of an Oscillatory Electrical Circuit. 555 



values which may be taken as typical of a fairly large 

 induction-coil : — 



&-* 



L 1 Ci=>66.10- 8 c.G:s. 



The coupling F is varied from 0*5 to 0*95, and the ratio 

 R 2 /L 2 from 100 to 2000. 



In each case the three roots of the cubic (6) were calcu- 

 lated by Cardan's formula, and hence the values of n, k ± , and 

 S found by (7). 



The results of these calculations are shown in Table I., 

 the first column giving values of h\ the second those of 

 RoLo, the third, fourth, and fifth columns the values of 

 k x , n, and 8 calculated as explained above. 



Table I. 

 Ri ..'Li = 50, LiCi = T'-66.i0- 9 c.G.s. 



7c\ R 2 /L 3 . & 1; n. • S. 



0-5 lOo" 10000 812-91 lOO'OO 



500 297-56 807"92 504-86 



1000 53000 792 98 1040-00 



1500 729-43 768 78 1641-13 



2000 87381 736-84 235236 



0-6 100 137-48 908-71 100-04 



500 434-58 901-30 505-63 



1000 788-10 878-76 1048-80 



1500 109827 841-47 1678-47 



2000 1322-85 789 01 247933 



0-7 100 19997 1049-10 10006 



500 663-23 1037*38 506-87 



1000 1220-58 1001-62 1058-85 



1500 1720-57 939-77 1725-51 



2000 2088-21 848-03 2654-92 



0-8 100 324-96 1284-38 100-07 



500 1121-05 126326 507-91 



1000 2090-73 1198-24 1068-54 



„ ' 1500 2985-30 1080-74 1779-38 



2000 3649-52 88452 2950 96 



09 100 699-96 1814-39 100-08 



500 2495-52 1758-10 508-94 



1000 4709-98 1581-05 1080-02 



1500 (5825-84 1228 04 1848-32 



2000 Imaginary 391921 



0-95 100 1449-95 2560-32^ 100-09 



500 5245-28 2407'02 509-45 



1000 9957-12 1887-70 1085-75 



1500 Imaginary 4057'57 



2000 3679-45 225-17 33641 21 



2 2 



