

542 Mr. F. B. Young on the Field at 



then, that abnormality diminishes the possibility o£ the exist- 

 ence of an inversion point by lowering the value o£ y n above 

 which inversion is impossible. How far this conclusion is 

 affected by the assumption cf>(0) = constant=l it is at present 

 impossible to say; and in the elucidation of this point there 

 is still plenty of scope for further research. 



University College, Dundee, 

 February 1907. 



XLIV. On the Relation of the Field at the Point of an Elec- 

 trified Needle to the Mechanical Force resulting. By F. B. 

 Young, B.A* 



THE present research was carried out in the Physical 

 Laboratory of University College, Bristol, under the 

 direction of Professor Chattock, in order to obtain a correc- 

 tion factor for certain values found by him for the field 

 which was just sufficient to produce discharge at the extre- 

 mity of a needle |. These values were obtained by measuring 

 the pull of an electrified plate on an earth-connected needle 

 opposite and normal to the plate and protruding through an 

 earth-connected surface. The needle being cylindrical and 

 ground to a hemispherical point this pull (P) is a function of 

 the field (/") at the centre of the point. 



Fig. 1 is a section of the point, R being its radius, S the 

 electrical density at the centre of the point, and o-S the 

 density at any other part of its surface. The pull on the 

 surface of the annulus shown, resolved parallel to the axis of 

 the point, is 



4tt 2 (o-S) 2 R 2 sin cos OcW; 

 whence 



P = 2tt 2 R 2 S 2 a 3 sin 20. dd 



77 



I CT Sll 



Jo 



sin 20 d0 ; 



• • (1) 



where 



a = 



v. 



2 er 2 sin 20 d0 



*. Communicated by Prof. A. P. Chattock. 

 t Phil. Mag-. Sept. 1891. 



