Part 24

In making the first fire in a morning with this grate, there is nothing particular to be observed. It is made as in other grates, the coals being put in above, after taking out the upper bar, and replacing it when they are in. The round figure of the fire when thoroughly kindled is agreeable, it represents the great giver of warmth to our system. As it burns down and leaves a vacancy above, which you would fill with fresh coals, the upper bar is to be taken out, and afterwards replaced. The fresh coals, while the grate continues in the same position, will throw up as usual a body of thick smoke. But every one accustomed to coal fires in common grates must have observed, that pieces of fresh coal stuck in below among the red coals have their smoke so heated as that it becomes flame as fast as it is produced, which flame rises among the coals and enlivens the appearance of the fire. Here then is the use of this swivel grate. By a push with your tongs or poker, you turn it on its pin till it faces the back of the chimney, then turn it over on its axis gently till it again faces the room, whereby all the fresh coals will be found under the live coals, and the greater part of the smoke arising from the fresh coals will in its passage through the live ones be heated so as to be converted into flame: whence you have much more heat from them, and your red coals are longer preserved from consuming. I conceive this construction, though not so complete a consumer of all the smoke as the vase, yet to be fitter for common use, and very advantageous. It gives too a full sight of the fire, always a pleasing object, which we have not in the other. It may with a touch be turned more or less from any one of the company that desires to have less of its heat, or presented full to one just come out of the cold. And supported in a horizontal position, a tea-kettle may be boiled on it.

The author's description of his Pensylvania fireplace, first published in 1744, having fallen into the hands of workmen in Europe, who did not, it seems, well comprehend the principles of that machine, it was much disfigured in their imitations of it; and one of its main intentions, that of admitting a sufficient quantity of fresh air warmed in entering through the air-box, nearly defeated, by a pretended improvement, in lessening its passages to make more room for coals in a grate. On pretence of such improvements, they obtained patents for the invention, and for a while made great profit by the sale, till the public became sensible of that defect, in the expected operation. If the same thing should be attempted with this vase stove, it will be well for the buyer to examine thoroughly such pretended improvements, lest, being the mere productions of ignorance, they diminish or defeat the advantages of the machine, and produce inconvenience and disappointment.

The method of burning smoke, by obliging it to descend through hot coals, may be of great use in heating the walls of a hot-house. In the common way, the horizontal passages or flues that are made to go and return in those walls, lose a great deal of their effect when they come to be foul with soot; for a thick blanket-like lining of soot prevents much of the hot air from touching and heating the brick work in its passage, so that more fire must be made as the flue grows fouler: but by burning the smoke they are kept always clean. The same method may also be of great advantage to those businesses in which large coppers or caldrons are to be heated.

_Written at Sea, 1785._

FOOTNOTE:

[60] From the Transactions of the American Philosophical Society, in which it was read January 28, 1786. _Editor._

TO MISS STEPHENSON.

_Method of Contracting Chimneys. Modesty in Disputation._

_Craven-Street, Saturday Evening, past 10._

The question you ask me is a very sensible one, and I shall be glad if I can give you a satisfactory answer. There are two ways of contracting a chimney; one, by contracting the opening _before_ the fire; the other, by contracting the funnel _above_ the fire. If the funnel above the fire is left open in its full dimensions, and the opening before the fire is contracted; then the coals, I imagine, will burn faster, because more air is directed through the fire, and in a stronger stream; that air which before passed over it, and on each side of it, now passing _through_ it. This is seen in narrow stove chimneys, when a sacheverell or blower is used, which still more contracts the narrow opening.--But if the funnel only _above_ the fire is contracted, then, as a less stream of air is passing up the chimney, less must pass through the fire, and consequently it should seem that the consuming of the coals would rather be checked than augmented by such contraction. And this will also be the case, when both the opening _before_ the fire, and the funnel _above_ the fire are contracted, provided the funnel above the fire is more contracted in proportion than the opening before the fire.--So you see I think you had the best of the argument; and as you notwithstanding gave it up in complaisance to the company, I think you had also the best of the dispute. There are few, though convinced, that know how to give up, even an error, they have been once engaged in maintaining; there is therefore the more merit in dropping a contest where one thinks one's self right; it is at least respectful to those we converse with. And indeed all our knowledge is so imperfect, and we are from a thousand causes so perpetually subject to mistake and error, that positiveness can scarce ever become even the most knowing; and modesty in advancing any opinion, however plain and true we may suppose it, is always decent, and generally more likely to procure assent. Pope's rule

To speak, though sure, with seeming diffidence,

is therefore a good one; and if I had ever seen in your conversation the least deviation from it, I should earnestly recommend it to your observation.

