TJilctile Materials under Combined Stress. 107 



slight variations for the same tube. The value of cr, Poisson's 



ratio, has been deduced from these by the formula <r= 9 p_^ > 



which is a method evidently liable to large errors ; these, 

 however, I do not think are serious enough to affect the 

 conclusions I have drawn from the tables of results, as the 

 chief conclusions are deduced from the stresses. I had 

 intended to deduce the value of o- directly from the internal 

 pressure tests ; the axial elongation due to a pressure p , 



producing stresses p\ and 2p h being -^(1 — 2a-), so that 



■pi 



er = 0'5 — y — x (axial strain). The method of attaching the 



tube conveying the oil to the specimen was not perfect, and 

 seemed to tilt the tube slightly as a whole, so that this 

 method was not used. Perhaps Regnault's method would 

 have been most appropriate. 



The results of the experiments are given in Tables V. (Solid 

 Bars), VI. (Steel Tubes), VII. (Copper Tubes), and VIII. 

 (Brass Tubes), where the observations made at the yield- 

 point and the results will be found. 



46. Results of the Experiments. — For the more ready 

 presentation of the results of the experiments, diagrams of 

 various types have been drawn, and will be described as 

 referred to. 



The Tests on Solid- Bars. — In the case of the solid-bar 

 tests it will be observed that the yield-point stresses (see 

 Table V.) rise as the course of tests proceeds: this indicates 

 that the yield-point of the outer layers must have been much 

 exceeded (§ 5). A glance at the torque-twist diagram 

 (fig. 15) for the torsion-tests will clearly demonstrate the 

 difficulty of locating the yield -point ; though the tables 

 merely embody my estimations of its occurrence, the curves 

 at any rate represent actual occurrences, and permit of the 

 ready comparison of points considered to correspond. The 

 results may be held, with previous torsion experiments, to 

 disprove the maximum-stress theory, as the ratios of the 

 maximum stresses in the torque and tension tests are 0*615 

 to 0'69 for the iron, and 0'565 for the steel. They are also 

 at variance with the maximum-strain theory, the values of 

 the ratio for the experimental values of a being - 75 and 0*71 

 respectively. In this and some of the succeeding figures the 

 time-effect is shown by observations giving different strains 

 under a constant stress; the first observations were taken 

 immediately the loads w r ere applied ; in some cases the 

 intervals of time are given. 



