Lines of Induction in a Mcnjiidic Field. 



235 



thickness. As a consequence, there will be a convergence of the 

 stream-lines on the area of greater thickness. 



When experiments with liquid layers of variable thickness were first 

 tried, a general resemblance was noticed between the stream-lines so 

 obtained and the lines of induction due to the presence of a permeable 

 substance in a uniform magnetic field. 



The main object of the present paper was to investigate accurately 

 whether complete correspondence between the two cases really existed, 

 and, should correspondence be established, to apply the method to the 

 solution of a number of two-dimensional magnetic problems. The 

 investigation thus involved 



(1) A mathematical treatment of the subject, by means of which 

 plotted diagrams could be obtained for comparison with experimental 

 results. 



(2) The construction of apparatus capable of giving exact results 

 which could be photographed. 



(3) The investigation of the laws connecting the rate of flow with 

 the thickness of film of the liquid used. 



The theoretical case selected as a test case was that of an elongated 

 elliptic cylinder placed with its major axis along the field, the 

 permeability being assumed to be 100. The lines of induction for this 

 case are shown in the accompanying diagram, and were calculated and 

 plotted by the method explained in the paper. 



DIAGRAM. 



If, for the moment, we assume that the liquid stream-lines are 

 identical with lines of magnetic induction, then the following corre- 

 spondence between the two cases holds : 



