ELECTRICAL CAPACITY 303 



regard to electricity, a part precisely analogous to the rdle of pressure, or of tempera- 

 ture, in the case of motions of fluids and of conducted heat. It would tax your 

 patience too much were I to give an exact definition of potential in a lecture like 

 this ; but you may get a sufficiently approximate notion of it in a very simple way 

 again by analogy. Suppose I wished to specify the power of the pump used to 

 compress air in an air-gun receiver. I should say it can produce a limiting pressure 

 of 40 or 100 atmospheres, as the case may be. If you try to go any farther it 

 leaks. This would be considered quite definite information. But, mark you, nothing 

 is said as to the capacity of the receiver. When the pump has done its utmost, 

 the receiver, be it large or small, contains air at the definite pressure of the 40 or 

 100 atmospheres which measure the power of the pump. 



A longer time will be required for a more capacious receiver, but the ultimate 

 pressure is the same in all. And when two receivers contain air at the same 

 pressure you may open a communication between them, but no air will pass, how- 

 ever much they may differ in capacity. Similarly, you may measure the power 

 of a flame or a furnace by the highest temperature it can produce. It will take a 

 longer time to effect this the greater is the thermal capacity of the body to be 

 heated ; but when two bodies are at the same temperature no heat passes from one 

 to the other. Similarly, the power of an electrical machine may be measured by 

 the utmost potential it can give to a conductor. The greater the capacity of the 

 conductor the longer time will be required for the machine to charge it ; but no 

 electricity passes between two conductors charged to the same potential. Hence 

 the power of a machine is to be measured by using the simplest form of a conductor, 

 a sphere, and finding the utmost potential the machine can give it. It is easily 

 shown that the potential of a solitary sphere is directly as the quantity of electricity, 

 and inversely as the radius. Hence electricity is in equilibrium on two spheres 

 connected by a long thin wire when the quantities of electricity on them are pro- 

 portional not to their surfaces, nor to their volumes, as you might imagine to 

 their radii. In other words, the capacity is proportional to the radius. This, how- 

 ever, is only true when there are no other conductors within a finite distance. 

 When a sphere is surrounded by another concentric sphere, which is kept in metallic 

 connection with the ground, its capacity is notably increased, and when the radii 

 of the spheres are nearly equal the capacity of the inner one is directly as its 

 surface, and inversely as the distance between the two spheres. Thus the capacity 

 is increased in the ratio of the radius of one sphere to the difference of the radii 

 of the two, and this ratio may easily be made very large. This is the principle 

 upon which the Leyden jar depends. 



We may usefully carry the analogy of the pump a good deal further. Supposing 

 the piston to be fully pressed home every stroke, the amount of work spent, even 

 if the whole be kept cool, on each stroke continually increases, so that more than 

 double the amount of work is required to charge the receiver to 40 atmospheres 

 instead of 20. The same holds with electricity. Each successive unit of the charge 

 requires more work to force it in than did the preceding one, because the repulsion 

 of all already in has to be overcome. It is found, in fact, that the work required 

 to put in a charge is proportional to the square of the charge. Of course less work 



