MECHANICS. 163 



As from the construction CL 2 = % LK 2 , if the radius 

 be called r, LK = L. , and CL = r 



so CE = , and CD - 2 r J- . CD is, there- 

 V& * 3 



fore, to CE, nearly as 7 to 5. 



In practice, as the tree from which the rectangular 

 beam is to be cut, can hardly ever be truly cylin- 

 dric, the first thing to be done is,, to inscribe, by 

 trial, the greatest circle possible, in the section of 

 the tree. The rectangle may then be found by the 

 construction above. 



243. If it is required to find the strongest rec- 

 tangular beam under a given perimeter or circum- 

 ference, divide the given circumference into six 

 equal parts, and take two of these for the depth 

 of the beam, and one for its breadth. 



These propositions are understood to be applicable, 

 not only to beams of wood, but to bars of iron, or 

 any other metal. 



244. If a beam, having one end firmly fixed in 

 a wall, project from it with a certain inclination 

 to the horizontal plane, the weight which it will 

 support at its extremity, is greater than that 

 which it would support if horizontal, in the ratio 

 of the square of the radius to the square of the co- 

 sine of the inclination. 



L 2 That 



