(m a new Electro-dynamic Expeiimenf. 383 



right one, whilst cot e is positive, i. e. whilst this angle is acute; 

 but it becomes smaller when the same angle is obtuse, because 

 then cot s is negative. Moreover, it is evident that its value 

 becomes so much greater as the angle s is smaller, and that it 

 increases ad injinitum like cot s in proportion as cot f ap- 

 proaches zero ; but it will be well to show that it always re- 

 mains positive, however near this angle be to two right lines. 

 For that, it is sufficient to observe that by calling a. the 

 angle of the triangle OL"L^^ comprised between the sides a and 

 r, and |3 that which is between the sides h and ?•, we have cot e 

 = — cot (a + /3), j9 = a sin a = 6 sin /3, r = a cos a. -\-h cos /3, 

 and consequently 



a-\-h — r=.a{\— cos a) -[- 6 (1 — cos /3) 



= j9 tang ^a + p tang ^ /3, 

 and 



i if [;, + (a + 6 _ ,.) CO. .] = 4 i/p ( 1 - 2=^;i±!J'gii), 



a value which always remains positive, however small the 



angles a and /3, since tang (« -f /3), for inferior angles at 7, is 



always larger than tang « + tang /3, and of course more so 

 than tang ^a + tang | /3. This value evidently tends towards 

 the limit ^ i i' p in proportion as the angles a and /3 approach 

 zero : it vanishes with p when these angles become null. 



Departing from this expression at the momentum of rota- 

 tion I'esulting from the mutual action of the two rectilinear 

 conductors situated in the same plane, round the point of inter- 

 section of their direction, and of the general fact proved ao-ain 

 by the expei-iment described in the beginning of this Memoir, of 

 the nullity of action of a conductor bent in an arc upon a por- 

 tion of the cu'cuit, the two extremities of which are in the pei- 

 pendicular raised in the centre of this arc upon the plane on 

 which it is described, I have devised an instrument founded 

 on the same principle as that which I presented about two 

 years ago to the Academy of Sciences, and described in my 

 Reciceil d' Observations Electro-dynamiqiies,*p. 224, &c. Its 

 object is also to determine by the number of oscillations of a 

 moveable conductor, the value of the action which a fixed 

 conductor exercises upon it; but which has not the inconve- 

 nience that was found in the first, of giving the experimental 

 measure of this action in a case in which it cannot be deter- 

 mined, by the aid of my formula, but by calculations of the 

 most complicated kind. I intend soon to publish the descrip- 

 tion of this instrument. 



When the point of intersection of the conductors OL", 



L,L„ 



