980 Forces acting upon the Poles of the Electric Arc. 



shall obtain approximately the total force on either electrode 

 if " i " in the above expression stands for the total current 

 in the arc. This gives for a current of 10 amperes and a 

 field of 25 volts per cm. in the body of the arc the following 

 values for P : — 



For electrons : P = either 0*006 dvne 



or 0-02 „ 



For carbon atoms : P = either 0*87 dyne 



or 2-U „ 



Xow, the Duffield effect for the same current is about 

 2 dynes, which is of the same order of magnitude as those 

 obtained as above on the assumption that the negative ion 

 is a single charged molecule. 



The weak point of the argument is, of course, the fact 

 that in flames and in the air drawn from the neighbourhood 

 of the arc, mobility measurements show that the negative ions 

 must be electrons and not molecules. But it is perhaps 

 possible that the nearly saturated state of the carbon vapour 

 in the arc makes the ions, so long as they remain in the 

 vapour, more complex than is generally supposed. 



Should the theory of negatively charged atoms be con- 

 sidered untenable, there is another possibility. It is seen 

 that electrons moving viscously with a mobility given by 

 the formula cannot account for more than a fraction per 

 ceni. of the Duffield effect. But little is known of the 

 conditions obtaining in the arc, and it is quite conceivable 

 that the mobility formula used breaks down entirely at the 

 high temperature of the arc, and that the mobility of 

 electrons at that temperature is far greater than measure- 

 ments at ordinary temperatures and in flames would lead 



one to expect. The formula P = — . v can be used to 



e 



determine at what average speed electrons would have 

 to move in order to give rise to a Duffield effect of 2 dynes. 

 The value is 1*5 x 10 6 cm ./sec. /volt/cm. The maximum 

 value of: mobilitv recorded for flames is 13,000 obtained by 

 Gold at 1800° C, which is about double the value (6000) 

 given by Weilisch's formula at that temperature. Whether 

 this is an indication of a deviation from the formula is, how- 

 ever, doubtful. 



The position, therefore, may be summed up as follows : — 



(1) Duffield's explanation of the mechanical pressure he 

 observed breaks down. 



(2) A pressure of the order of magnitude observed would 



