166 OUTLINES OF NATURAL PHILOSOPHY. 



246. If a j-ectangular beam, fixed ia a -wal, 

 project horizontally to the length I ; if the -depth of 

 its section be a, and the weight of a cubic foot of 



the timber be p\ then if l=:HJ 9 the beam 



will be just able to support its own weight. 



To apply this theorem, the value of s must be found 

 from experiment. In the case of a rectangular 



beam, we have sab. | = W x -, supposing the 



/w 2 



; beam supported at both ends, 240. ; and therefore 



"W x I 



2-7- I* 1 BUFFON'S experiments, a and b 

 a & 



s = 



were equal ; and in one where a was six inches, and 

 I equal seven feet., W was 19250 Ib. Therefore 



s = 1925 ? x 7 = 19250 x 56 = 1078000. In 



this same experiment, the weight of the beam was 

 128 Ib., and therefore a cubic foot weighed 73.2 



= , so that s = kj = 85.8 feet nearly. 

 ' p 



The following Table contains the mean results of 

 BUFFON'S experiments. They were made on oak 

 beams, cut from trees newly felled, and full of sap. 

 The weight of the timber varied from 73 to 75 

 French pounds to the cubic foot ; its strength varied 

 in the same proportion. 



TABLE. 



