with the Flow of Electricity in a Plane. 41 



Resistance of an equilateral triangle. Poles on two of the 



angles. 



§25. The images of A for this case are shown in fig. 6, 



Fig. 6. 



3 • * 



A 



2 • 



• A— °B 



1 • • 



2 • • • 



3 • 



Images of the pole A in an equilateral triangle. 



being on the vertices of equilateral triangles V3 times the 

 linear dimensions of the original one. Take the images in rows 

 as before (§ 23), calling the line A B row ; and find the product 

 Q^, for each row separately. 



n 2.4.5.7.8.10... 3V3 ,—„ 



Q ° = 3 .3.6.6.9.9... " TfiF = V ° 2 «°)*(°), 



02= P + 3 5 2 + 3 7 2 + 3 ll 2 + 3 13 2 + 3 



Wl 3* + 3*3 2 + 3'9 2 + 3' 9 2 + 3 'l5 2 + 3'** -<?^ 6 )> 



02 _ 2 2 + 2 2 .3 4 2 + 2 2 .3 8 2 + 2 2 .3 10 2 + 2 2 .3 



^ 2 ~~ 2 2 . 3 ' 6 2 + 2 2 . 3 ' 6 2 + 2 2 . 3 ' 12 2 + 2 2 . 3 ' ' * =A K 2 V3 )> 



l 2 + 3 2 .3 5 2 + 3 2 .3 , 7 2 + 3 2 .3 



^ 3 ~3 2 + 3 2 .3 3 2 + 3 2 .3 9 2 + 3 2 .3-** = <H^^)> 



. . . . . . . • . . . i 



and 



Q = 2™ <£( V3)f (2 V3)tf>(3 V3)f (4 V3) . . . . 



Now 



,, N 1 2 + ^ 2 5 2 + ^ 



3 2 + ^ 2 3^ + ^ 2 9 2 + ^ 2 



l + 3tanh 2 ^ 

 b 



