532 Dr. A. Kussell on the Effective Resistance 



When the value of x is not less than 7, the inaccuracy of the 

 formula 



£ x V2+1/4 \l2x 



Z7TX 



is less than 1 in 10,000. 



Heaviside * has given the formula X=e A 2 /2ttx, but in 

 order to get a four-figure accuracy with this formula x would 

 have to be greater than 1500. 



In a similar manner, we find that 



z = x (-W-i-8^> • • • • < 28 > 



W = X (w + 8^ + i) <*> 



These formulae also give the ratios Y/X, Z/X, and W/X- 

 They correspond to (11), (12), and (13), and give a four- 

 figure accuracy when x is not less than 8. 



By the binomial theorem, we also readily deduce the fol- 

 lowing formulae corresponding to (14) and (15) : — 



Y = 7I~87l^~8^ * ' ' (30) 

 and 



w 1 1 3 n 



Y - V2 + Tx + %J& { } 



To test these formulae let us take the low value of 6 for x. 

 We find from (20) and (21) that 



ber6=-8*858 and bei6=-7«335. 



These results are in exact agreement with their values found 

 by direct computation from the series given in (5) and (6) . 

 The accuracy of the formulae rapidly increases as x increases. 

 In the following table the numbers obtained by sub- 

 stituting 10 for x in formulae (20), (21), (24), and (25) 

 are compared with the numbers given by Kelvin f and by 

 Mascart and Joubert f. 



* ' Electrical Papers/ vol. ii. p. 184. 

 "j~ L.c. ante. 



