158 OUTLINES OF NATURAL PHILOSOPHY. 



multiplied into the area of the sections, and into 

 the distance of the centre of gravity of the sections 

 from the points round which the beams turn in 

 breaking, the whole being divided by the lengths of 

 the beams. 



We are indebted to GALILEO for this theorem. He 

 was the first who attempted to reduce the strength 

 of the materials used in the mechanical arts, to the 

 measures of geometry and arithmetic. Dialogo Se- 

 condo, Opere, torn. in. p. 63., &c. See also ibid. 

 p. 213., a Commentary on what GALILEO has writ- 

 ten on this subject, begun by VIVIANT, and com- 

 pleted by GUIDO GRANDE. 



It is obvious, that the hypothesis of the beam break- 

 ing short over, and turning as on a hinge, is not 

 the precise fact ; and therefore the conclusion dedu- 

 ced from this hypothesis cannot be expected to be 

 more than an approximation. It does not appear, 

 however, that more refined views, or more compli- 

 cated speculations, have led to results agreeing 

 better with experiment than the simple hypothe- 

 sis of GALILEO. . 



237- In a beam, of which the section is a rec- 

 tangle, having the breadth b, and the depth c, 



n Tj f 



W n - 7- . The strength, therefore, all other 

 2 / 



things remaining the same, is as the breadth mul- 

 tiplied into the square of the depth. 



This proposition has been brought to the test of ex- 

 periment by BUFFON, in a great number of trials, 

 made with great accuracy, and on a large scale. 



The 



