220 Mr. 0. Heaviside on the Speed of Signalling 



abscissas represent time, from t = to t = AOa, the unit being 



ckl 2 

 a — , 2 log e 10. The ordinates represent the arrived current, 



the maximum strength being in all cases =100. 



1. m — 0, n = 0. Let N be the percentage amount of received 

 current at time t, then 



N 2 _t a * a < 



zrjr- = 1 + - 2 COS 17T6 T . 

 100 7T 



2. m = 0, tt = ^. 



tana + - =0, 

 N - v , 12 cos a _^i 



=1+1 ■ 6 T , 



100 r 5+cos2a 



3. 7)i—0, n = l. 



tana-f-a = 0, 



N =1-42 e ~ T 



100 cosa+ sec a 



4 m=0, n = 2. 



tan a + 2a = 0, 



N _ ^ 6 cos a "j** 

 100"" 2+cosa € "* 



5. ???=0, 71 = GO . 



N - 4 -cos «r ,(«-;y 



=1-4 X g 4cA:f» . 



100 + 7T 2i-l 



6. 7?i = l, n = l. 



, 2a 



tan a = -it- — 



100"" "*3 + a 2 ' 



Curve (1) is the arrival-curve when no resistance is inserted 

 at either end ; curve (2) when a resistance equal to one half 

 the cable's resistance is inserted at either end ; curve (3) when 

 a resistance equal to the cable's is inserted at either end ; and 

 curve (4) when twice the cable's resistance is inserted at either 

 end. (5) shows the curve of arrival of the potential at the 

 insulated end of a cable when the other end is raised to a con- 



