532 THE STRENGTH 



74. If the weight be appHed at the end, and 

 the strength of the beam be as the strain upon 

 it. Putting c' for the co-efficient 6|, or 6, 

 just found, we have W = "^-^^ where W and 

 d are constant, and consequently a d varies as 

 Z. We may therefore make either a ox d the 

 variable quantity, but it will be more economical 

 to make the depth d constant. If vre do this, 

 and make the thickness of the rib submitted 

 to tension uniform, that rib will form a triangle 

 w^hose vertex is at the end, where the weight 

 is applied. — In like manner, where the weight is 

 to be applied at the middle of the beam only, the 

 stretched rib, then at the bottom, may be 

 uniformly tapered from the middle to the ends, 

 forming two triangles, instead of the parabolas 

 before employed. In this case, the lines C A 

 and C B (fig. page 470), and their corre- 

 spondent ones on the other side, will be straight. 



75. We might now point out other modifica- 

 tions in beams, and particularly those of steam 

 engines; which, as appears from the experi- 

 ments, should have a large equal rib or flange at 

 top and bottom, with, perhaps, a thin solid sheet 

 between them; differing, in the size of the 

 ribs, only, from the form in figure 26, plate 

 4th of Tredgold's Essay on the strength of cast 

 iron. This is for double engines ; but for single 



