MRS. H. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
305 
surface of volatilisation is the same in each case. In other words, the area of the 
crater increases with the length of the arc with a given surface of volatilisation. 
Now, I shall show presently that, in the normal state of the arc, the area of the 
volatilising surface is directly proportional to the current, but is independent of the 
length of the arc ; it follows, therefore, that with a given constant current the area 
of the crater increases with the length of the arc, as I have found it to do by actual 
measurement. * 
The area of the crater, then, if we define it as that part of the positive carbon 
that is far brighter than the rest, is not a function of the current only, as has 
hitherto been affirmed. It is a function of the current, the length of the arc, and, 
until the arc has become normal after any changes have occurred in the length or 
the current, of the time after the change was made. The cross-section of the vapour 
film, on the other hand, is proportional to the current, as we shall now see. 
The Film of Vapour in Contact ivith the Positive Carbon acts like a Back E.M.F. 
Let a be that area of the film that uses its heat in volatilising fresh carbon, and 
let x be the part of which the heat is lost by conduction, radiation, &c. Then the 
whole area of the film is a + x, and its resistance, if we consider the thickness of the 
film to be constant, is 
V 
a + x 
where p is a constant. The heat generated per second in 
p . ci- 
the film varies as —-— and, of this, only-is used in volatilisation. 
Cl -\- X Cl -{- X 
The quantity of carbon volatilised per second is, therefore, proportional to 
a n\~ an A 2 
> or ;-— • 
Cl -X Cl -\- X [Cl -f- Xy 
But, therefore, since the temperature at which volatilisation is taking place is 
a constant one, viz., the lowest possible, the quantity of carbon volatilised per second 
must be proportional to the area of the surface from which it is volatilised, /.<?., to a. 
qa = — j where q is constant, 
1 (a+xf 1 
That is, a + x, the area of the vapour film, is proportional to A, the current. 
Again, from the above, 
a + x A 2 
p (a + x) <[ ’ 
but 
therefore 
Cl -f- X 
V 
1 
7 
where f is the resistance of the film, 
q(a + x) 
J = 
A 2 
(!)• 
VOL. CXCIX.—A. 
* ‘ The Electric Arc,’ p. 154. 
2 R 
