CHAP, iv.] ELECTRICITY AND MAGNETISM. 203 



sphere possesses unit capacity. The capacities of spheres 

 are proportional to their radii. Thus, a sphere of one 

 metre radius has a capacity of 100. The earth has a 

 capacity of about 630 millions (in electrostatic units). 

 It is almost impossible - to calculate the capacities of 

 conductors of other shapes. It must be noted that the 

 capacity of a sphere, as given above, means its capacity 

 when far removed from other conductors or charges of 

 electricity. The capacity of a conductor is increased by 

 bringing near it a charge of an opposite kind ; for the 

 potential at the surface of the conductor is the sum of 

 the potential due to its own charge, and of the potential 

 of opposite sign due to the neighbouring charge. Hence, 

 to bring up the resultant potential to unity, a larger 

 quantity of electricity must be given to it ; or, in other 

 words, its capacity is greater. This is the true way of 

 regarding the action of Leyden jars and other accumu- 

 lators, and must be remembered by the student when he 

 advances to the consideration of the theory of accumu- 

 lators, in Lesson XXII. 



248. Surf ace -density. 1 This term was applied 

 by Coulomb to denote the amount of electricity at any 

 point of a surface. It was mentioned in Lesson IV. that 

 a charge of electricity was never distributed uniformly 

 , over a conductor, except in the case of an insulated 

 sphere. Where the distribution is unequal, the density 

 at any point of the surface may be expressed by con- 

 sidering the quantity of electricity which exists upon a 

 small unit of area at that point. If Q be the quantity 

 of electricity on the small surface, and S be the area of 



1 The word Tension is sometimes used for that which is here precisely 

 defined as Coulomb defined it. The term tension is, however, unfortunate ; 

 and it is so often misapplied in text-books to mean not only surface-density 

 but also potential, and even electric force (i.e., the mechanical force exerted 

 upon a material body by electricity), that we avoid its use altogether. The 

 term would be invaluable if we might adopt it to denote only the mechanical 

 stress across a dielectric, due to accumulated charges ; but so long as the 

 above confusion lasts, it is better to drop the term entirely, and the student 

 will have one thing fewer to learn and to unlearn. 



