498 Prof. E. Edlund on the Magnitude of 



be expressed by 



AGMfipX sin u /^\ 



(r» + p 8 )* ' 



where C is a constant. 



Let us suppose a steel magnet, whose poles have an inten- 

 sity N and are distant 21 from each other, is so placed that its 

 axis produced passes through the centre of the magnetized 

 needle, and forms a right angle with the magnetic meridian. 

 If the distance a between the centre of the magnet and that of 

 the needle is great enough, and if the derivative angle u and 

 the distance \ be sufficiently small, the action of the magnet 

 upon the needle will be expressed by the formula 



2CN/A cos u__2C~N/jl\ cos u __ 8GN fiX cos u ,c>\ 



(a- If (a + l) 2 a 6 K J 



From equations (2) and (3) we obtain 



Mp _ 2NZcotM / 4 x 



{f + p 2 f a 6 



Introducing into equation (1) the value of the left-hand side 

 of equation (4) and the value of o>, we obtain 



x=- 



1864ANZcotwAr 



a 3 



(5) 



Let us suppose the same magnet (whose poles have the inten- 

 sity N and are distant from each other 21) in rotation about 

 its axis, simultaneously with a concentric cylinder of metal, 

 having the radius p. According to the memoir several times 

 mentioned, the sum A of the forces of induction, produced 

 between the central portion of the cylinder and the plane 

 passing through one of its poles at right angles to the length 

 of the cylinder, is expressed by the formula 



A = 2/cN^r L_- * 1 . . (6) 



where v denote s the a ngular velocity of the cylinder. 



Replacing s/P+p 2 by m and v /4/ 2 + j p 2 by n, and inserting 

 in equation (5) the value of £N7 obtained from equation (6), 

 we obtain, finally, 



__ 932nm cot u .A Ar ,rj\ 



(n-~m)vd i 



We may now proceed to determine by experiment the values 

 of A, a, and u. 



