494 



REPORTS ON THE STATE OF SCIENCE. — 1919. 



between P/F and k is deduced in the following manner, which may be 

 regarded as typical of the methods applicable wherever the ratios between 

 the principal stresses are known. In the general equation for strain- 

 energy 



W,,.=l,(X^ + Y-^ + Z-^)- 



ME 



(YZ+XZ+ZX) 



substitute the expressions for the principal stresses, 



_,^y^[-(^-^-l)-(A:^ + l)(F-l) + (F+l)]} 



Equating this quantity to the strain-energy in simple tension, 

 W^=F72E, wo have 



P-^ . (F-- l)^ 



F^ -3(1 _2o-) + 2^^(1+0-) 



whence, substituting m = l/o- = 4, we have 



P 2(A:^-1) 



F~y6+10p 



which expression gives one of the two graphs, IV, plotted in the diagram. 

 The validity of the constant limiting strain-energy hypothesis, as a 





/- 



FruvcipaL Stress Constanb. 

 ■PrincipaL Straim Constant, 

 1I[:TarufentixiLStress Constant. 

 \^rL(/niiinff Strairv-Enjerg^ Canstanl. 



'Xvfarksdi Pointfr Indicate Coolc&KobcrtsoTk 



rfXperim.z T,'taLSesn Us forMU ft StechTube s. 

 ZS 



IS 



SO 



3-5 



■?<.' 



l^02aK) BjcUu} Ic,-IicU£i^cd'/l!ztzrmd'Di-::meCerofTaie. 

 Fig. 20. 



serviceable approximation to a law that is doubtless more complex, 

 may be inferred not only from scientific investigation of cases, such as the 

 above, that admit of exact calculation and measurement, but also from 



