The Magnetic Field of any Cylindrical Coil. 367 



of necessity be a small uncertainty, as there is no datum-point 

 between 339° and 1052° ; but this cannot amount to more 

 than a very few degrees. 



In conclusion, we may point out that plotting our meldo^ 

 meter-readings against other observers' melting-points does 

 not give a smooth curve. 

 University College, London. 



XXXYI. The Magnetic Field of any Cylindrical Coil. 

 By W. H. Everett, B.A.* 



APPLYING Ampere's formula for the magnetic force 

 at any point due to an element of current, the force 

 perpendicular to any plane circuit, carrying a current i, is 

 found to be, at any point P, 



od^O 





h 2 y< 



h being the distance of P from the plane of the circuit, and 

 r, 6 the polar co-ordinates of any point of the circuit referred 

 to the projection of P as origin. 



The longitudinal force at any point due to a current in a 

 cylindrical coil, or solenoid, is given by a second integration. 

 It is the sum or difference of two terms, each of the form 



= inh I- 



dO 



\/r* + h 2 ' 



where h denotes the distance of the point from an end plane 

 of the solenoid, and n the number of turns per unit length 

 of h. The depth of the coil, normal to the cylindrical surface, 

 is assumed to be inconsiderable. The limits of integration 

 are and 2ir for any point whose projection, taken parallel 

 to the axis, falls within the solenoid. 



Similarly, the transverse force at any point, due to a sole- 

 noid, is found to be 



~R — in£( . T r ) ds, 



VvV + V VV + A 2 V 



the summation being vectorial. 



The latter two formulae can be readily applied, for approxi- 

 mate calculation, to a cylindrical coil of any cross-section, 



* Communicated by the Physical Society, being abstract of paper read 

 November 8, 1895. 



2 C 2 



