Field of Circular Currents. 385 



Since the deviations of odd orders vanish for a circular 

 coil, we have next to discuss the deviation of fourth order, 

 which is given by 



H&Vv-W) =«, . (16) (Fig. 2.) 



as is evident from (A). The curves of constant deviation 

 have different branches, all of which resemble hyperbolas, 

 with asymptotes inclined to the axis of £ at angles of 

 ±40° 53' 48" and the normals at the vertices inclined 

 at ±20° 58' 32" and ±66° 7' 18'.. The distribution oi 

 the deviation about the centre is shown in fig. 2. 

 The deviation of sixth order is given by 



i-f8(5?S-20fV + 8& 5 ) = e, (17) (Fig. 3.) 



The curves of constant deviation are more complicated than 

 the preceding, but have branches resembling hyperbolas, 

 of which the asymptotes are inclined to the axis of f at 

 angles of +27° 57' 34" and +56° 7' 8". The normals 

 at the vertices are inclined to f at angles of +14° 8' 56", 

 + 42° '39' 11", ±73° 37' 44". The inspection of fig. 3 

 will at once show how the deviation of this order is very- 

 small near the centre, but increases very rapidly as we 

 recede from it. For practical purposes the deviation of 

 higher order will be generally negligible, and if necessary 

 the calculation will not entail much labour. 



Axial Component Y of a Single Coil. 



As to the axial component Y, the discussion of the 

 deviations can be made in the same manner as already 

 indicated, so that it will be only necessary to tabulate 

 them. The common characteristics of the curves of constant 

 deviation are that they all resemble hyperbolas and are 

 separated by asymptotes, which form the boundaries of 

 positive and negative deviations, as is evident from the 

 figures at a glance. 



Deviation of second order for Y-component : — 



i^-tr) = *. • • • (18) (Fig. 4.) 



Asymptotes : ±35° 15' 52". 



Normals at the vertices : 0°; ±90°; 180°. 



