ON THE ABSOLUTE UNIT OF ELECTRICAL RESISTANCE 161 

 where H^ x log. (r + / y? + r 2 ) , 



o _ 1.3.5. . 2t- 



'2 1 (2* -1)2 



' 2t - 3 (it - l)(2i - 3) 2.4 



D = C 2 *' 8 _ i(t'-l)..(* 6) 



'2i 5 (2i-i)(2t 3)(2i - 5) 2.4.6' 



E t = &c., &c. 



Substituting the limits for x, r and a, we find 

 + V ^ 2 



o = i / 1 f ^ ___ ^_ 1 / If r 3 \\ 



\ X \(ff + X z )l (r 2 + JT')i "^ ^ + a?)l (r 2 + z*)*J J ' 





The needle consisted of two parallel lamina? of steel of length, Z, and 

 a distance, W, from each other. As the correction for length is small, 

 we may assume that the magnetism of each lamina is concentrated in 

 two points at a distance n / from each other, where n is a quantity to 

 he determined. 

 Hence 



W 



where cos & /71 .., _,, seeing that the needle hangs parallel to 



* 



the coils. In short thick magnets, the polar distance is about Z and 

 the value of n will be about f . For all other magnets it will be between 

 this and unity. In the present case n = f nearly. 



As all the terms after the first are very minute, this approximation 

 is sufficient, and will at least give us an idea of the amount of this 



source of error. 

 11 



