Striated Electrical Discharge. 261 



the graph satisfies the known differential equation ; it is there- 

 fore an arch of the type occurring in fig. 5 ; and since both 

 p and y are already determined at the point n which is not 

 on the axis y = 0, this arch is completely determined by the 

 part of the graph already drawn. This arch again enters 

 the region in which y is less than 77 at some point v, and so 

 on, until it finally emerges at some point s, and takes the shape 

 of a line similar to J) ft in fig. 6. The point ft on this curve 

 at which the graph satisfies the condition for a cathode may 

 be taken for the actual cathode, and in this case the graph we 

 have arrived at w T ill satisfy the appropriate terminal conditions 

 at each electrode. 



The graph so obtained also satisfies the true physical equa- 

 tions at every point. For so long as y is greater than 77 it 

 satisfies the mathematical equations, with which the physical 

 equations are supposed to coincide, and in the region for 

 which y is less than 77 it must, from the way in which it has 

 been constructed, satisfy the physical equations. 



Further, the smaller 77 becomes, the more closely will this 

 graph approach to the known graph in fig. 5, so that if 77 be 

 sufficiently small, the graph in fig. 5 may be supposed to 

 represent the real graph if we allow for the existence of the 

 disturbing forces by rounding off the corners B, C, 1). 



This effect of disturbing forces finds a parallel in almost 

 every branch of physics. Consider, for example, liquid 

 flowing along the edge of an obstacle. Let us draw a graph 

 giving the reciprocal of the velocity of the fluid at the various 

 points of the edge, the velocity being determined by the 

 hydrodynamical equations for the motion of a non-viscous 

 incompressible fluid. At a point of the graph corresponding 

 to a sharp corner on the obstacle there will be a cusp on the 

 axis exactly similar to the points B, C, D in fig. 5, showing 

 that the theoretical velocity at these points is infinite. In 

 the actual flow the velocity is not infinite on account of the 

 viscosity of the fluid, and the effect on the graph of this dis- 

 turbing influence is therefore a " rounding-off " of sharp 

 corners. 



§ 11. We are now in a position to give a physical inter- 

 pretation of the solution which is represented by the graph 

 in fig. 6. 



As is well known, both theory and experiment show that 

 light may be expected to appear at points for which q—an 1 n 2 

 is negative; that is to say, wherever the number of ions that 

 recombine is greater than the number produced by dissociation. 

 Equation (8) shows that q — an^ is negative or positive 

 Phil. Mag. 8. 5. Vol. 49. No. 298. March 1900. T 