I am, &c.

B. FRANKLIN.

TO MICHAEL HILLEGRAS ESQ.

_Respecting covering Houses with Copper.[61]_

_London, March 17, 1770._

DEAR SIR,

I received your favour of November 25, and have made enquiries, as you desired, concerning the copper covering of houses. It has been used here in a few instances only, and the practice does not seem to gain ground. The copper is about the thickness of a common playing card, and though a dearer metal than lead, I am told, that, as less weight serves, on account of its being so much thinner, and as slighter woodwork in the roof is sufficient to support it, the roof is not dearer on the whole, than one covered with lead. It is said, that hail and rain make a disagreeable drumming noise on copper; but this I suppose is rather fancy; for the plates being fastened on the rafters, must, in a great measure, deaden such sound. The first cost, whatever it is, will be all, as a copper covering must last for ages; and when the house decays, the plates will still have intrinsic worth. In Russia, I am informed many houses are covered with plates of iron tinned, such as our tin pots and other vases are made of, laid on over the edges of one another like tiles; and which, it is said, last very long, the tin preserving the iron from much decay by rusting. In France and the Low Countries, I have seen many spouts or pipes for conveying the water down from the roofs of houses, made of the same kind of tin plates soldered together; and they seem to stand very well.

With sincere regard, I am,

Yours, &c.

B. FRANKLIN.

FOOTNOTE:

[61] The two following letters, and the accompanying paper, appeared in several periodical publications, both English and American, many years before the death of Franklin, which is sufficient to give them authenticity. _Editor._

TO SAMUEL RHOADS, ESQ.

_On the same Subject._

_London, June 26, 1770._

DEAR FRIEND,

It is a long time since I had the pleasure of hearing from you directly. Mrs. Franklin has indeed now and then acquainted me of your welfare, which I am always glad to hear of. It is, I fear, partly, if not altogether, my fault, that our correspondence has not been regularly continued. One thing I am sure of, that it has been from no want of regard on either side, but rather from too much business, and avocations of various kinds, and my having little of importance to communicate.

One of our good citizens, Mr. Hillegras, anxious for the future safety of our town, wrote to me some time since, desiring I would enquire concerning the covering of our houses here with copper. I sent him the best information I could then obtain, but have since received the inclosed from an ingenious friend, who is what they call here a civil engineer. I should be glad you would peruse it, think of the matter a little and give me your sentiments of it. When you have done with the paper, please to give it to Mr. Hillegras. I am told by Lord Despencer, who has covered a long piazza, or gallery, with copper, that the expence is charged in this account too high, for his cost but one shilling and ten-pence per foot, all charges included. I suppose his copper must have been thinner. And, indeed, it is so strong a metal, that I think it may well be used very thin.

It appears to me of great importance, to build our dwelling houses, if we can, in a manner more secure from danger by fire. We scarcely ever hear of fire in Paris. When I was there I took particular notice of the construction of their houses, and I did not see how one of them could well be burnt, the roofs are slate or tile, the walls are stone, the walls generally lined with stucco or plaster, instead of wainscot, the floors of stucco, or of six square tiles painted brown, or of flag stone, or of marble; if any floors were of wood, it was of oak wood, which is not so inflammable as pine. Carpets prevent the coldness of stone or brick floors offending the feet in winter, and the noise of treading on such floors, overhead, is less inconvenient than on boards. The stairs too, at Paris, are either stone or brick, with only a wooden edge or corner for the step; so that on the whole, though the Parisians commonly burn wood in their chimneys, a more dangerous kind of fuel than that used here, yet their houses escape extremely well, as there is little in a room that can be consumed by fire except the furniture: whereas in London, perhaps scarcely a year passes in which half a million of property and many lives are not lost by this destructive element. Of late, indeed, they begin here to leave off wainscoting their rooms, and instead of it cover the walls with stucco, often formed into pannels like wainscot, which being painted, is very strong and warm. Stone staircases too, with iron rails, grow more and more into fashion here: but stone steps cannot, in some circumstances, be fixed; and there, methinks, oak is safer than pine; and I assure you, that in many genteel houses here, both old and new, the stairs and floors are oak, and look extremely well. Perhaps solid oak for the steps would be still safer than boards; and two steps might be cut diagonally out of one piece. Excuse my talking to you on a subject with which you must be so much better acquainted than I am. It is partly to make out a letter, and partly in hope, that, by turning your attention to the point, some methods of greater security in our future building may be thought of and promoted by you, whose judgment I know has deservedly great weight with our fellow-citizens. For though our town has not hitherto suffered very greatly by fire, yet I am apprehensive, that some time or other, by a concurrence of unlucky circumstances, such as dry weather, hard frost, and high winds, a fire then happening may suddenly spread far and wide over our cedar roofs, and do us an immense mischief. I am,

Yours, &c.

