EQUILIBRIUM OF A SPHERICAL ENVELOPE. 95 



and the lines of pressure are the circles orthogonal to them. These circles are 

 so drawn in the figure that the differences of the values of G and H are ^$ir. 



The spiral lines which pass through the intersections of these circles are 

 the principal lines of stress in the case of twists applied to the spherical 

 surface at the extremities of the chord AS. 



In the case of a sphere acted on by fluid pressure, if the pressure is a 

 function of the distance from a given point, we may take the line joining 

 that point with the centre of the sphere as an axis, and then the lines of 

 equal fluid pressure will be circles, and the fluid pressure N will be a function 

 of 6, the angular distance from the pole. If we suppose the total effect of 

 pressure balanced ,by a single force at the opposite pole, then we shall have 

 for the equilibrium of the segment, whose radius is 6, 



= a f JVsin20cZ0 ........................... (28), 



Jo 



and p a 



to determine p n the tension in the meridian, and p a that hi the parallels of 

 latitude. 



