796 



Mr. A. Ferguson on the Construction and 



The above problem possesses, however, more academic 

 than practical value, as, apart from the difficulties en- 

 countered in winding such a coil, it becomes impossible 

 to calibrate the coil in order to detect any irregularity in 

 the windings — a matter of primary importance. 



§ 11. The Helmholtz condition can also be readily worked 

 out for, say, two square "coils " of side 2c with their planes 

 at a distance 2/ apart. 



Fig. 6. 



e-^e 



*i 



i 



I r 





— -G 



4+x 



G- ^ — ' "^ ,- -© 



Consider the field at a point P, distant x units from 0, the 

 mid-point of the coils. We have at once, from equation (ii.), 



ge =8.*/ 1 - I 1 L_l 



/f I (2c 2 +/-V)* • <* +/-** h (2 C 2 +/^ 2 )* • c'+f+w 2 J 



C 2 + j 2) \ T ^2a 2 + ai^ J 2 2a 2jJ * 



+ terms in a? 4 &c. . . . > 



16«'e 



(2o 2 +/ 2 ) I (c 2 +/ 2 ) 



where, for convenience, we put 



a = 2c 2 -i-f 2 , h = c 2 +f 2 . 



The condition that the coefficient of x 2 shall vanish is 

 given by 



66' 6 -30c 4 / 2 -41c 2 / 4 -13/ 6 = 0, 

 or putting / 2 = X, 



13X 3 + 4l6' 2 X 2 + 30c- 4 X-6^ = 0, 



