on a new Electro-dynamic ExperimeJit. 385 



which every fixed conductor impresses on the moveable con- 

 ductor on which it acts, if we observe that 



sin^ fl + cos^5 = (sin 9 -f- cos 9) (1 — sin 9 cos 9), 

 and that 9= '.= = > (^_,) 



gives 

 sin 9 cos 9 = I sin £ = i cos r; and sin 9 + cos 9 = v^^cos - »j, 



1 / 2 \ 



we shall have M = —7^ a i i' cos i « ( 1 ). 



<v/2 2 ' \ COS ;, / 



When the moveable conductor is displaced ever so little 

 from the situation of equilibrium, the angle 9 becomes 9 + d 9 

 with reference to one of the fixed conductors, and 9 — d 9 with 

 reference to the other ; so that the difference of the two mo- 

 menta, which was null in that situation, becomes, after being 

 displaced, 



2-J7- d 9= —aii' (cos 9 — sin 9) (-:-n> — ^+ ^"i — , +1 ^dfl. 



This value is always negative when we take, as we suppose 

 it here, the angle s double of 9 on that side where this angle is 

 acute, and consequently after the opposite direction of the 

 electric currents in the two sides of this angle, which requires 

 that the momentum M should tend to increase it, the mo- 



d M 

 mentum 2 —^-f d 9 will tend to diminish it on the side where 



d 9 is positive, and to increase it on the side where the same 

 differential is negative ,* i. e. to bring back the moveable con- 

 ductor to the position of equilibrium, which might besides 

 easily be seen a priori. 



If we introduce in the value just obtained the angle ij in- 

 stead of % we find 



dM — / 4 2 V 



2-rx- d 9 = — a z 2%/2 sin I « ( -— r— + -zz ^ 1 ) d 9. 



a 6 * \ cos- » cos J) ■* y 



This momentum must be measured, either by the torsion 

 of a thread, or by the number of oscillations made by the two 

 moveable conductors, in a given time, by means of observations 

 made simultaneously * upon these conductors, when we wish 

 to verify the results deduced from my formula, comparing 

 them with those of experience. 



I have also devised another apparatus which may serve for 

 the same verifications, by calculating, and afterwards mea- 



* By comparing among themselves measures determined by successive 

 operations, we also comjiletely avoid the inaccuracy produced by the vari- 

 ations of the energy of the pile, which necessarily alter the results deduced 

 from experiment. We may also measure in a direct manner the momen- 

 tum M by the torsion of a thread. 

 Vol.66. No. 331. Nov. 1825. 3 C suring 



