34 PROCEEDINGS OF THE AMERICAN ACADEMY. 



r = the linear resistance of the line (ohms per wire km.). 

 g = the linear leakance of the line (mhos per wire km.). 

 / = the linear inductance of the line (henrys per wire km.), 

 c = the linear capacitance of the line (farads per wire km.). 

 n = the frequency of the impressed emf. at A (cycles per second), 

 w = 2 7r n, the angular velocity of the impressed emf. at A (radians 

 per second). 



The attenuation constant of the line is 



D.C. a=V^J ^; A.C. a=Vtr+jlo>)(g+jc«>) h ^Z. 



(1) 

 In the D. C. case a is a real numerical quantity which we may, for conven- 

 ience of subsequent operation, define as a "linear hyperbolic angle," or 

 " hyperbolic angle " per km. of length. Although it is a simple numeric 

 per unit length of line, yet, since it forms the basis of argument in hyper- 

 bolic tables, we may call it a " hyperbolic angle " per unit length of 

 line, and denote a hyperbolic unit angle as a " hyp." In the A. C. case 

 a is a plane-vector "hyperbolic angle," or complex quantity, per unit 

 length of line. 



The hyperbolic angle subtended by the line AB is 



D. C. = La hyps ; A. C. 6 = La hyps Z. (2) 



is a real numeric for the D. C. case, and a plane- vector, or numeric at 

 a definite angle in the reference plane, for the A. C. case. The surge- 

 resistance, or surge-impedance, of the line is 



D. C. z = i/ - ohms ; A. C. z = a/ r + jU ohms Z. (3) 



The surge-impedance of an A. C. line is the impedance that the line 

 offers at any point of its length to the propagation of waves of the fre- 

 quency considered. It is a vector resistance, or impedance, often closely 

 approximating numerically to yY/c. The surge-icidmittance of a line is 

 the reciprocal of its surge-impedance. 



In wave-propagation theory, and also in the steady-state theory here 

 considered, 6 and z, the hyperbolic angle and surge-impedance of a line, 

 are its fundamental characteristics ; while r, g, I, and c are its sec- 

 ondary or incidental characteristics. 



