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XIX. The Magnetic Field close to the Surface of a Wire con- 

 veying an Electrical Current. By Professor Gr. M. Minchin, 

 M.A* 



AT a meeting of the Physical Society on March 10, 1893f, 

 I gave an expression for the conical (" solid ") angle 

 subtended at any point, P, in space by a circle occupying any 

 position. 



When the circle is the seat of an electric current, this 

 conical angle is the measure of the magnetic potential pro- 

 duced at P by the current. The conical angle is usually 

 expressed by a series of spherical harmonics, or, rather, by 

 two such series, one of which is to be used when the distance 

 of P from the centre of the circle is less than the radius of 

 the circle, and the other when it is greater. The expression 

 which I have given consists of two complete elliptic integrals 

 of the third kind, which for convenience I reproduce here. 



In fig. 1 let A C B be the circular current ; P'" any point 



Fig. 1. 



»o 



POB 



Fig. 2. 



in space at which the value of the conical angle subtended by 

 the current is XI ; V the central axis perpendicular to the 

 plane of the current ; A B the diameter of the current deter- 

 mined by the plane P'O V; v the sine of the angle P'OY; 

 jo=AF, p / = BP / ; z the perpendicular from P / on AB. 

 Then, a being the radius B, and OF = r, we have 



°=*-£{^ n G£*) + S n (i^*)}' (1) 



* Communicated "by the Physical Society: read June 9, 1893. 

 t Phil. Mag. April 1893. 



Phil. Mag. S. 5. Vol. 36. No. 219. Aug. 1893. P 



