صور الصفحة
PDF
النشر الإلكتروني

Indeed, youth is generally so much more delighted with mathematical studies, than with the unpleasant tasks that are sometimes imposed upon them, that I have known some reclaimed by them from idleness and neglect of learning, and acquire, in time, a habit of thinking, diligence, and attention-qualities which we ought to study by all means to beget in their desultory and roving minds.

[To be continued.]

ON THE STRENGTH OF TIMBER.

By John Baines, jun.

ACCORDING to the theory of mechanics, the transverse strengths of prismatic beams of timber, lying parallel to the horizon, are as the areas of their sections multiplied into the distance of their centres of gravity from the place where their fractures terminate, and that product divided by their lengths, or weights. In order, therefore, to examine how near this theory approaches to real practice, we have collected the following experiments, made with oak timber by Banks, Buffon, and Emerson. In these experiments the ends of the beams were not fixed down, but laid loose on their supporters. From these experiments we have calculated, according to theory, the weight required to break a beam one foot long and one inch square, taking the experiment made on the beam seven feet long and four inches square for the standard, as being an ordinary-sized beam. The weights given in the following table are pounds avoirdupoise,

[blocks in formation]

First, to ascertain whether the lateral strengths of prismatic beams be as the cubes of their like sides, or not, we will compare the 4th, 7th, 14th, and 23rd experiments with the 5th, 8th, 16th, and 25th, in the following manner, viz.

I. As 18: 187::28:

[ocr errors]

1496, too little by

89, or the 0595 1150, or the ⚫1108 2950, or the 0802 76, or the 0039 whole.

part

of

the

II. As 43 5312::53: 10375, too little by
III. As 63 : 15525:: 83: 36800, too little by
IV. As 53: 7125::73: 19551, too much by

Hence it appears that the strengths of beams of the same length, are not exactly as the cubes of their like sides; but the difference is so inconsiderable in the 4th stating, as almost to establish the rule. We will therefore compare the 9th and 17th experiments with the 11th and 21st.

V. As 63: 18950:: 88: 44918, too little by 2731, or the 06082 part of VI. As 43: 4025 :: 8: 32200, too little by 600, or the 0186 the whole From which we are led to this conclusion, viz. that although the above results do not exactly correspond with the experiments, yet there is reason to believe that if the timber were equally strong from the centre to the circumference, they would deviate but little. This, however, is not the case, for in tracing the process of vegetation, we observe that the ligneous coats of a tree, formed by its annual growth, are concentric cylinders, thrust into each other, and united by a medullary substance. These, it is evident, are not all of equal strength; for, those nearest the centre, being the oldest, are undoubtedly the hardest and strongest. Hence, a small beam, cut from the centre, will be proportionably stronger than a large one of the same length, cut from the same tree; and this agrees with experiment. Secondly, To know whether the strengths of prismatic beams of the same area be inversely as their lengths, or not, compare the 9th, 15th, 21st, and 27th experiments with the 14th, 25th, 26th, and 31st. I. As 7: 18950 :: 8: 16581, too much by II. As 8: 26050:: 10: 20840, too much by III. As 9: 32800 :: 10: 29520, too much by IV. A814: 5300::20: 3710, too much by Here, then, is a wide difference in the 4th stating, both from the theory and the other three; and this difference has been suggested to be owing, at least in part, to the weights of the beams. We will, therefore, add the weight of each beam to the weight given in the above table, and then state as below, viz.

I. As 7: 19051 :: 8: 16669, too much by II. As 8: 26173 :: 10: 20938, too much by III. As 9: 33031; 10: 29728, too much by IV. Asl4: 5441 :: 20: 3809, too much by

1056, or the 0637
1365, or the
1770, or the
485, or the

part

0695

of

0600 the 1308) whole

of

1028, or the '0616 part
1266, or the 0644
1721, or the 0579
383, or the 1006) whole

S

the

But the results still differ from the theory, and among each other; they are, however, nearer the truth than before, and probably the inequality of the compression before, and at the time of breaking, may account for the remaining difference.

The following deductions are made from what has been above investigated, viz. That

1. The mean strength of a rectangular beam one foot long, and one inch square, is 576 pounds.

2. In working proportions for the strength of timber when the lengths of the beams are the same, the results ought to be increased by the one eighteenth part of the whole when the third term of the stating is greater than the first, but decreased by the one-nineteenth when it is the less.

3. When the ends of the beams are the same, and the weight of the beam not taken into the account, the result ought to be decreased the onefourteenth part of the whole when the third term of the stating is greater than the first, but increased by the one-thirteenth when it is the less. But when the weight of the beam is added, the result must be decreased the one-fifteenth part in the former case, and increased the one-fourteenth in the latter.

It is perhaps necessary to add, that the weights expressed in the above table, are snch as will, in a minute or two, break the beams; and that two-thirds of these weights will impair their strengths after acting a considerable time one-half is the greatest that can safely be applied when its pressure or suspension is to be permanent.

December, 1817.

QUESTION 1. By Lysis.

A person by his natural strength is just able to raise up a weight of 300 lbs. what weight would he be able to sustain on an inclined plane, the elevation of which is 60°. by means of a rope going round the weight, (which is circular,) one end whereof is attached to the top of the plane, the other held in his hand?

QUESTION 2. By the same.

If a square and an equilateral triangle be inscribed in a circle, a circle inscribed in both the square and triangle, and again a square and anequilateral triangle be inscribed in these circles, and so on ad infinitum: What will be the diameter of the circle, when the sum of the areas of the triangles minus the rectangle of the sum of the areas of the squares and triangles is a maximum ?

QUESTION 3. By Philo.

