GEOMETRICAL MEAN DISTANCES. 119 



If the figure is within the interior of the corona, the geometrical 

 mean distance being the same for all points, the mean distance is 

 equal to that of the centre to the corona, and is independent of the 

 shape of the figure. 



6th. For a point situate in a circle of radius a, and at a distance r 

 from the centre, the mean distance will be obtained by considering 

 the point as external to the circle of radius r and inside the comple- 

 mentary corona. We thus find 



and for the centre 



R = tf-i = o '60663 a. 



yth. For two circles external to each other the geometrical mean 

 distance R is the distance of the centres, since the action of two 

 currents parallel to circular sections (756) only depends on this 

 distance R. 



8th. The geometrical mean distance R 2 of a point to a straight 

 line, enables us to determine the geometrical mean distance of all 

 points of a right line of length #, which gives 



3 ~, or 



2 



9th. In like manner for a rectangle with sides a and , we have 



.. 



6 o 1 ' a 2 - 6 a 



2 a b 2 b a 25 

 + - - arc tan - H arc tan , 



3 b a 3 a b 12 



and for a square of side a, 



/.R 9 = /.# + -/. 2 + -- = /.a- 0-80508, 

 3 3 12 



where 



R 2 = 0-447050. 



