TABLE FOR TRANSMISSION LINE PHENOMENA. 179 



8. To Find cosh-i (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/i), (29) 



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



9. To Find cosh-^ (— P -\- jU), 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) = ± {fl + j (tt - ^ + 2irn)\, (30) 



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



10. To Find cosh-i ( — 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 + ./• (tt + ^ + 2irn)], (31) 



where a and (p 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 / = respectively resistance, capacity, and inductance per 

 loop unit of lengtli 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, 

 /3 = 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 ^ _ 



a = Wlcg{h), (32) 



^ = coVkfih), (33) 



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

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

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



