486 Mr. J. L. W. Gill on the Distribution of 



writing K fl 1 ' 6 for - (K/ ,6 + K 2 1M3 + . , . K n 1 ' 6 ), which is a 

 constant. 



B 1 ™=KJ*(f(E))™, 



B, =K,/'(H) (3) 



The latter part of equation (3) obviously represents the 

 induction at some definite point of the specimen, which is the 

 result deduced by Prof. Fleming. 



The induction at the centre of the specimen may be repre- 

 sented by the equation 



Bmax.-K c /(H) (4) 



Combining equations (3) and (4) 



^3 = tt~ = constant (0) 



B max. K c v 



This is the result deduced by the author. 



For very short specimens it is well known that the functions 

 representing the induction at different sections are straight 

 lines below saturation. In such cases the above results are 

 correct a priori. As the length of the specimen increases 

 these functions deviate from straight lines but are more or less 

 similar. It was to determine the range and limit of this 

 similarity that so many observations were taken. 



From the above equations it 'follows that similar relations 

 exist for any function of the induction. 



It has been found from the observations that the ratio of 

 the mean value of the induction to the maximum is *745. 



The effect of saturation can be seen most plainly by com- 

 paring specimens Nos. 1 and 2, Table II. For specimen 

 No. 1 the value of K and the ratio of B x to B max. varies 

 from an induction of about 10,000, while for specimen No. 2 

 these ratios remain constant up to an induction of 14,000. 



From the B-H curves for the centre of these specimens, 

 shown in fig. 3, it will be seen that saturation begins at a 

 much lower value of the induction for specimen No. 1 than 

 for No. 2, 



This explains the difference referred to. 



Law of Distribution of Induction. 



Since a complete mathematical analysis of this problem is 

 at present impossible, no attempt has been made to derive 

 theoretical equations. Other writers have derived equations, 

 but these are either based on hypotheses which are not 

 altogether warrantable or are deduced by approximation. 



