264 



ELECTRICAL MEA8UREMEN / > 



extra high voltages, above 50 kv. It is not so well adapted for 

 low voltages for the spheres must be brought very near tog- 



The spheres should be at least twice the gap distance from 

 surrounding objects and greater than this if one sphere is 

 grounded. 



If the current be limited to less than 1 amp. by water-tube 

 resistances, pitting of the spheres is avoided and they need be 

 repolished only occasionally. 



When neither sphere is grounded, it is possible to calculate 

 mathematically the relation between the breakdown voltage and 

 the length of gap. The dielectric stress will be a maximum at 

 the points where the line joining the centers of the spheres cuts 

 their surfaces. If the value of the potential gradient at this 

 point be denoted by g, then it may be shown that 



(11) 



/ kv./cm. 



V is the potential difference and x the distance apart of the 



V 

 surfaces. is therefore the average potential gradient; / is a 



factor which depends on x and the radius of the spheres, a; 

 it is the quantity which must be multiplied into the average 

 gradient to give the maximum gradient and has been expressed 

 in the form of an infinite series by A. Russell 5 . 



TABLE II. VALUES OF /, NEITHER SPHERE GROUNDED, COMPUTED BY 



A. RUSSELL 



a 



0.0. 

 0.1. 

 0.2. 

 0.3. 

 0.4. 

 0.5. 

 0.6. 

 0.7. 

 0.8. 

 0.9. 

 1.0 

 1.5. 

 2.0. 



1.000 



1.034 



1.068 



1.102 



1.137 



1.173 



1.208 



1.245 



1.283 



1.321 



1.359 



1.559 



1.770 



3.0 2 214 



4.0 2.677 



These values are plotted in Fig. 150. 



