The second column. The seventh 1616. In order to give an idea of the method of representing the strength of wood of the same scantling, but of different lengths, by the ordinates of a curve, we annex fig. 612. to explain by it the result of the experiments of Buffon, given in the second table. The ordinates of the polygon N, O, P, Q, &c. represent the results of the experiments made upon beams 5.330 in. square, of different lengths, whose primitive strength varied in each piece. 1617. The ordinates of the regular curve, m, l, i, h, g, f, e, d, c, b, Z, show the results of the calculation according to the rule, taking the same primitive strength for each piece. 1618. After what has been said in a preceding page, it is easy to conceive that the primitive unequal strengths would form an irregular polygon, whereof each point would answer to a different curve; whilst, supposing the same primitive strength to belong to each piece, there should be an agreement between the strengths and scantlings which constitute a regular curve. 1619. Thus it is to be observed that the points O and P of the regular polygon only vary from the regular curve, m, l, k, i, &c., because the ordinate LO is the product of a primitive strength diminished by the mean primitive strength which produced the ordinate of the curve KP. Hence the point P is above the properly correspondent point k. 1620. For the same reason, the point c is above its corresponding point X, because the relative ordinate Ce is the product of a primitive strength greater than the mean which produced the point X. Fig. 612. 1621. Referring to the second table, we find that the primitive strength answering to the point O is but 60-76, and the value of the ordinate LO 2502, whilst that of the point P is 68 34, and the value of the ordinate KP 3364; and as the ordinates Ll and Kk corresponding to the curve are calculated upon the same primitive strength of 64.36, which for Ll gives 2726, and for KP 3092: it follows that, in considering all these quantities as equal parts of a similar scale, the point P of the polygon should be (3364-3092=) 272 of these parts above the corresponding point k of the curve, and the point O 224 of those parts (2726-2502) below the point 7. 1622. To render the researches made, available and useful, the table which follows has been calculated so as to exhibit the greatest strength of beams from pieces 3·198 in. square, up to 19.188 in. by 26 65 in. The first column contains the length of each piece in English feet. The table is for oak; and it is to be recollected that the weight is supposed to be concentred in the middle of the bearing of the beams, and hence double what it would be if distributed over the whole length of each piece. Experience, as well as investigation of the experiments, shows, that in order to resist all the efforts and strains which, in practice, timber has to encounter, the weight with which it is loaded ought to be very much less than its breaking weight, and that it ought not to be more than one tenth of what is given as the breaking weight in the following table, beyond which it would not be safe to trust it. The abstraction of the last figure on the right hand, therefore, gives the practicable strength by simple inspection. In a subsequent page, the reduction of the strength of oak to fir, which is in more general use in this country, will be introduced, so as to make the table of more general utility. TABLE VI. Showing the greatest Strength of Oak Timber lying horizontally, in pounds averdupois. |