132 Prof. J. Trowbridge on the Production of 



58. Practical Conclusions and Note. — The result, then, of 

 these experiments, as applicable to practice, is that the condi- 

 tion for initial yielding of a uniform ductile material is the 

 existence of a specific shearing-stress ; and that the interme- 

 diate principal stress is without effect. 



Note. — Cases of more than one principal stress are met with 

 most frequently in boilers, hydraulic cylinders, and crank- 

 shafts. In the former cases the results obtained above lead to 

 the same dimensions as are obtained by the consideration of 

 the greatest stress only, while the maximum -strain theory 

 would lead to the adoption of too small a thickness. In the 

 case of crank-shafts, or " combined bending and twisting," 

 both the greatest stress and greatest strain theories lead to too 

 small dimensions, the corresponding well-known formula 3 for 

 the " equivalent bending moment " being 



i(M+ VM 2 + r P) and |M + f </M 2 + T 8 



respectively, where M is the applied bending-moment and T 

 the applied twisting-moment. The greatest shearing-stress 

 theory leads to the (greater) value VM 2 + T 2 for the equiva- 

 lent bending-moment, and where the dimensions are thus 

 determined that formula should be used. A lower factor of 

 safety might, however, be used in such cases, where there is a 

 large reserve of understressed material. 



It may also be noted that the specific shearing-stress at the 

 yield-point is better determined by taking one half of the 

 tensional yield-point stress, than from the results of torsional 

 experiments in which the sharpness of the yield-point is 

 masked, as explained in § 10 and shown in fig. 15. 



[I have pleasure in expressing my thanks for assistance 

 rendered in the tests by Messrs. Ash worth, Howe, Knowles, 

 Rebboli, Nichols, Vail, and Heichert ; the latter of whom also 

 assisted me in the construction and erection of the greater 

 part of the apparatus.] 



VI. The Production of the x-Rays by a Battery Current. 

 By John Trowbridge *. 



I HAVE lately completed the installation of a plant of 

 twenty thousand storage-cells in the Jefferson Physical 

 Laboratory. This gives me over forty thousand volts and a 

 comparatively steady current through a large resistance. 

 One of the most interesting questions in relation to this 

 battery was the possibility or impossibility of producing the 

 * Communicated by the Author. 



