40 Prof. Helmholtz. On an Electrodynamic Balance. [Apr. 7, 



of the balance. Now the force is zero if the middle of the movable 

 coil is at the same height as that of the fixed coil. The force is again 

 zero if the distance of the two coils becomes infinite. Between those 

 two zero points there exists a maximum value of the force, which 

 corresponds nearly to that situation where the upper surface of one of 

 the coils is at the same height as the under surface of the other. 

 Between the central position of the two coils and this position of 

 maximum force, therefore, the differential coefficient of the force 

 related to increasing distance of the centres is positive, and turns into 

 negative when we pass the position of the maximum. This differential 

 coefficient becomes again zero at an infinite distance. Therefore, 

 between the position of maximum force and infinite distance there must 

 be a distance where the differential coefficient of the force has itself a 

 negative maximum, and the second differential coefficient, therefore, is 

 zero. This is the position which must be given to the coils. As always 

 the distance of one pair of the coils is diminished as much as that of 

 the other pair is increased, the variation of the force depends only on 

 the second differential coefficient. If this is positive, the electric 

 current produces unstable equilibrium ; if it is negative, the stability of 

 the equilibrium is increased ; that is to say, the balance becomes less 

 sensitive than it is without current. If the coils are brought into the 

 right distance, neither the sensibility nor the stability of the balance is 

 altered, and by this circumstance itself the right position can be found 

 out. 



If the instrument is well adjusted, you can determine the weight 

 which balances the electrodynamic force with errors not exceeding 

 one milligramme. As the force exerted by the current is proportional 

 to the square of its intensity, you determine the intensity of a current, 

 which is counterbalanced by one gramme with an . accuracy of -^wo o"? 

 and the force which opposes the electrodynamic force and measures it 

 is gravity alone, and therefore not subject to any variations, like those 

 of terrestrial magnetism, or like the elasticity of a twisted wire on 

 which one of the coils is suspended. 



The observations of the electrochemical equivalent of the current 

 corresponding to one gramme of weight, performed by different 

 observers during the course of last year, have given a very satisfactory 

 agreement. 



III. " On the Internal Forces of Magnetized and Dielect ideally 

 Polarized Bodies," By Professor H. Helmholtz, For. Mem. 

 R.S. (Oral Statement at the request of the President.) 



The Society then adjourned over the Easter Hecess to Thursday, 

 April 28th. 



