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Theori/ of tlw Quadratif EJectrometev. 239 



The late Dr. John Hopkinson^ pointed out the imper- 

 fection of the usnal formula oiven in Maxwell f, and also 

 gave an empirical formula which closely represented his 

 experiments. The general result is well known, namely, that 

 the sensibility of the electrometer rises to a maximum as the 

 potential of the needle is raised, and that any further increase 

 in the potential of the needle reduces the sensibility. 



The same effect occurs in the extremely sensitive electro- 

 meters made by Bartels, of Gottingen, several of which have 

 been in use in the Cavendish Laboratory for some time. 

 In these instruments the needle is made of silvered paper, and 

 hung by a single quartz fibre. The quadrants are about 



cms. radius by 1 cm. deep, and the air-space between 

 the quadrants is about 1 mm. The quadrants are mounted 

 on ebonite, and are not adjustable. 



There is no guard-tube for the fibre, and no leyden-jar 

 attached, the insulation being extremely good. With the 

 needle charged to about 100 volts, a deflexion of 1000 mms. 

 per volt, on a scale about 1 metre from the mirror, can 

 readily be obtained, the needle being nearly dead-beat at this 

 sensibility, and quite steady. The shift of the needle during 

 charging is generally but a small fraction of the deflexion for 



1 volt. A maximum sensibility occurs at about 100 volts, but 

 this of course depends on the fineness of the fibre. The 

 sensibility seems to go on diminishing after this, at least 

 until verv hioh voltaoes are used. 



In examining the theory I found that Hopkinson^s formula 

 could be readily explained. 



The referee to whom my paper was sent pointed out that 

 my conclusions conflicted with the experiments of Ayrton 

 and Sumpner | on a White pattern electrometer. I have 

 therefore added to my paper a discussion of their results. 



It will be convenient to give my modified theory of a 

 symmetrical instrument first, and then compare my con- 

 clusions with Ayrton and Sumpner^ s results. 



Let us first indicate the usual theory. Suppose Yj, V2, and 

 V3 are the potentials of the two pairs of quadrants and the 

 needle respectively. 



The energy of the system is given by 



E = icuVr + lc2^\' + icssVr + c,,Y,Y, + c,^Y,Y, + c,,-V,Y„ (1) 



and the force in the direction 6 is given by 



2^^^^ +2B^ -^^2W^^ + B(9 ^^ -^ ^d^'^'^Te ' ^ ^ 



* Phil. :\rag. [5] vol. xix. 1885, p. 291. 

 t '■ Electricity and Magnetism/ vol. i. 

 X Phil. Trans. 1891, vol. clxxxii. p. 519. 