In what order must I plant 14 trees to make 21 rows, each row to contain 3 trees?

History of Trades and Manufactures.

HISTORY OF THE YORKSHIRE ALUM-TRADE.
༢༠།༠་༠༠༠༧༧༦༨༠༠༠་ལ་

THE following account of this important branch of trade, which has now for more than two hundred years been almost exclusively confined to this county, will no doubt be interesting to the greater part of our readers. It is extracted, by permission of the publishers, from the Rev. George Young's History of Whitby and the Abbey of Streonshalh.

I. Introduction of Alum making. On this subject much uncertainty prevails, and very contradictory statements have been given. In Gough's Topography (vol. ii. p. 449), we are told, that, according to Sanders's Gesta Britannica, alum-making was first brought into England by Sir John Bourchier, in 1609; but we find from other authorities that Sir John did not introduce the art, but only contributed to improve it. In Aubrey's "Lives of eminent Men," subjoined to the "Letters from the Bodleian Library," (vol. ii. p. 281,) it is stated, that Thomas Chaloner, Esq., "about Ao..... riding a hunting in Yorkshire (where the allum workes now are) on a common, took notice of the soyle and herbage, and tasted the water, and found it to be like that where he had seen the allum workes in Geru anie. Whereupon he gott a patent of the king (Cha. I.) for an allum worke (which was the first that ever was in England), which was worth to him two thousand pounds per annum, or better:" &c. This story is strangely erroneous both as to the time and person. It is clear that the alum-works were established at Guisborough when Drayton's Poly-olbion* was written, and consequently many years prior to the reign of Charles I., for the Poly-olbion was published in 1613, the year in which Sir Thomas Chaloner of Guisborough died; and hence we may infer, that the generally-received account, which makes Sir Thomas the first founder of the alum-works, is the true account.

• The following is a part of his " Catalogue of the Wouders of the North-Riding :"-
"My Scarborough, which looks as though in heaven it stood,
To those that lye below, from the Bay of Robin Hood,

Even to the fall of Teis; let me but see the man,
That in one tract can shew the wonders that I can.
Like Whitbies selfe I thinke, ther's none can shew but I
O'r whose attractive earth there may no wild geese flie,
But presently they fall from off their wings to ground;
If this no wonder be, wher's there a wonder found!
And stones like serpents there, yet may yee more behold,
That in their natural Gyres are up together rold.
The rocks by Moultgrave too, my glories forth to set
Out of their cranied cleeves can give you perfect jet,
And upon Huntcliff Nab, you every where may find
(As though nice nature lov'd to vary in this kind)

The exact time when Sir Thomas Chaloner introduced the art is not known, but the year 1595 is the earliest date assigned. In his travels on the continent, Sir Thomas visited the pope's alum-works in Italy; and, having ascertained that alum might be got on his estate at Guisborough, he engaged some of the pope's workmen to accompany him to England, and for that purpose conveyed them on board a vessel by concealing them in large casks. With the assistance of these workmen, who passed by the name Russel. he began an alum-work at Belman-Bank, near Guisborough, which is uniformly considered here as the first alum-work in Britain. Some years probably elapsed before the art was duly established, for the rock here varies so much from that in Italy, that several trials must have been made before the proper process could be fixed; and according to some accounts, which ascribe the improvement of it to Sir John Bourchier, the art was not brought to perfection till the year 1608.*

The pope's monopoly of the alum-trade, which had been enjoyed by the court of Rome for ages, being thus destroyed, his holiness is said to have excommunicated all the parties concerned; and, when we consider the value that was set on this monopoly, and the jealousy with which it was preserved, nothing is more probable. Yet, that the pope issued on that occasion the tremendous curse which Grose, Charlton, and others have published, as the curse fulminated against Sir Thomas and the alumn-makers, is an assertion for which I can find no evidence; though we may suppose, that his irritated holiness would launch out one of the worst maledictions

Stones of a spherick forme of sundry mickles fram'd,
That well they globes of stone, or bullets might be nam'd
For any ordnance fit: which broke with hammers blowes,
Doe headless snakes of stone within their rounds enclose.
Marke Gisborough's gay scite, where nature seems so nice,
As in the same shee makes a second paradice,
Whose soyle imbroydered is, with so rare sundry flowers,
Her large okes so long greene as summer there her bowers
Had set up all the yeare, her ayre for health refin'd,
Her earth with Allome veines most richly intermin'd."

Poly-olbion, Part II. p. 146.

Sir John, according to Howes, joined with Lord Sheffield, president of the North, Sir Thos. Chaloner, Sir David Foulis, and others who had estates in this quarter, in bringing the art to perfection. See Rapin, v. ii. p. 176.

† A curious passage in bishop Latimer's fifth sermon, preached before King Edward, shows how narrowly this monopoly was watched, above 50 years before, and what a mighty crime it was to attempt to infringe on it. "I heard a great while ago a tale of one (I saw the man that told me the tale not long ago in this auditorie), he hath travelled in mo countries than one. He tolde me that there was once a Pretor in Rome, Lord Maior in Rome, a rich man, one of the richest marchants in all the citie, and suddenlie he was cast into the Castell Angell. It was heard of, and everie man whispered in anothers eare, What hath he done? hath he killed any man? No. Hath he medled with Alam, our holy fathers marchandice? No. Hath he counterfeited our holy fathers Buls? No. For these were hie treasons. One rounded another in the eare and said: Erat dives, he was a rich man. A great fault. Here was a goodly prey for that holy father. It was in Pope Julius time, he was a great warriour. This prey would helpe him to maintaine his warres, a jolly prey for our holy father." Latimer's Sermons, (1596) fol. 64.

« السابقةمتابعة »