TABLE FOR TRANSMISSION LINE PHENOMENA. 179 



8. To Find cosh^ (P — jU), where P and U are Positive and 



Real. — This case differs from the preceding only in that, by (24), 

 sinh A and sin B have opposite signs, so that 



cosh-i (P - jU) = ± \a -j{<p + 27r/0, (29) 



Where a and (p have the values given by (26) and (27). 



9. To Find cosh-^ (— P + jV), where P and U are Positive 



and Real. — This case differs from that of Section 7 only in that cos B 

 is negative, so that 



cosh-i (- P + jU) = ± {« + i (tt - ^ + 27r«)}, (.30) 



where a and (p have the values given in (26) and (27). 



10. To Find coshi ( — P — jU), where P and U are Positive 



and Real. — This case differs from that of Section 9 in that sinh A 

 and sin B have opposite signs, whence 



cosh-i (- P - jV) = ± {a + i (tt + ^ + 27rw)), (31) 



where a and ip have the values given in (26) and (27). 



11. Attenuation Constant, Retardation Angle, and Surge 

 Impedance of a Smooth Electric Transmission Line Without 

 Leakage. — If 



r, c, and I = respectively resistance, capacity, and inductance per 

 loop unit of length of a smooth line, 

 CO = angular velocity of impressed e.m.f. in radians per 



second, 

 a = real attenuation constant of current per unit of length 



of line, 

 j3 = retardation angle per unit of length of line, 

 Zi= surge impedance of the line, 

 Ri and Xi= respectively surge resistance and surge reactance of 

 the line, 

 then 1 _ 



a = Wic g{h), (32) 



IS = Wkfih), (33) 



1 These equations are obtained by introducing the g- and /-functions into 

 familiar equations. Compare Pierce: Electric Oscillatioris and Electric Waves, 

 pp. 327 and 329, McGraw-Hill Book Co., 1920. 



