ing should be perfectly drowned in water, and the fluid strained and run into a pit, from whence, after remaining if necessary during a whole winter, or more, it may be cut out hot, as smooth as custard, and capable of receiving a very great proportion of sand without becoming harsh and brittle. All substances containing a quantity of carbon combined with oxygen, are highly useful ingredients; such as skim-milk, whey, molasses, skimmings of sugar pans, sugar, vinegar, beer, wine lees, all sorts of washings of breweries, distilleries, and sugar houses. These substances, by giving their carbon to the lime, convert the cement into a calcareous sand stone in a more expeditious manner, than by any process dependent upon attraction from the atmosphere. But though blood, oils, and curds have been recommended, the animal or vegetable mucilage they contain is injurious to their durability. The celebrated cement of Adams, of which oil was a considerable ingredient, after standing with every appearance of permanence for some years, began then to fail, and actions being brought against him by Lord Stanhope (Mahon) and others upon his warrantec, this artist, so deservedly considered as one of the brightest ornaments of the English school, was ruined in fortune, by the damages awarded against him. Before I close my remarks on this cement, I will add, that all cements of every kind acquire the quality of hardening in proportion to the working and beating they get, and no remark can be more just than that of Mr. Joncs, that "the patience bestowed will amply reward you." 2. and 3. Use of Timber in Walls. In all professions, there are prejudices of practice, which become national. That of filling their walls with what they call bond timbers is one of those practices, which every English architect receives by inheritance. The white ants have been serviceable to architecture in expelling it from Bengal. A piece of timber bedded in a wall can be of service, only for the following uses: 1. If it be laid under the joists or timbers of a floor, it serves to spread the weight equally along the wall; or if under the end of a girder, to give to the girder a broad base or bearing upon the wall. 2. To tie the wall together lengthwise, in order to prevent its spreading at the top. When the foundation is equal, it is evident that bond timbers become useless, excepting in the first case.-But it has been customary in England to put them regularly into the walls, from the bottom to the top, at the distance of several feet asunder; taking care that one piece shall be laid so as to receive the skirting, another the surbase, &c.—A specimen of this practice might have been seen in the north wing of the Capitol, in which the bond timber had a considerable share in the failure of the work, and in the necessity of a thorough rebuilding of the interior. Bond timbers do injury by the following means: A piece of timber laid along the wall, takes up in its whole length the place of solid materials. It is laid in wet mortar; and the work above, as the moisture descends, keeps it wet for some time. It swells. It is on three sides inaccessible to the air. At last it dries with the wall and shrinks. If the timber occupies less than half the thickness of the wall, the wall will not follow it, the outer part being the heaviest, but the timber occupying less space than before, becomes loose. In heavy buildings, being moist and excluded from the air for a long time, it will probably be rotten beforc that time. The plaistering that covers it will crack. In fact, if it ever was useful, it ceases entirely to be so. To prevent these timbers from moving outwards as they get loose, they have some times been made thicker within the wall than on their exterior side, sometimes they have been tied in by short cross pieces. But all this does not remove the evil. As to the convenience of bond timbers for fastening on the the dressings—the same end may be much better accomplished by driving in very dry oak plugs, after the building is finished and dry. If however the foundation be unequal, it is evident that the tendency of one part of the wall to sink into a soft place while the rest is supported by a harder part of the foundation can only be resisted by timber strong enough to hold up the wall that is over it. This is very inadequately done by timbers lying at distances from each other only on the inside of the work. Where there is such a foundation, it is infinitely better to combine the strength of all these timbers, and, laying them in the trench, to cover them well from the access of air, and build the wall upon them. But piling is always the best thing that can be done even if no very hard bottom can be reached.Bond timbers ought never to be depended on. I have already extended my remarks to a length which I did not intend or foresee-and yet I cannot avoid adding to them what I think necessary to meet the inclination, supported by our Italian prejudices, which the very clear and able manner in which Mr. Jones has described the Hindoo method of constructing terraces might excite, to make further experiments on the construction of flat roofs for our American houses. In crowded cities, where the court yards are generally small and buried from the light and air by tall houses, terraces on the roofs are almost necessary, for the view and enjoyment of the heavens, and for many domestic purposes. But they are every where, excepting beyond the region of frost, the most difficult and precarious part of the construction of the house. Lead, copper, sheet-iron, tarred and sanded paper, calcareous cements, all have been tried, all have had temporary success, all have produced permanent inconvenience. The range of the expansion and contraction of lead, together with the range through 100 degrees of Fahrenheit's thermometer, to which our climate is subject, renders lead an improper metal for the purpose of a terrace. It is liable to be torn to pieces by its own motion.-Copper is very expensive, and is soon corroded by verdigrease. Iron requires constant painting, is sooner corroded by rust, but is otherwise the most convenient material and the cheapest.-Sand, tar, and paper, succeed better to the northeastward, than in the middle and southern States, but is not easily or securely to be connected with gutters, and is a dirty sort of covering.-Calcareous cements have in no instance as yet succeeded, and the smallest crack, admitting water in winter. during the frost, is fatal to them. Fortunately, we have no rational use for flat roofs. Our cities are roomy, and our habits and their population will for many centuries keep them so. Our houses are low and our yards airy. I cannot conceive a single argument in favour either of the beauty or utility of terrace roofs in our country. Those that have them scarcely ever use them. The cold in winter and the heat in summer drive us from them. A beautiful prospect may justify the partial use of them, in particular situations, but neither architectural beauty, nor the general wants of our wintry climate call for their introduction.-To the southward beyond the reach of frost, however, the information contained in this paper may be highly useful. No. LVII. A general method of finding the roots of numeral equations to any degree of exactness; with the application of Logarithms to shorten the operation: by John Garnett of New Brunswick N. Jersey. Read January 20th, 1809. Suppose an equation, ax+bx2+cx3+dx4+ex5 &c. v, to find x. RULE. Find, by trial, any near root as x.' Then, by substitution, ax'+bx'2+cx'3+dx'4+ex's &c. = v Multiply each term by the index of the power of x', and divide by x'. B. Multiply each term again by its power of x', and divide by 4x'. Let the products, d+5ex, &c.D: and so on, continually, until all the powers of x' are destroyed, so that e, &c.=E. Then will Ax +Bx2 +Cx"3 +Dx"4 +Ex"5 &c. v-v', be a New Equation whose roots will all be less by x', and the value, v-v', less by v' than the roots of the original equation. And if the roots and value of this new equation be diminished in the same manner, by another near root, as x'', and so on, continually, the root and value may become less than any assignable quantity, and the sum of all the near roots will be equal to x, the root of the original equation. Ff This rule will be found virtually the same as that given by Newton, Raphson, Jones, Simpson &c. and, if applied to the extraction of simple powers, will be found the same precisely as the one usually given in common arithmetic, thus for Whence x=x+x"+x′′ - 463, the required Root This form will serve for all numeral equations, and with nearly the same labour; as for |