﻿18 Prof. L. N. Gr. Filon : Investigation of Stresses 



If i be given by the equation 



2/ 3^' 2 



sm- — =- = 



3 -4(^"-l)' • • 



then we have a fork or loop in ECF according a- 



■ (20) 



and a fork or loop in DCH according as 



It appears from the last two inequalities (by addition) 



that if - >/ we can never have loops in both ECF and 



DCH simultaneously ; if — </,-, we can never have forks in 



these two sectors simultaneously. It appears also that. as 

 qb" 2 increases negatively, i steadily increases to 90°. Its 

 lowest value corresponds to the numerically lowest negative 

 value of qV 2 , which we have seen to be — 2*91 from equa- 

 tion (16). This gives for i the value 72 c 30' nearly. It 

 appears, therefore, that i is always greater than this value. 



We have, therefore, for values of />/,-, or < — — i Q a fork in 

 one sector and a loop in the other, as shown in fig. 9. and if 



77 



i lies between i and — —i a loop in both sectors, as shown 

 in fig. 8. 



When q is small negatively. qlP is a large negative 

 quantity and i is nearly 90°. "We have therefore a loop in 

 both sectors. As q increases negatively we find, if i exceeds 

 72° 30* or falls below 17° 30', that in one of the sectors the 



