352 Mr. H. A. Rowland 0:1 Magnetic Distribution. 



The value of Q" e between and 1 includes the lines of force 

 passing out at the end of the bar, and is therefore too large. 



Fig. 4. 



Plot of Table X. 



In fig. 4 we have a plot of the results found for this bar. The 

 curves are such as we should expect from our theory, except for 

 the variations introduced by the causes which we have hitherto 

 considered. Thus the sharp rise in the curve when near the end 

 of the bar has already been explained in connexion with Table III. 

 A small portion of it, however, is due to those lines of induction 

 which pass out through the end section of the bar j and in future 

 experiments these should be estimated and allowed for*. 



To estimate the shape of the curve theoretically in this case, 

 let us take equation (4) once more, and in it make s ! = oo and 

 s" = \/R<R', which will make it apply to this case. We shall 

 then have A'=— 1, and A" = oo, whence for the positive part 

 of Q" 6 we have 



Q"e 



_ *&ALi r 1 , OgKar-6) _ ^(x-b) i _ «&AL .r(x-b) \ 2 



9.W.V 1 ' 9.P'- i i — € i > 



2K J 



and for the negative part 



Q "«= _ fiS (1 + e ^ x ' b)) (1 -•""> ; 



therefore the real value is 



Q "«= " fw 0**- 4) («-'*-2) +•— )■ 



* When considering surface-density, we should also allow for the direct 

 action of the helix, though this is always found too small to be worth 

 taking into account except in very accurate experiments. 



