ON STANDARDS OF ELECTRICAL RESISTANCE. 499 



disk hung centrally over it, from one end of the beam of a balance. In two 

 papers entitled " Measurement of Electostatic Porce produced by a Battery " 

 and " Measurement of the Electromotive Force required to produce a spark in 

 Air between parallel metal plates at different distances," published in the Pro- 

 ceedings of the Royal Society* for February 1860, I described applications 

 of this electrometer, in which, for the first time I believe, absolute electro- 

 static measurements were made. The calcidations of diiferences of potentials 

 in absolute measure -were made according to the formula quoted above (§ 17) 

 from my old paper on " The Elementary Laws of Statical Electricity." 



§ 19. This formula is rigorous only if the distance between the disks is 

 infinitely small in comparison with their diameters ; and therefore, in my 

 earliest attempt to make absolute electrostatic measurements, I used very 

 small distances. I found great difiiculty in securing that the distance should 

 be nearly enough equal between diff'erent parts of the plates, and in measu- 

 ring its absolute amount with sufficient accuracy ; and found besides serious 

 inconveniences in respect of sensibility and electric range : later I made a 

 great improvement in the instrument by making only a small central area 

 of one of the disks moveable. Thus the electric part of the instrument 

 becomes two large parallel plates with a cii'cidar aperture in one of them, 

 nearly filled up by a light circular disk supported properly to admit of its 

 electrical attraction towards the other being accurately measured in absolute 

 units of force. The disk and the perforated plate surrounding it will be 

 called, for brevity, the disk and the guard-plate. The faces of these two 

 next the other plate must be as nearly as possible in one plane when the 

 disk is precisely in the position for measuring its electric force, which, for 

 brevity, will be called its sighted position. The space between the disk and 

 the inner edge of its guard-ring must be a very small part of the diameter 

 of the aperture, and must be very small in comparison with the distance 

 between the plates ; but the diameter of the disk may be greater than, equal 

 to, or less than the distance between the plates. 



§ 20. Mathematical theory shows that the electric attraction experienced 

 by the disk is the same as that experienced by a certain part of one of two 

 infinite planes at the same distance, with the same difference of electric 

 potentials, this area being very approximately the mean between the area 

 of the aperture and the area of the disk, and that the approximation is very 

 good, even although the distance between the plates be as much as a fourth or 

 fifth, and the diameter of the disk as much as three-fourths of the diameter of 

 the smaller of the two plates. This conclusion will be readily assented to 

 when we consider thatf the resultant electric force at any point in the air 

 between the two plates is equal numerically to the rate of conduction of 

 heat per unit area across the corresponding space in the following thermal 

 analogue. Let a solid of uniform thermal conductivity replace all the air 

 between and round the plates ; and in place of the plates let there be hollow 

 spaces in this solid. Let these hollow spaces be kept at two uniform tempe- 

 ratures, differing by a number of degrees equal numerically to the differ- 

 ence of potentials in the electric system, the space corresponding to the 

 disk and guard-ring being at one temperature, and that corresponding to tlie 

 opposite plate at the other temperature ; and let the thermal conductivity of 

 the solid be unity. If we attempt to draw the isothermal surfaces between 



* Phil. Mag. September and October 1860. 



t " On the Uniform Conduction of Heat through Solid Bodies, and its connexion with 

 the Mathematical Theorv of Electricity," Cambridge Mathematical Journal, Feb. 1842, 

 and Phil. Ma^. July 1854. 



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