Striated Electrical Discharge. 



255 



terminal conditions. To satisfy these, the closed curve would 

 have to meet the lines A A', BB'. Now if it crosses either of 

 these lines it cannot give a solution at all, and if it is to touch 

 either of them the curve (a) must pass through the point of 

 contact, and this has been seen to be impossible. 



Fie;. 3. 



z-* 



A 



It might, however, be urged that near the electrodes the 

 volume-equations of § 3 give place to other and different 

 volume-equations ; and if this were so, there is nothing to 

 prevent all the conditions of the problem from being satisfied. 



Under these circumstances, the examination of whether 

 closed curves can or can not occur in the p, y graph becomes 

 a matter of importance. The necessary and sufficient con- 

 dition that closed curves shall be an impossibility is that the 

 curve (a) shall only meet the axis of y in one point, and this 

 condition will in future be spoken of as condition A. 



