288 

 equations 



BELL SYSTEM TECHNICAL JOURNAL 



p-i = pi cosh Ti - Fi^sinh Ti, 

 Si 



V2 = Vi cosh Ti - ^ sinh Ti. 



Suppose then that we wish to join this structure to other structures, 

 with different characteristics and with different area conducting tubes. 

 At the junction of the structures, we have by equation (14) 



p3 = p2, Vz = Fo. 



Combining these with the above, we have 



pz = pi cosh Ti — Fi-^' sinh Ti, 

 F3 = Vi cosh Ti - ^ sinh Ti. 



Writing a set of equations similar to the above for the second structure 

 and combining, we have 



pi = Pi { cosh Fi cosh r2 + -^ -~ sinh Fi sinh F2 ) 



\ S2 Zoi / 



- Vi^i sinh Fi cosh F2 + 



Si 



Z02 Sj^ 

 Zo. 02 



cosh Fi cosh F2 



Zoi 02 



Vi = Vi{ cosh Fi cosh F2 + :^-^sinh Fi sinh F2 



Zo., Si 



^—^ ( sinh Fi cosh F2 + -^ -;— cosh Fi sinh Fo 

 Zo. \ oi Zo., 



We can also write this in the form 



= P^ 



F4= Vi 



In fact if we combine 77 structures of this kind, we can write the 

 equations 



p,= PiA - Vi^B, 

 Vr,= ViC-^'D, 



(56) 



