326 Prof. W. B. Morton and Mr. L. J. Close on Hertz's 



Fig. 4. 



4. Distribution of Smaller Stresses. 



There are two questions suggested by these graphs which 

 require further examination. The first is the distribution of 

 the stresses p 2 p s , and in particular the loci in the body at 

 which they vanish and change sign. As the result of some 

 further calculation, these loci are found to have approxi- 

 mately the forms shown on fig. 5. There is a region, 

 surrounding the origin and based on a circle very slightly 

 smaller than the circle of contact, within which all three 

 principal stresses are pressures. The boundary of this 

 region is marked p 2 = 0. Springing from the top of this 

 is the locus ps = 0, above which both p 2 and p 3 are negative ; 

 below it, and outside the former region, there is a hoop- 

 pressure, while the smaller principal stress in the axial plane 

 is a tension. The main stress p ± is everywhere a pressure. 



As the area of contact shrinks to a point, the locus p 2 = 





