To measure round timber, let the mean circumference be found in feet and deci mals of a foot : square it, multiply this square by the decimal 0.079577, and the product by the length. Example. Let the mean circumference of a tree be 10.3 feet, and the length 24 feet. Then 10.3x 10.3 X0.079577 X 24 = 202.615, the number of cubical feet in the tree. The founda tion of this rule is, that when the circum ference of a circle is 1, the area's 0.079 5774715, and that the areas of circles are as the squares of their circumferences. But the common way used by artificers for measuring round timber differs much from this rule. They call one fourth part of the circumference the girth, which is by them reckoned the side of a square, whose area is equal to the area of the section of the tree; thereihre they square the girth, and then multiply by the length of the tree. According to their method, the• tree of the last example would be computed at 159.13 cubical feet only.
In speaking of the strength of timber, or of several kinds of wood, Mr. Emerson says that, from experiments which he has made, a piece of'good oak, an inch square and a yard long, supported at both ends, will bear in the middle tier a short time about 330/bs. avoirdupois, but will imme diately break with a greater weight. Such a piece, he adds, ought not in practice to be trusted for any length of time with more than one-third, or perhaps one fourth, part of the weight ; he then gives a table of the different degrees of Strength of several sorts of wood. Other writers, who have entered at large on the subject, have considered the strength of materials, timber, &c. as subject to four different kinds of strain. 1. As they may be torn asunder, as in the case of ropes, stretch ers, king-posts, tye-beams, &c. 2. As they may be crushed, as in the case of pillars, posts, and truss.beams. 3. As they may be broken across, as happens to a joist or lever of any kind. 4. As they may% be wrenched or twisted, as in the case of the axle of a wheel, the nail of a press, &c. It would carry us much be yond the limits of this work to enter at large on these several subjects, we shall therefore confine ourselves to some obser vations on the strains upon timber, which may be practically useful.
With regard to the cohesion of wood, we may premise, 1. that the wood immedi ately surrounding the pith, or heart, of the tree is the weakest, and its interiority is so much more remarkable as the tree is older. This at least is asserted by Mos chenbroek as the result of experiments ; but M. Buflon says, that his experience has taught him that the heart of a sound tree is the strongest; but he gives no in stances. It is certain, from many observa tions on very large oaks and firs, that the heart is match weaker than the exterior parts. 2. The wood next the hark, com monly called the white or blea, is also weaker than the rest; and the wood gra dually increases in strength as we recede from the centre to the blea. 3. The wood is stronger in the middle of the trunk than at the springing of the branches, or at the root ; and the wood. of the branches is weaker than that of the trunk. 4. The wood of the north side of all trees which grow in our European climates is the weakest, and that of the south-east side is the strongest ; and the difference is most remarkable in hedge row trees, and such as grow singly. The heart of a tree is never in its c re, but always nearer to the north side, and the annual coats of wood are thinner on that side. In confor mity with this, it is a general option of carpenters, that timber is stronger whose annual plates are thicker. The trachea, or air-vessels, are weaker than the simple ligneous fibres. These air-vessels are the same in diameter and number of rows in trees of the same species, and they make the visible separation between the annual plates. Therefore, when these are thicker, they contain a greater pro portion of the simple tigneous fibres. 5. All woods are more tenacious while green, and lose very considerably by drying after the trees are felled. The only au thor who has put it in our power to judge of the propriety of his experiments, is Muschenbroek. He has described his me
thod of trial minutely, and it seems unex ceptionable. The woods were all formed into slips fit for his apparatus, and part of the slip was cut away to a parallelopiped of one-fifth of an inch square, and therefore one-twenty-fifth of a square inch in section.
The absolute strengths of a square inch were as follow : lbs.
Locust tree . . . . 2.),100 ,lujeb 18,500 Beech, oak . . . 17,300 Orange . . . . • 15,500 Alder • 13,900 Elm 13 200 Mulberry 12 500 Willow 12 500 Ash 12,000 Plum 11,800 Elder 10,000 Pomegranate . . . . 9,750 Lemon 9,250 Tamarind 8,750 Fir 8 330 Walnut 8,130 Pitch pine 7,650 Quince 6,750 Cypress 6,000 Poplar • .
Cedar 4,880 M. Muschexbroek has given a very mi nute detail of the experiments on the ash and the walnut, stating the weights which were required to tear asunder slips taken from the four sides of the tree, and on each side in a regular progression from the centre to the circumference. The numbers of this table corresponditig to these two timbers may therefore he considered as the average of more than fifty trials made of each ; and he says that all the others were made with the same care. We cannot therefore see any rea son fbr not confiding in the _results ; yet they are considerably higher than those given by some other writers. M. Pitot says, on the authority of his own experi ments, and of those of M. Parent, that sixty pounds- will just tear asunder a square line of sound oak, and that it will bear fifty with safety. This gives 8,640 for the utmost strength of a squareinch, which is touch inferior to Muschenbroek's valuation. We may add to these, Ivory ° 16,270 Bone 5,250 Horn 8,750 Whalebone . . . . 7,500 Tooth of sea-calf . . 4,075 • The reader will surely observe, that these numbers express something more than the utmost cohesion ; for the weights are such as will very quickly, that is, in a minute or two, tear the rods asunder. It may be said in general, that two-thirds of these weights will sensibly impair the strength after a considerable while, and that one-half is the utmost that can re main suspended at them without risk for ever ; and it is this last allotment that the engineer should reckon upon in his con structions. There is, however, consider able difference in this respect. Woods of a very straight fibre, such as fir, will be less impaired by any load which is not sufficient to break them immediately. According to Mr. Emerson, the load which may be safely suspended to an inch square, is as follows : Iron 76,400 Brass 35,600 Hempen rope . . 19,600 Ivory 15,700 Oak, box, yew, plum tree 7,850 Elm, ash, beech . . . 6,070 Walnut, plum . .• . . 5,360 Red holly, elder, plane, crab . . . . 5,000 Cherry, hazle . . . 4,760 Alder, asp, birch, willow 4,290 Lead 430 Freestone 914 He gives us a practical rule, that a cy finder whose diameter is d inches, loaded to one-fourth of its carry as follows Experiments on the transverse strength of bodies are easily made, and according ly are very numerous, especially those made on timber, which is the case most common and most interesting. But in this great number of experiments, there are very few from which we can draw much practical information.- The experiments have in general been made on such small scantlings, that the unavoidable natural inequalities bear too great a proportion to the strength of the whole piece, Accord ingly, when we compare the experiments of different authors, we-find them differ enormously, and even the experiments by the same author are very anomalous. The completest series that we have yet seen is that detailed by Belidore in his " Science des Ingenieurs." They arc contained in the following table. The pieces were sound, even-grained oak. The column b, contains the breadth of the pieces in inches ; the column d, con tains their depth ; the column 1, contains their lengths ; column p, contains the weights (in pounds) which broke them when hung on their middles; and in is the column of averages or mediums.