388 Note 13: electric distribution on two cylinders 



To indicate the degree of approximation, the value of f and of the successive 

 terms of the denominator are given below. 



8 Denominator of (34) and (35) 



b 



ist term 2"d term 3 r "l term 



10 3-68888 2-68888 - 0-43151 



20 4-38203 3-38203 - 0-13680 



30 478749 378749 - 0-09775 



50 5-29832 4-29832 - 0-07191 



100 5-99146 4-99146 - 0-05291 - 0-13566 



looo 8-29405 7-29405 - 0-02818 - 0-00892 



The observed capacities of Cavendish's cylinders may be deduced from the 

 numbers given in Art. 281 by taking the capacity of the globe of 12-1 inches 

 diameter equal to 6-05, and their capacities as calculated by the formula of this 

 note are given in the following table. 



Capacity by As measured by 

 Length Diameter fo rmu i a Cavendish 



72 -185 5-668 5-669 



54-2 -73 5-775 5754 



35-9 2-53 5-907 6-044 



The agreement of the calculated and measured values is remarkable. 



NOTE 13, ARTS. 152, 280. 

 [Electric Distribution on] (wo cylinders. 



In the case of two equal and parallel cylinders at distance c, _the linear 

 densities being uniform and equal to A t and A 2 , the part of the potential energy 

 arising from their mutual action is 



-i jX^dx = fafadx - AA (4! log r - 2f) , 



\ / 



where r 2 = 4/ 2 + c 2 . 



If the two cylinders are in electric communication with each other A, A 2 , 

 and the capacity of the two cylinders together is approximately 



_ 2/ _ 

 4/ r 2l r - c ' 



If a cylinder is placed at a distance d from a conducting plane surface and 

 parallel to it, then the electric image of the cylinder will be at a distance c = zd, 

 and its charge will be negative, so that the capacity of the cylinder will be 

 increased. The capacity of the cylinder in presence of a conducting plane at 

 distance \c, is , 



. 4/ . r + zl r - c 



log J- -i- log +-J- 





Thus in Cavendish's experiment he used a brass wire 72 inches long and 

 0-185 i' 1 diameter. Tin: capacity of this wire at a great distance from any other 



