326 
MRS. H. AYRTON ON THE MECHANISM OF THE ELECTRIC ARC. 
the ratio of the new current to the old, then the resistance of the arc must have been 
diminished more than the current was increased, and that hence the P.D. must have 
diminished as the current increased, and SV/SA must be negative (provided always 
that the specific resistance of the arc had not been altered). Similarly, when the 
ratio of the cross-sections are smaller than that of the current SV/SA must be 
positive. 
In order to see the effect of the cores on these ratios, in the experiments of which 
the results are given in Tables III. and IV., Tables V. and VI. have been drawn up, 
in which the cross-section ratios are found by dividing the cross-section for each 
current by the cross-section for the next smaller current; and the current ratios by 
dividing each current by the next smaller current. For the non-normal ratios 
the larger cross-sections were taken from the non-normal sets in Tables III. and IV. 
and the smaller from the normal , because it is the effect of the core when the 
alternating current is superimposed on a normal arc that we are considering, and 
because also the non-normal numbers in these Tables were found by suddenly 
increasing the current when the arc was normal. For the normal ratios both currents 
were taken from the normal sets. 
For instance, the normal cross-section for a current of 8 amperes with the + solid- 
— cored carbons in Table III. (p. 321) is 14 % and the non-normal cross-section for 
10 amperes is 19'0, while the normal cross-section for the same current is 2075. 
Thus, when the current is increased from 8 to 10 amperes, the current ratio is 
- 8 - = P25, the non-normal cross-section ratio with these carbons is = P34, and 
the normal is - ° 4 7 p = P46. In this case, therefore, SV C /SA was negative, both when 
the change of current was non-normal and when it was normal, for both the cross- 
section ratios, P34 and 1'46, are greater than 1"25, the current ratio. Of course to 
imitate the effect of an alternating current completely it would be necessary to 
suddenly diminish the current as well as suddenly increasing it, but as this would 
only alter the signs of both SV and SA, without materially changing their relative 
values, it is not necessary for our purpose. 
The non-normal ratios show the effect of the core on the change in the cross- 
section, i.e., in the resistance of the arc, and therefore on 8V, when the frequenc} T of 
the alternations is so great that the carbons do not change their shapes ; and the 
normal, when it is so small that the changes are slow enough for the arc to rema n 
practically normal throughout. 
