662 PROCEEDINGS OF SECTION H. 



being 2-8 per cent., 1-8 per cent., and 6-5 per cent, in the three cases, 

 or 3-7 per cent, as the average of all experiments ; and hence we may 

 take it that the removal of a little metal from the tension corner of a 

 beam of square section set with a diagonal vertical will actually increase 

 the strength of the beam by a small percentage. 



Although this disagrees with the abstract argument of the earlier 

 part of this paper, yet further consideration shows that it is only to 

 be expected if one brings into account the fact that the material of the 

 beam is not absolutely homogeneous in texture, while still regarding 

 each layer as acting independently of those adjacent to it. For it is 

 to be noticed that while the strength of a beam depends upon its modulus 

 of section, yet its deflection depends upon the product of the modulus 

 and the distance " h " from the neutral axis to the outer edge of the 

 section, i.e., upon the moment of inertia of the section ; and although 

 the modulus in this type of beam increases on truncating the section, 

 yet the moment of inertia is diminished, so that the truncated beam will 

 deflect more than that of full section. Hence, on testing a beam of full 

 se tion to destruction, as soon as the outer layers break the deflection 

 must be increased, even though the load is not enough to complete 

 fracture. Were the material perfectly homogeneous, so that every 

 particle had an identical breaking point, then, as the load approached 

 the critical point, the material would break in such infinitesimally thin 

 layers that the increase of deflection would be perfectly gradual, the 

 load coming on to the remaining section without shock ; but the 

 metal not being quite homogeneous is bound to break across a layer 

 of appreciable thickness, causing a sudden increase of deflection, and 

 thereby transferring the load to the remaining section with a jerk, 

 which may overcome its modulus of resistance, although a static load 

 of the same amount could have been carried in safety. And, further, 

 when the outer layer becomes stressed beyond its limit and fails, it will 

 break at one point only in the form of a minute crack, causing a spot 

 of local concentration of stress, and thereby reducing the strength 

 of the sound section underneath ; just as from this cause a beam has 

 its strength more affected by a narrow saw cut being made on its sur- 

 face than by having the whole of its surface removed to an equal depth. 



The above experiments were carried out at University College, 

 London, by the courtesy of Professor J. D. Cormack, to whom the 

 author's best thanks are due for permission to make use of the testing 

 apparatus in the Engineering laboratory of that institution. 



6.— BENDING STRESSES IN WIRE ROPES. 

 By R. W. CHAPMAN, M.A., B.C.E. 



7.— ARTESIAN WATER SUPPLY IN SOUTH AUSTRALIA. 



By S. SMEATON, B.A. 



