362 Prof. J. A. Pollock on the 



by V units, it acquires a velocity which may be found from 

 the expression for the work done, viz. : — 



I mv 2 = Ye, 



where v is the final velocity, and e the ionic charge. If then 

 at any section of a circuit, energy is communicated to the 

 ions so that they are projected from that section with a 

 velocity v, there is at the section what is electrically equi- 

 valent to an electromotive force which is given by the 

 expression 



V = i'^ (1) 



v being now the velocity of projection. 



Considering that electrons and positive ions are projected 

 from the surface of glowing carbon, with velocities depending 

 on the temperature, we should therefore expect to find in a 

 circuit containing a junction of heated carbon and a gas, 

 what may be called a surface potential-difference at the outer 

 layer of the carbon. This surface electromotive force is, in 

 any instance, the difference between that due to the pro- 

 jection of electrons, and that arising from the emission of 

 positive ions. As it is likely that the value of mv 2 /2e is far 

 greater in the case of electrons than in that of positive ions, 

 it is only necessary, for purposes of general description, to 

 consider the electromotive force due to the projection of the 

 former. 



If the hot carbon is the negative electrode, so that the 

 electrons are projected in the direction in which negative ions 

 are being carried by the field, the surface potential-difference 

 is a forward electromotive force helping the flow of the 

 current, as discovered by Mr. Duddell at the cathode of the 

 arc. If, on the other hand, the hot carbon is the positive 

 electrode, so that the electrons are projected in a direction 

 opposite to that in which negative ions are being carried by 

 the field, the surface potential-difference is a back electro- 

 motive force, opposing the flow of the current, as at the arc 

 anode. 



The theory thus accounts in a simple way for the existence 

 and direction of the electromotive forces as found by experi- 

 ment. With the values of the forces, previously given in 

 section 2, knowing that e/m for electrons is equal to 1*86 X 10 7 

 electromagnetic units, by substitution in equation 1, we arrive 

 at the result that at the anode of the arc, electrons are pro- 

 jected with a velocity of 2*5 x 10 8 , and at the cathode with a 

 velocity of 1*5 X 10 8 , centimetres per second. 



