little at its joints) is regularly tacked down upon the sheeting, under the copper covering, as the work proceeds from eaves to ridge. It prevents the jingling sound of hail or rain falling upon the roof, and answers another purpose to be mentioned by-and-by. In order to shew the regular process of laying down the roof, we must begin with fastening two sheets together lengthwise. The edges of two sheets are laid down so as to lap or cover each other an inch, and a slip of the same copper, about three and a half inches broad, called the reeve, is introduced between them. Four oblong holes, or slits, are then cut or punched through the whole, and they are fastened or riveted together by copper nails, with small round shanks and flat heads. Indents are then cut 14 inch deep upon the seam at top and bottom. The right hand sheet and the reeve are then folded back to the left. The reeve is then folded to the right, and the sheets being laid on the roof in their place, it is nailed down to the sheeting with flat-headed short copper nails. The right hand sheet is then folded over the reeve to the right, and the whole beat down flat upon the cartridge paper covering the sheeting, and thus they are fastened and laid in their places, by nailing down the reeve only; and by reason of the oblong holes through them and the reeve, have a little liberty to expand or contract with the heat and cold, without raising themselves from the sheeting, or tearing themselves or the fastening to pieces. Two other sheets are then fixed together, according to the first and second operations above, and their seam, with the reeve, introduced under the upper ends of the seam of the former, so as to cover down about two inches upon the upper ends of the Y 2 up former former sheets: and so far the cartridge paper is allowed to cover the two first sheets. This edge of the paper is dipped in oil, or in turpentine, so far before its application, and thus a body between the sheets is formed impenetrable to wet, and the reeve belonging to the two last sheets is nailed down to the sheeting as before, and the left hand sheet is turned down to the right. Four sheets are now laid down, with the seam or joint rising to the ridge; and thus the work is continued, both vertically and horizontally, till the roof be covered, the sides and ends of each sheet being alternately each way, undermost and uppermost. The price for copper, nails, and workmanship, runs at about eight pounds ten shillings per hundred weight, or two shillings and three-pence per foot, superficial, exclusive of the lappings; and about two shillings and eight-pence per foot upon the whole; which is rather above half as much more as the price of doing it well with lead. TO PETER COLLINSON, ESQ. AT LONDON. SIR, Magical Square of Squares. ACCORDING to your request I now send you the arithmetical curiosity, of which this is the history. Being one day in the country, at the house of our common friend, the late learned Mr. Logan, he showed me a folio French book filled with magic squares, wrote, if I forget not, by one M. Frenicle, in which he said the author had discovered great ingenuity and dexterity dexterity in the management of numbers; and though several other foreigners had distinguished themselves in the same way, he did not recollect that any one Englishman had done any thing of the kind remarka ble. I said, it was, perhaps, a mark of the good sense of our English mathematicians, that they would not spend their time in things that were merely difficiles nuga, incapable of any useful application. He answered, that many of the arithmetical or mathematical questions, publicly proposed and answered in England, were equally trifling and useless. Perhaps the considering and answering such questions, I replied, may not be altogether useless, if it produces by practice an habitual readiness and exactness in mathematical disquisitions, which readiness may, on many occasions, be of real use. In the same way, says he, may the making of these squares be of use. I then confessed to him, that in my younger days, having once some leisure (which I still think I might have employed more usefully) I had amused myself in making these kind of magic squares, and, at length, had acquired such a knack at it, that I could fill the cells of any magic square of reasonable size, with a series of numbers as fast as I could write them, disposed in such a manner as that the sums of every row, horizontal, perpendicular, or diagonal, should be equal; but not being satisfied with these, which I looked on as common and easy things, I had imposed on myself more difficult tasks, and succeeded in making other magic squares, with a variety of properties, and much more curious. He then shewed me several in the same book, of an uncommon and more curious kind; but as I thought none of them equal to some I remembered to have made, he desired me to let him see them; and accordingly, the next time I visited him, I carried him a square of 8, which I found among my old papers, and which I will now give you, with an account of its properties. (See Plate XI.) The properties are, 1. That every strait row (horizontal or vertical) of 8 numbers added together makes 260, and half each row half 260. 2. That the bent row of 8 numbers, ascending and descending diagonally, viz. from 16 ascending to 10, and from 23 descending to 17; and every one of its parallel bent rows of 8 numbers make 260.-Also the bent row from 52 descending to 54, and from 43 ąscending to 45; and every one of its parallel bent rows of 8 numbers make 260.-Also the bent row from 45 to 43, descending to the left, and from 23 to 17, descending to the right, and every one of its parallel bent rows of 8 numbers, make 260.-Also the bent row from 52 to 54, descending to the right, and from 10 to 16, descending to the left, and every one of its parallel bent rows of 8 numbers make 260.---Also the parallel bent rows next to the above-mentioned, which are shortened to 3 numbers ascending, and 3 descending, &c. as from 53 to 4 ascending, and from 29 to 44 descending, make, with the two corner numbers, 260.---Also the 2 numbers 14, 61 ascending, and 36, 19 descending, with the lower 4 numbers situated like them, viz. 50, 1, descending, and 32, 47, ascending, make 260.---And, lastly, the 4 corner numbers, with the 4 middle numbers, make 260. So this magical square seems perfect in its kind. But these are not all its properties; there are 5 other curious |