644 LOUIS VESSOT KING 



surface r=b, and of these maxima (ii)' is the greatest. The maxi- 

 mum shearing stress is therefore 



I I Pr'-BQ' I max =P— j- • —±-j- (6) 



I— cr I+p l—0 2 /C 2 



It follows from this discussion that elastic breakdown of the 

 nickel-steel jacket commences at the interior surface and, as defor- 

 mation continues, extends gradually to the outer surface. The 

 surfaces of shear in this case are the system of cylindrical surfaces 

 whose traces on a plane perpendicular to the axis of the cylinder are 

 equiangular spirals intersecting orthogonally and cutting all radii 

 at angles of 45 . An examination of the nickel-steel jackets shows, 

 in fact, that the surfaces of shear approximated roughly to this 

 system. The polished outer surface of stressed specimens showed 

 indications of fine longitudinal ribs, while in such as were actually 

 ruptured it was noticed that the surface of rupture conformed to 

 that predicted from theory. As the rupture occurred when the 

 nickel-steel was stressed very much beyond the elastic limit, the 

 actual surfaces of shear are determined by very complex conditions 

 involving the effect of internal friction, with which we shall deal in 

 a later section. 



Numerical results.— A rough verification of the preceding results 

 may be made by calculating the relation between the load and the 

 increase of diameter of the nickel-steel jacket according to equa- 

 tion (5). For nickel-steel we take a' = 0.327 and //=io.8Xio 6 

 pounds per sq. in., values employed in the writer's paper just 

 referred to. In one set of experiments (referred to as 0.25-centi- 

 meter wall) b= 1 .00 cm., c= 1 . 25 cm., giving from (2) 



When the jacket is filled with tallow we may take a = |, /x = o, /3 = o, 

 so that equation (5) gives 



£/'A=i.34X(P/y), 



or in terms of the total load, W=wb 2 P, we obtain 



2V (inches) = 2. 52Xio- 7 XJ'F (pounds) (7) 



