836 



as possible, and to allow it to be clearly seen from any external 

 position with as little embarrassment as possible, a cage made like a 

 bird's cage, with an extremely fine wire on a metal frame, inside the 

 glass shade used to protect the instrument from currents of air, &c., 

 may be substituted with advantage for the tinfoil network lining of 

 the glass. It appears therefore that a properly constructed electro- 

 meter is an instrument for measuring, by means of the motions of a 

 moveable conductor, the difference of potentials of two conducting 

 systems insulated from one another, of one of which the case or cage 

 of the apparatus forms part. It may be remarked in passing, that it 

 is sometimes convenient in special researches to insulate the case or 

 cage of the apparatus, and allow it to acquire a potential differing 

 from that of the earth, and that then, as always, the subject of 

 measurement is the difference of potentials between the principal 

 electrode and the case or cage, while in the ordinary use of the 

 instrument the potential of the latter is the same as that of the 

 earth. Hence we may regard the electrometer merely as an instru- 

 ment for measuring differences of potential between two conducting 

 systems mutually insulated ; and the object to he aimed at in per- 

 fecting any kind of electrometer (more or less sensitive as it may be, 

 according to the subjects of investigation for which it is to be used), 

 is, that accurate evaluations in absolute measure, of differences of 

 potential, may be immediately derivable from its indications. 



9. Relation between electrostatic force and variation of electric 

 potential. 7, otherwise stated, is equivalent to this : The ave- 

 rage component electrostatic force in the straight line of air between 

 two points in the neighbourhood of an electrified body is equal to 

 their difference of potentials divided by their distance. In other 

 words, the rate of variation of electric potential per unit of length in 

 any direction, is equal to the component of the electrostatic force in 

 that direction. Since the average electrostatic force in the line joining 

 two points at which the values of the potential are equal, is nothing, 

 the direction of the resultant electrostatic force at any point must be 

 perpendicular to the equipotential surface passing through that 

 point ; or the lines of force (which are generally curves) cut the 

 series of equipotential surfaces at right angles. The rate of varia- 

 tion of potential per unit of length along a line of force is therefore 

 equal to the electrostatic force at any point. 



