204 ELEMENTARY LESSONS ON [CHAP. iv. 



that small surface, then the surface density (denoted by 

 the Greek letter p) will be given by the equation, 



o- Q 

 P ~~~S 



In dry air, the limit to the possible electrification is 

 reached when the density reaches the value of about 20 

 units of electricity per square centimetre. If charged to 

 a higher degree than this, the electricity escapes in 

 " sparks " and "brushes" into the air. In the case of 

 uniform distribution over a surface (as with the sphere, 

 and as approximately obtained on a flat disc by a parti- 

 cular device known as a guard-ring), the density is found 

 by dividing the whole quantity of the charge by the 

 whole surface. 



249 Surface-Density on a Sphere. The surface 

 of a sphere whose radius is r, is 4?rr 2 . Hence, if a 

 charge Q be imparted to a sphere of radius r, the surface- 

 density all over will be p or, if we know the 



surface - density, the quantity of the charge will be 

 Q 4irrV 



The surface-density on two spheres joined by a thin 

 wire is an important case. If the spheres are unequal, 

 they will share the charge in proportion to their capacities 

 (see Art. 37), that is, in proportion to their radii. If the 

 spheres are of radii 2 and i, the ratio of their charges 

 will also be as 2 to i. But their respective densities will 

 be found by dividing the quantities of electricity on each 

 by their respective surfaces. But the surfaces are pro- 

 portional to the squares of the radii, 2'.*., as 4 : i ; hence, 

 the densities will be as i : 2, or inversely as the radii. 

 Now, if one of these spheres be very small no bigger 

 than a point the density on it will be relatively 

 immensely great, so great that the air particles in con- 

 tact with it will rapidly carry off the charge by convection. 

 This explains the action of points in discharging con 

 ductors, noticed in Chapter I. Arts. 35 c, 42 and 43. 



