icith the Flow of Electricity in a Plane, 



45 



may notice how nearly they divide the interval allowed to them, 

 2 — 2 cos 6, in the ratio 1 : 3. The quantity which actually 



does this is ~— — ; and this quantity agrees with the known 



values of f(&) to an extent shown in the Table. 



9. 



f(0). 



3+ COS 



2 











45 



60 



90 



180 



20 



1-854 



1766 



1-57 



10 



20 



1-853 



175 



1-50 



10 



The maximum divergence appears to occur about when 

 = 90°. 



The empirical formula, then, 



2 -») o»y 



0kS g \ p 3+ cos 



gives the resistance of any isosceles triangle with poles on the 

 equal angles 6 with sufficient accuracy for a practical purpose ; 

 and it becomes very accurate indeed when the equal angles are 

 small. The value of Q indicated by it for the case 0=30° is 



1'Q33n ' an( ^ ^ ven ^ ure t° think that the real value will be found 



to differ from this only in the last place of decimals. 



The resistance to the flow of electricity from a central elec- 

 trode of radius p to the periphery of a regular polygon of n 

 sides is, to the same degree of approximation as the above, 



^ lo 4rrr~^' (20) 



r 3 + cos - 

 n 



r being the radius of the inscribed circle. 



§ 28. And here I would remark that the thickness (8) of the 

 plate in which the flow takes place has never been limited in 

 any way ; so the plate may extend itself into a cylinder of any 

 length, provided the point poles extend themselves into lines at 

 the same time. Also, though we are using the language of 

 dynamic electricity only, yet the resistance obtained applies 

 equally well to heat if we substitute hot and cold bodies for 

 sources and sinks, temperature for potential, and isothermals 

 for equipotential lines. Further, by reason of the analogy be- 

 tween conductivity and inductive capacity, we obtain at the 



