Material Stresses, and their formal solution. 23$ 



particular interest for .examination. The special case when 

 the forces acting per unit of volume are negligible compared 

 with the impressed surface tractions only needs consider- 

 ation from the simplification which is made in equations (/3) 

 and (y) by the null values of Vj, V 2 , and V 3 . For the 

 consequence is that V 2 (P + Q + R) is also null. It is hardly 

 necessary to emphasize further the simplifications which 

 follow in equations (2) and (3). 



Cylindrical and Spherical Polar Coordinate Systems. 



Provided the points in the material body which we are 

 considering are sufficiently distant from the polar axis, or 

 from the pole, as the case may be, the solutions already given 

 may be readily adapted to either of these systems. 



But if this is not the case, further points will arise for 

 consideration. It will naturally be noted that no definition 

 is given of ic sufficiently distant." I shall content myself by 

 stating the conditional Stress Equations corresponding to 

 equations (/3) and (7) in the Cylindrical Polar Coordinate 

 system, as follows : — 



p m(m + n) 2m (I 3 1 "d 2 



+ |i)(P+Q^-R) 

 V^^W + Q + R,-^* 



+ |i) (P+Q+R) 



^ P \r Br ^ r> $0 2 ) + r*\ ^ + W ) ' 

 L n(m ± «) p + Q + R) _ 2™_/|: 1|. 



+4 d 9 ;)(p + Q + i {) 



7) 2 V- 



09') 



