446 Mr. S. Butterworth on the Coefficients of 



For purposes of computation it is convenient to write (8) 



47T 



- log.r(l + ftr 2 + /3 2 r 1 + /V 5 + ....) 



(9) 



and to tabulate a 05 a i • • •? A • • • as functions of //-. This is 

 done in Table I. 



When /jl = the circles are coplanar and (8) reduces to 



Mi 



in 



; ^- 2 -r2 r2 ( Xl -6)-8T92" 4 ( X ~S) 



175 6 / 

 (512) 2r V r 



251\ 

 140/ 



(10) 



in w 



hich 



*i = lo g< 



16 



Formulae (4), (8), and (10) converge fairly rapidly so 

 long as r is less than unity. They will give a rough 

 approximation up to r = l*6 but fail for larger values. 



Table I. 

 Values of coefficients in formula (9). 



fl. 



«*• 



*i- 



««■ 



* 3 . 



! 



ft- 



ft- 



ft- 



o-o 



0-7726 



-0-1817 



-0-00487 



-0-00066 



-0-0938 



-0-00549 



-000067 



01 



0-6773 



-0-1414 



-0-00217 



-0-00009 



- 0-0909 



-0-00495 



-0-00053 



0-2 



0-5903 



-0-0962 



+0-00208 



+ 00071 



-0-0825 



-0-00340 



-0-00017 



0-3 



0-5102 



-00473 



+0-00577 



+0-00107 



-0-0684 



-0-00107 



+0-00028 1 



0-4 



0-4361 



+0-0044 



+0-00829 



+0-00098 



-0-0488 



+0-00166 



+ 0-00063 ! 



0-5 



3671 



+0-0578 



+ 0-00921 



+0-00045 



-0-0234 



+0-00424 



+0-00069 ; 



0-6 



0-3026 



+01123 



+0-00318 



-0-00021 



+ 0-0075 



+ 0-00597 



+0-00037 



0-7 



0-2420 



+0-1671 



+000507 



-0-00090 



+0-0441 



+0-00(504 



-000027 



0-8 



0-1848 



+0-2216 



-0 00006 



-0-00098 



+0-0862 



+0-00341 



-0-00084 



0-9 



0-1308 



+0-2752 



-0-00701 



-0-00019 



+01341 



-0-00305 



-0-00052 



10 



00795 



+0-o274 



-001531 



+0-0017 



: +0-1875 



-0-01462 



+ 0-00214 , 



4. In order to test whether the formulae are adequate to 

 represent the mutual induction for the range which is most 

 useful in practice, i. e. from the coaxial position to the 

 position where the mutual induction is zero, Table II. has 

 been prepared. In this table, x is the distance of the planes 

 of the circles and p the distance of their axes, the radii of 

 the two circles being unity. The results are plotted in 



