218 Royal Society :— 



circuit of small resistance, or where the battery is arranged for 

 quantity. 



Secondly, if the organ have a heavy wind, and the pipes have 

 narrow windways, so that the greater portion of the pressure at 

 the windway is due to friction, velocity communicated to the ex- 

 ternal air, &c, and only a small part to the reaction of the sound- 

 impulses, then even considerable variations of the work trans- 

 formed into sound will not alter perceptibly the pressure at the 

 windway or the velocity of exit : thus, on superposition, the two 

 vibrations would retain their form, and the intensity of the swell 

 of the beat would be in the extreme case four times that of the 

 single vibration. This case is analogous to the introduction of 

 a resistance into an electric circuit whose resistance is already 

 great, or where the battery is arranged for tension. 



XXVIII. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from p. 148.] 



December 5, 1872. — Kear-Admiral Gr. H. Richards, C.B., Vice- 

 President, in the Chair. 



THE following communication was read : — 

 " Investigation of the Attraction of a Galvanic Coil on a 

 small Magnetic Mass." By James Stuart, M.A., Fellow of Trinity 

 College, Cambridge. 



From investigations given by Ampere, we can deduce an ex- 

 pression for the potential U at an external point Q of a closed cir- 

 cular galvanic current carried by a wire of indefinitely small section. 

 Let a be the radius of the circle ; let the distance of Q from C, 

 the centre of the circle, be r ; and let the line C Q make an angle 

 with the normal to the plane of the circle. Then it can be shown 

 that when r is less than a, 



U=2«Jc j - 1 +-I\- I - 3 ? B +^ • - 5 • P fl - • • • } ; 

 { a x 2 a 3 3 2 . 4 a 5 J 



and when r is greater than a, 



11-2^1 - la2 p+ 1 - 3 . a4 p-Lil^. a6 p+ I 



V - M \ ~§?*> + tt ? • 274^ ?*'+—/• 

 where Tc depends only on the intensity of the current, and where 

 P„ P 3 , P 5 are defined by the equation 



1 = 1 + T> + P/? 2 + 1> 3 + 



^/l — 2a?cos0-f-# 2 



If, therefore, X represents the resolved part perpendicular to the 

 plane of the circle and towards it of the force exerted by the current 

 on a unit of magnetism placed at Q, and if T represent the resolved 

 part of that force parallel to the plane of the. circle and directed 



