ATMOSPHERIC ELECTRICITY. 



515 



We have already employed the term " potential," a word of fre- 

 quent occurrence in modern electrical works. An insulated, charged 

 conductor exerts influence in every direction about it. The term " elec- 

 trical potential " expresses the value of that influence at any specified 

 point where there is electrical force. When any force acts, energy is 

 expended in doing work ; and the numerical value of the scientific ex- 

 pression " work " is the measure of the energy expended or the resist- 

 ance overcome. " Work " means the product of the force into the dis- 

 tance over which it acts. The lifting of five pounds through a dis- 

 tance of ten feet requires the expenditure of fifty foot-pounds of work. 

 Hence " electrical potential " may be defined in terms of work as fol- 

 lows : The electrical potential at any point is the toork required to 

 carry a unit of electricity from that point to infinity. It is of course 

 understood that the " unit of electricity " is carried against the attrac- 

 tion due to an electrified body. 



Potential is accordingly a mathematical and exact expression for 

 all the work possible to be done against the attraction of a given amount 

 of electricity resident at some specified place. In exactly the same way 

 gravitational potential at any point may be defined as the work re- 

 quired to carry a unit mass of matter from that point to infinity against 

 the attraction of gravitation. 



Electrometers have been constructed by Sir William Thomson, with 

 marvelous skill and inventive genius, designed to measure the potential 

 at any point or of any body. It is susceptible of easy proof that the 

 potential of a sphere, charged with electricity, Q, is everywhere equal 

 to Q divided by its radius R. Further, the capacity of a body for elec- 

 tricity is the quantity required to charge it to emit potential ; and, as 

 potential varies with the charge, we readily find that the capacity of 

 a sphere is numerically equal to its radius. 



To apply this to condensation, suppose that drops of water of unit 

 radius, unit capacity, and unit potential, coalesce to form drops of 

 radius two : what will be the capacity and potential of such larger 

 drops ? Since the volume of spheres varies as the cube of their radii, 

 eight of the small drops will be required to make one large one. The 

 large drop will, therefore, contain eight times as much electricity as 

 each of the small ones. As compared with the small, drops, its capaci- 

 ty, being equal to its radius, will be only doubled, while its charge 

 will be increased eightfold ; and its potential will, therefore, be four 

 times as great as that of the small drops, since potential of a sphere 

 equals quantity of electricity divided by capacity of sphere. If its po- 

 tential is quadrupled, its inductive influence on other bodies and its 

 tendency to discharge are increased in the same ratio. 



When, therefore, condensation occurs, aggregating minute globules 

 of water into larger ones, the electric tension of the mass of descend- 

 ing vapor is immensely increased, without any corresponding increase 

 in the total quantity of electricity present. 



