Electrical Resistance of Gases. 207 



planes situated at distance 1 from each other. The resistance 

 upon the unit of section being r , and the magnitude of the 

 section or, the resistance upon the entire section will be r a = ki. 

 In the time-unit this element is repelled the path-length h, 



whence the work done will be kih. Now h= -^-. in which 



oa 



expression 8 is a constant, as we have seen above. The mecha- 



ki? 

 nical work of this element will therefore be -k— . If this 



Mi? ° a 

 quantity be multiplied by b, the product k— will be equal to 



the work of the entire current. If, lastly, this expression be 



multiplied by the thermal equivalent of the unit of work, and 



if the constant 8 be made to enter into k, the quantity of heat 



produced by the current during the time-unit will be equal to 



Akli 2 



, which is known to be in accordance with experiment. 



The calculation can be effected with equal facility, on the 

 same principles, in the case in which the section and the nature 

 of the conductor vary from one part to another. 



(d) With respect to the production and distribution of free 

 asther at the surface of a galvanic conductor, these can best be 

 explained in the following manner: — 



Let us imagine a tube in which a mass of gas is set in 

 motion by a force acting at one extremity, while the gas can 

 issue freely at the other. Let us assume, further, the resist- 

 ance of the tube to the motion of the gas to be, as is in reality 

 the case, proportional to the length of the tube. If x be the 

 distance between a certain section-plane and the open extre- 

 mity of the tube, the resistance undergone in that plane by the 

 motion can be put proportional to x. We neglect altogether 

 the influence which may be exerted upon the resistance by the 

 difference of density and velocity of the gas. Let D' denote 

 the density of the gas at the above-mentioned plane, and D its 

 density at the open extremity of the tube. Every one knows 

 that, from the moment the motion in the tube has become 

 constant, the excess J)' — D is proportional to x. The density 

 of the gas therefore goes on increasing from the open end of 

 the tube to that at which the force acts. Suppose now the 

 two extremities of the tube joined so as completely to enclose 

 the moving mass of gas. The gas will evidently undergo in 

 one portion of the tube an expansion equal to its increase of 

 density in the other ; and at the transition-point between the 

 two portions it will have the same density as if it were at rest. 

 If the tube is everywhere equal, this transition-plane (neutral 

 plane) will divide the tube into two equal parts. At equal 



