The Critical Field at a Discharging Point, 637 



of the figures so obtained would most, certainly throw Light 

 on the question of the relation between the drop-weight 

 and capillary-rise methods, and would form a valuable first 

 contribution to the settlement of the question as to how much, 

 if at all, the drop-weight method depends on the contact- 

 angle. 



University College of North Wales, 

 Bangor. 

 Ji.lv L915. 



LXV. The Critical Field at a Discharging Point. 



By Dr. A. M.Tyndall*. 



rpOWNSlONl) li:«s shown that the following theorem may 

 -L be deduced Erom his theory of the ionization of a gas 

 by collisions: — 1 1" Y is the potential difference necessary to 

 produce discharge between two conductors A and B through 

 a gas at pressure />, then the same potential difference Y will 

 also produce discharge between two conductors A' and IV 

 obtained from A and 1> by reducing the Linear dimensions in 

 the ratio 1//', the gas being at a pressure p' = k-p. Expe- 

 rimental verification of this theorem has been obtained for 

 cylindrical discharge by Townsend and Edmundsf, and for 

 discharge from a hemispherically (aided point to a plane by 

 Edmunds J. 



Using Bailie's values Cor the minimum sparking potential 

 at short distances as in Townsend's treatment of cylindrical 

 discharge, and making the assumption for mathematical con- 

 venience that the point can be regarded as a paraboloid of 

 revolution, Edmunds has further deduced the following- 

 expression for the critical tield at the surface of a point 

 (namely, the field when discharge just starts or ceases): 



x - p ( 30+ 7=p> d) 



where X is the tield in kilovolts per cm., a is the effective 

 radius of a paraboloid point in cms., and P is the pressure 

 of the air in atmospheres. The values of the minimum 

 discharge potential between a point of this shape and a plane 

 calculated from the above expression for X were compared 

 with experimental measurements, and considering the extent 



* Communicated by the Author. 



t Townsend and Edmunds, Phil. Mag. vol. w\ii. p. 781). 



\ Edmunds, Phil. Mag. vol. xxviii. p. 284. 



