Air-cavities on the Strength of Materials. 



11 



Now 

 *S=-6(A+C)^, 



f=(2A-3C)f-3B^ +«**,, 

 |=(2A-30)| -3B^-{6A-9C)^+15B^ + « y , 



*'_„ = _3(A + C)^-5B^ + 15C^ + 25B^. 



Hence the equations 

 _(A + 6C + ^ + ^-g6(A + C) + 6A-24C-^]^=0, 



_(A + 6O + ^ + «,-[-\(A + C) + 6A-24C- 4 ^]^=0; 



and similarly from the z equation 



- g lH A + C) + 6A-24C- 4 ^]^=0. 



These three equations hold when r=a. 

 Hence 



i° 2 B -6(A + C)^ +300=0, 



and 



^+(A + 6C) = aa 3 . 



From which and (4) we find 



A 6X + b/ju 3 



A = 7- — {— oca 3 . 



9X + 14/* 



3(X + ^) 5 i 



t> = 7w rr~ our. > 



9X+14/A ' 



3 (X + /i) 



(5) 



