N 



sin 0^ cos 0. = 

 i=l 



z 



Thus, for N > 2, 



^ -||-NMao + NpS2 + Iq + N | m (z-') ( z-')^ dz-' l- + a i N p g S^ [l6d] 



+ iNpga^S(O)- MQgZQ- Ng J m (z/) z.' dz/ | 



N 

 - NpS^y-Q = - pgaQA[S(0)- kTg] y sin 0^ sin (kag cos 0^ - cot) 



i=l 



Similarly, for N > 2, the p-equation becomes 



p jlNMa^ + NpS2 + Jq + N J m (z/)(zp^ dz.'j + p |n p g S^ 



+ iNpga^S(O)- Ng J m(z.')z/ dz/j 



N 

 + N pSj Xq = pg aQ A [S(0) - kTg] ^ cos 0^ sin (k ag cos 0^ - cot) 



i = l 



N 



+ 2pgkAT-^ y cos (kaQ cos 0^ - cot) [I6e] 



i=l 



Under the same assumptions, we obtain for the last equation 



N 

 •y |Kq + 2NMaQ| = - 2pgkaQATQ y^ sin0. cos(kaQ cos 0. - wt) [I6f] 



i = l 



In the case of N = 1 , the above equations reduce to Newman's equa- 

 tion for a single spar. If N = 2, these equations do not hold. However, 



20 



