698 



BELL SYSTEM TECHNICAL JOURNAL 



TABLE II 



No. 



Admittance Y{p) 

 Illustrative System 

 Cause and Effect 



Cause: Unit Impulse 

 Effect: ^UYip) 



19 



Y{p) =exp {x - \x\^p' + 1) 

 Vertical atmospheric waves, axis of x 

 vertically upwards, velocity = 1, height 

 of homogeneous atmosphere = \. Cause: 

 Vertical displacement at x = 0. Effect: 

 Vertical displacement at time t of particle 

 whose undisturbed position is x. 



h{t- \x\) - 



\x e' 



ylt"^ - 



X /i(V/2 - a;2). 



\x\ < t 



865^ 



20 



Y(-h) = exp (x - |3c:| V/?" + 1) 

 2Vp2 -f- 1 



Same as 19, except Cause: Vertical force 

 at x = 0. 



^/o(V/2-jc2), 



\x\ < t 



866 



21 



Y(p)=^ylpKr(rylp) 



Flow of heat in infinite plane. Cause: 

 Temperature impulse at origin, tempera- 

 ture maintained zero along x-axis, except 

 at origin. Effect: Temperature of point 

 with coordinates (x, y) at time t. 



4Tt' 



exp 



(-i} 



< i 



921 



22 



Y{p) 



= i[l-exp(- 



erf 



< / 



2^vt 



Horizontal oscillations of deep viscous 

 fluid, axis of y vertical, bottom plane 

 y = 0, kinematic coefficient of viscosity 

 V. Cause: Applied horizontal force. 

 Effect: Displacement of particle at y at 

 time t, y assumed small. 



803 



23 



(?) 



Zw 



Water waves radiating from center in an 

 unlimited sheet of uniform depth h, 

 gravity constant = g. Cause: Pressure 

 at the origin. Effect: Velocity potential 

 at distance r, time t. c^ = gh. 



1_ 



2x 



< / 



/2 - 



912 



