y 



ON A ROTATIONAL MOTION OF THE CATHODE DISC 

 IN THE CROOKES TUBE.* 



Francis E. Nipheb. 



It is well known that the equations which represent the 



properties of the magnetic field external to a conductor, are 



inconsistent when applied to points within the body of the 



conductor. Assuming the total magnetic force within to be 



tangent to a circle whose center is at the wire center, and the 



surfaces of equal potential are radial planes. Assuming the 



force due to an element of the conductor of infinite length 



2dt 

 and of section ds to be , it follows that the force at any 



point without the conductor varies inversely, and at an in- 

 ternal point, directly as the distance from the center. If 

 now within the wire, we assume any radial plane as a datum 

 equipotential plane, and determine the locus of any other 

 equipotential surface, such that the difference of potential, 

 measured along the lines of force, is constant, this surface 

 turns out to be one having as a cross-section, a spiral known 

 as the lituus having the radius as an external asymptote, and 

 reaching the center after an infinite number of turns. It is 

 evident that these internal surfaces of equal potential cannot 

 be both radial planes, and spiral cylinders. 



Maxwell disposes of this absurdity to which the equations 

 lead, in the single sentence which closes section 606 of his 

 Electricity and Magnetism. He says: " Within the substance 

 of the conductor, there is no such thing as magnetic poten- 

 tial." 



It has long seemed to me that this failure of the equations 

 must be the result of leaving some elements of the problem 

 out of the discussion. I have spent a great amount of time 

 in seeking for some rotational phenomenon hitherto unrepre- 



* Bead before The Academy of Science of St. Louis, May 4, 1896. 



(181) 



