364 Note 2 : distribution of attracting ftma in thin rods 

 so that if A,, denotes the mean linear density, 



2 r + 



when n = 2, A = A,,, or the density is uniform. 



Since the fluid is in equilibrium in all these cases, the potential is uniform 

 throughout the body. We may therefore determine the value of the potential 

 at any point within the body by finding its value at any selected point, as for 

 instance at the centre. If de be an element of the fluid, and r its distance from 

 the given point, the corresponding element of the potential due to the force 



whose value is er~ n is er l ~ n . 



n i 



We thus find for the potential of the sphere 



n - i 



When n becomes equal to 4, V becomes infinite. 

 When n is equal to 2, V= Qa~ l . 



For the plate bounded by parallel planes, V is infinite, except for values 

 of n between 3 and 4, for which 





(n -i)(- 3) 



/T\ 



where <T O is the quantity of fluid in unit of area of the plate. 

 For a circular disk 



in which n must be between i and 3. 

 When n = 2, V =- Oa~ l . 



2 * 



For an infinitely narrow rod 



