704 



BELL SYSTEM TECHNICAL JOURNAL 



TABLE II 



No. 



zz 



34 



35 



Admittance Y{p) 

 Illustrative System 

 Cause and Effect 



Y{p) = 



sinh {atp) 

 ap 



Same as 32, except Cause : Initial velocity 



Y{p) =-cos (aV|p|)e!''pl 

 P 



Waves on deep water, axis of y vertically 

 upwards, axis of x in the surface, density 

 = p, gravity constant = g, 3^ = 0. 

 Cause: Initial surface-impulse along x 

 axis. Effect: Velocity potential at time 

 t at point (x, 3'). 



h = 



V27r| 



a = t^lg^ 



Y{p) = ^sin (a^l\p\) 



Same as 34, except EfTect: Surface eleva- 

 tion at time t at point .r. 



Cause: Unit Impulse 

 Effect: SJcY(p) 



2a' 



622 



— at < X < at 



y 



+ 



irp{x^ + y^) 4pV7r(— y + ix) 



X exp - 

 Xerf 



+ 



a^ 



4{— y -\- ix) _ 

 ia 



\3/2 



2 V — y -\- ix 

 ia 



a' 



4pV7r(— y — ixY'^ 

 X exp - 



Xerf 



845 



4(— 3^ — ix) 

 ia 



2V" 



y — IX 



2^^px^^|g p\x\^2Trg\x\ 



X { [cos {^Th')-Tvh's[n (^7r/?-)]C(/?.) 

 + [sin i^irh^) +wh-' cos (^7r/i2)]5(/0 



843* 



+ 



36 



^^, . /- sin (ay \p\) 1 1 



Same as 34, except Cause: Initial surface 

 elevation. 



v.? 



2i^Tr{- y + ix) 



X exp - — — r-r 



|_ ^- y -\- tx) 



^ ia 



Xerf — -= 



2 V — 3; + i"x 



2W7r(- 3* - ix) 

 r a2 



X exp 



Xerf 

 846 



+ 



4{— y — ix) 

 ia 



2^J — y — i 



tx 



