272  Mr.  A.  Russell  on  the 
Table  XIII. 
Calculated  Values  of  the  Disruptive  Voltages  between  large 
Spherical  Electrodes. 
V=kilovolts    (direct    pressure).       V'  =  effective    kilo  volts 
(alternating  pressure)  when  V'  =  V/^/2. 
x  in  cms. 
2  cm.  spheres. 
20  cm.  spheres. 
200  cm. 
spheres. 
2000  cm 
V. 
.  spheres. 
V. 
y. 
V. 
V. 
V- 
V. 
V. 
o-i 
4-5 
3-2 
4-6 
3-25 
4-6 
3-25 
4-6 
3-25 
0-5 
17-0 
12-0 
19-4 
13-9 
19-8 
14-0 
19-8 
140 
10 
28-8 
20-3 
37-7 
26-7 
38-8 
27-4 
38-8 
27-4 
5-0 
611 
43-3 
163 
115 
187 
132 
191 
135 
10-0 
280 
198 
370 
262 
381 
269 
5O0 
604 
427 
1625 
1150 
1860 
1320 
100-0 
2795 
1980 
3690 
2610 
500-0 
6030 
4270 
16200 
11500 
1000-0 
28000 
20000 
5000-0 
60000 
42500 
If  the  electrodes  were  infinite  planes,  the  direct  pressure 
required  to  produce  the  disruptive  discharge  when  they  were 
50  metres  apart  would  be  190  million  volts. 
With  spherical  electrodes  of  10  metre  or  less  radius, 
about  60  million  volts  would  be  sufficient  to  spark  over  the 
same  distance.  We  suppose  of  course  that  the  P.D/s  are 
established  sufficiently  slowly  to  allow  the  Faraday-tubes  to 
attain  their  positions  of  statical  equilibrium  approximately 
before  the  discharge  occurs. 
Appendix  II. 
The  Capacity  Currents  to  the  Electrodes. 
The  formulas  (9)  and  (10)  enable  us  to  find  at  once  the 
analytical  expressions  for  the  electrostatic  coefficients  of  two 
equal  spheres.  If  Q,  Q'  denote  the  charges  and  Y1  and  V2 
the  potentials  of  the  electrodes,  we  have  * 
Q  =  K1.1V1  +  KP2V2 
and  Q'=KrtVs  +  Ka.iY1. 
In  our  case  Kri  —  K22  •     By  making  V2  =  0,  we  get  by  (9) 
and  by  (10) 
Ki-i  =  a 
Ki-o  = 
-f*     7 
l-g 
2n-l 
y- 
,,2h 
7 
?T 
Russell.  '  Alternating-  Currents/  vol.  i.  p.  89  et  seg. 