B. FRANKLIN.

_Paper referred to in the preceding Letter._

The carpentry of the roof being formed with its proper descents, is, in the first place, sheeted or covered with deals, nailed horizontally upon the rafters, after the same manner as when intended to be covered with lead. The sheets of the copper for this covering are two feet by four, and for covering the slopes of the roof are cast so thin, as to weigh eight or nine pounds, and for covering the flats or gutters, ten or eleven pounds each, or about one pound, or a pound and a quarter, to the superficial foot.

A string of strong cartridge paper (over-lapping a 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 1¾ 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 up 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 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.

_Magical Square of Squares._

SIR,

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 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 remarkable.

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 nugæ_, 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_ V. Fig. 3.)

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 ascending 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 ones, which, at some other time, I will explain to you.

Mr. Logan then shewed me an old arithmetical book, in quarto, wrote, I think, by one Stifelius, which contained a square of 16, that he said he should imagine must have been a work of great labour; but if I forget not, it had only the common properties of making the same sum, viz. 2056, in every row, horizontal, vertical, and diagonal. Not willing to be out-done by Mr. Stifelius, even in the size of my square, I went home, and made, that evening, the following magical square of 16, which, besides having all the properties of the foregoing square of 8, _i. e._ it would make the 2056 in all the same rows and diagonals, had this added, that a four-square hole being cut in a piece of paper of such a size as to take in and show through it just 16 of the little squares, when laid on the greater square, the sum of the 16 numbers so appearing through the hole, wherever it was placed on the greater square, should likewise make 2056. This I sent to our friend the next morning, who, after some days, sent it back in a letter with these words: "I return to thee thy astonishing or most stupendous piece of the magical square, in which----" but the compliment is too extravagant, and therefore, for his sake, as well as my own, I ought not to repeat it. Nor is it necessary; for I make no question but you will readily allow this square of 16 to be the most magically magical of any magic square ever made by any magician. (_See the Plate._)

I did not, however, end with squares, but composed also a magic circle, consisting of 8 concentric circles, and 8 radial rows, filled with a series of numbers from 12 to 75 inclusive, so disposed as that the numbers of each circle, or each radial row, being added to the central number 12, they make exactly 360, the number of degrees in a circle; and this circle had, moreover, all the properties of the square of 8. If you desire it, I will send it; but at present, I believe, you have enough on this subject. I am, &c.

B. FRANKLIN.

TO THE SAME.

_Magical Circle._

SIR,

I am glad the perusal of the magical squares afforded you any amusement. I now send you the magical circle. (_See Plate_ XII.)

Its properties, besides those mentioned in my former, are these.

Half the number in any radial row, added with half the central number, make 180, equal to the number of degrees in a semi-circle.

Also half the numbers in any one of the concentric circles, taken either above or below the horizontal double line, with half the central number, make 180.

And if any four adjoining numbers, standing nearly in a square, be taken from any part, and added with half the central number, they make 180.

There are, moreover, included four other sets of circular spaces, excentric with respect to the first, each of these sets containing five spaces. The centres of the circles that bound them, are at A, B, C, and D. Each set, for the more easy distinguishing them from the first, are drawn with a different coloured ink, red, blue, green, and yellow.[62]

These sets of excentric circular spaces intersect those of the concentric, and each other; and yet the numbers contained in each of the twenty excentric spaces, taken all around, make, with the central number, the same sum as those in each of the 8 concentric, viz. 360. The halves, also of those drawn from the centres A and C, taken above or below the double horizontal line, and of those drawn from centres B and D, taken to the right or left of the vertical line, do, with half the central number, make just 180.

It may be observed, that there is not one of the numbers but what belongs at least to two of the different circular spaces; some to three, some to four, some to five; and yet they are all so placed as never to break the required number 360, in any of the 28 circular spaces within the primitive circle.

These interwoven circles make so perplexed an appearance, that it is not easy for the eye to trace every circle of numbers one would examine, through all the maze of circles intersected by it; but if you fix one foot of the compasses in either of the centres, and extend the other to any number in the circle you would examine belonging to that centre, the moving foot will point the others out, by passing round over all the numbers of that circle successively. I am, &c.

B. FRANKLIN.

FOOTNOTE:

[62] In the plate they are distinguished by dashed or dotted lines, as different as the engraver could well make them.

TO THE REV. FATHER BECCARIA.

_Describing a new musical Instrument composed of Glasses._

_London, July 13, 1762._

REV. SIR,