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O, P, Q, &c. represent the results - * -
of the experiments made upon : 3. i
beams 5-330 in. square, of different -
lengths, whose primitive strength is
varied in each piece. -
1617. The ordinates of the re- *
gular curve, m, l, i, h, g, f, e, d, c, -
b, Z, show the results of the cal-
culation 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 un-
equal strengths would form an
irregular polygon, whereof each #:
point would answer to a different 3
curve; whilst, supposing the same
primitive strength to belong to

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each piece, there should be an it o
agreement between the strengths 2
and scantlings which constitute a or
regular curve. %
1619. Thus it is to be ob- || |or gol
served that the points O and P #!

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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 or-
dinate of the curve K.P. Hence
the point P is above the properly

correspondent point k.
162O. For the same reason, the l
point c is above its correspond-

ing 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.

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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 (3364–30.92=) 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 l. 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 second column, the proportion of the depth to the length; and The third, the greatest strength of each piece in pounds averdupois. 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.

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Length of Propor- || Breaking || Length of Propor- Breaking | each Piece tion of Weight in each Piece tion of Weight in

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10-66 1 O 57285 12-79 12 47083 14.92 14 37854 17 O6 16 34.404 19:19 18 3Ol 64 21:32 20 26719 23:45 22 24003 25-58 24 21689 27.72 26 19377 29'85 28 18060 31 '98 | 30 16000

8.983 10 55.738 10'66 12 45804 12'44 14 387,57 14-21 16 33449 15-99 18 29226 17.77 20 26142 19'54 22 23325 21:32 24 2.1087 23-10 26 19139 24-97 28 17557 26'65 30 16144

7.994 10 57285 9°594 12 47.093 11-19 14 398,54

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