfor the friction of its parts, and other resistances.

The second general problem in mechanics is, to determinethe proportion which the power and weight ought to bear toeach other, that when the power prevails, and the machine isin motion, the greatest effect possible may be produced by itin a given time. It is manifest, that this is an inquiry of thegreatest importance, though few have treated of it. When

the power is only a little greater than that which is #

to sustain the weight, the motion is too slow ; and thou a ^greater weight is raised in this case, it is not suffi'' 1 ® 11 ^compensate the loss of time. When the weight is muchthan that which the power is able to sustain, it is raiseless time ; and this may happen not to be sufficient to c ^pensate the loss arising from the smallness of the load’ought, therefore, to be determined when the product o| ,weight, multiplied by its velocity, is the greatest P° ssl . fe nfor this product measures the effect of the engine in a S\ ^time, which is always the greater in proportion as the j twhich is raised is greater, and as the velocity with win 0is raised is greater. s ;$

The simple machines by which power is gained are ^in number, viz., the lever, the wheel and axle, orperitrochio, the pulley (or rather system of pulley 8 /’ tsinclined plane, the wedge, and the screw. Of these, all •- ^of mechanical engines consist; and in treating of them, 'to settle their theory, we must consider them as mecha nlC ‘exact, and moving without friction. For the propertiesapplications of the mechanical powers, see Lever, *(inclined), Pullet, Wedge, and Wheel . c ;r-

MEDALLION (from the French ), in architecture, a ^cular tablet, on which are embossed figures, bustos, or-ornaments. , 0 ge

MEDIAEVAL ARCHITECTURE, comprises all ^styles which were prevalent during what are coin®°| oithough unfairly, styled the dark ages, viz., from thethe Roman empire to the revival of classic art. It ( ; a n,those styles which may be peculiarly termed Ch rlS ( } t eamongst which may be enumerated the Romanesq"®’' jjicByzantine, and Lombardic , and more especially thestyle. These are treated of under their distinctive tin® ’ fl fMEDIAN./E, in Vitruvius , the columns in the midthe portico, where the intercolumniation is enlarged. , orMEMBER (from the French ) any part of an edi» c ’any moulding in a collection. ,$te'

MENSURATION (from the Latin mensura, i (1ment) that branch of mathematics which is ern P|. 0 ? 0< jie9 >ascertaining the extension, solidities, and capacities of jb©and in consequence of its very extensive application , t [i6various purposes of life, it may be considered as one ^ eS :most useful and important of all the mathematicalin fact, mensuration, or geometry, which were 8 j l(JI iC©nearly synonymous terms, seem to have been the root t j c,all the other exact sciences, with the exception of a 1 ' 1have derived their origin. . (if 1 .

As soon as men began to form themselves into soCie jtl'idirect their attention towards the cultivation of thebecame as necessary to have some means of di stlI ?°. 0l) #8“one person’s allotment from another, both as to pos'l 1quantity, as it did to enumerate the number of fd iel ^ r g8 v ®and herds ; and hence, in all probability, the fo rI °j.rise to the science of mensuration, as the latter did ° eaC b 0arithmetic ; and though we may easily imagine the ^ jt 1them remained for ages in a rude uncultivated statei ** jfrom this period that we must date their commence*! 1 fe rewtherefore, to state the precise time when they were o ^.. lC e <8 jor by whom they were first introduced, would be to ^ s |i^the origin of society itself : on this head, therefoi e » g firobarely observe, that in all probability theythe humblest efforts of unassisted genius, called f° y In'great mother of invention, necessity ; and thatsince grown up by slow and imperceptible degie®have at length acquired the dignity of the m0 0 ^a ll \,sciences ; as the acorn which is first accidentally . gt jofield, is in due course of time converted into the *** J