488 Mr. J. L. W. Gill oh the Distribution of 



derived a similar formula (Phil. Mag. (1875) vol. 1. pp. 257 

 and 348) . He compared a rod magnetized by a helix to an 

 electric circuit. His formula is more general than the others, 

 but it cannot be said that it represents the real distribution 

 with any degree of accuracy, as his own observations show. 



From the experiments above described, it was found that 

 the linear distribution of free magnetism was almost the 

 same as in the case of an ellipsoid magnetized uniformly. 



In the case of the ellipsoid the equation relating the total 

 flux N at any section to its distance x from the centre is 



G£o+ey-' <e » 



N max. being the flux at the centre and a the semi-axis. 



If the leakage or circuital distribution of lines of force for 

 a bar of uniform section were the same as in the case of the 

 ellipsoid the distribution of induction would be represented 

 by the equation 



( b\ /.y 



\B max./ \a J v J 



a being a constant depending on the dimensions of the 

 specimen. 



A comparison of this equation with the curves of distribu- 

 tion obtained from the experiments indicated that the real 

 distribution might be represented by an equation of the form 



(*=.)"+©;-' » 



Assuming as before that the functions of the field repre- 

 senting the induction at different sections are similar (an 

 assumption which the results deduced above would indicate 

 to be correct), it follows that the functions representing the 

 distribution for different fields are also similar. This would 

 also indicate that the distribution might be represented by a 

 function of the nature of equation (8). 



From the numerous observations taken it was found that 

 the real distribution for all Aalues of B max. below saturation 

 is represented very accurately by the equation 



B M /x\ 2 

 (b^T.) +(a) =1 W 



This formula gives the real distribution much more 

 accurately than any other with which the author is acquainted, 

 and can be applied over as great a range. At first sight it 

 would appear that the permeability was neglected since it 



