41 8 Note 27: dielectric capacities 



NOTE 27, ART. 376. 



Electrostatic capacity of different substances. 



Cavendish Boltzmann Wiillner Gordon 



Shellac* 4-47 2-95103-73 2-746 



Rosin 2-55 



Rosin and bees'-wax . . . 3-38 



Dephlegmated becs'-wax 3-7 



Plain bees'-wax 4 



Sulphur SchiJto 3-84 2-88 to 3-21 2-579 



Ebonite 2-21102-76 3-15 2-56 2-284 



Paraffin 1-81102-47 2-32 1-96 1-994 



Black caoutchouc 2-12 



vulcanized 2-69 2-497 



NOTE 28, ART. 383. 

 Capacity of a Cylindrical Condenser. 



The rule by which Cavendish computed the charge of a condenser consisting 

 of two cylindrical surfaces having the same axis is given at Art. 313. 



If R is the external and r the internal radius, and / the length of the cylinders, 



T 7? -1 V 



then Cavendish's expression for the "computed charge" is - R -_ -- /. 



The true expression for the capacity is 



i / 



2 log R - log r 

 when the logarithms are Naperian. 



We may express log R - log r in the form of the series 

 R - r 2 /R - A 3 2 /R - 



2 



/R - A 3 2 /R - n 5 , 

 U + ~r) + 5 \M + r) + *" 



R+~r 3 

 and we thus find as an approximate value of the capacity 



r\ 

 f) 



4 R - 





4 R-r I - 3 \FTf ~ 45 T J' 



The first term agrees with Cavendish's rule, for the "capacity" is half the 

 "inches of electricity," but the other terms show that Cavendish's rule gives 

 too large a value for the computed charge. 



* [In Kaye and Laby, Physical and Chemical Constants, 191 1, the value for shellac 

 is given as 3 3-7 and for rosin as 1-8 2-6. The value for crown glass is given as 5 7 

 and for flint as 7 10, both well above shellac, as Cavendish found, but in a different 

 order. Cavendish's results are tabulated in Note 15, supra. It is found by Eguclii, 

 Proc. Phys. Math. Soc. of Japan, 1 920, that a mixture of resin and beeswax, solidified 

 under pressure, exhibits permanent polarization, which is absent in the separate 

 substances.] 



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