﻿592 Coefficients of Mutual Induction of Coaxial Coils. 



13. In order to illustrate the method of working for short 

 coils, take a coil having 



outer radius = (( = 4 cm., 



inner radius = 6 = 2 cm., 



length = c = 4 cm. 



Then z = c/a = l„ r= b/a =0'5. 



By (44) L 1 /27rVa r, = 0-229167. 



By (47 a) 



M(c)/27rW>=f(l, l)-2(0-5) 3 f(l, 0-5) + (0-5) 5 f(2, 1), 



=0-045477- i x 0-048216+ i x 0-026022, 

 = 0-034236, 



M(0)/2ttW= (l + p) x 0-122062- j. x 0-150930, 



= 0-088144. 



Therefore L = L 2 - 2M(0) +2M(c) 



= 27r 2 nV(0-121351) 

 = 2453'9/r. 

 The Stefan- "Weinstein * formula for the same coil gives 

 L=2459-5« 2 , 



so that the error in using the latter formula for this coil is- 

 0*23 per cent. 



14. Conclusion. 



In applying the formulae and tables, their range of appli- 

 cation should be borne in mind. They are intended to be 

 used only when the inner and outer diameters of the coils 

 differ appreciably (b/a<0'8), and when the coil-lengths 

 are not too small (c/a>0*2). An exception to this rule is 

 Table V. which (with graphical interpolation) holds for all 

 values of b/a. For coils whose dimensions are outside these 

 limits the usual solenoid or circular filament formulae are 

 more suitable, the geometric mean distance correction being- 

 applied to the channel section. 



It should also be noted that no allowance is made for the 

 insulation space of the winding. 



Finally, by successive differentiation of the formulae for 

 the function X, many known formulae for the mutual induc- 

 tion between solenoids, flat coils, and circles may be obtained. 



* Fleming, ' Principles of Electric Wave Telegraphy/ p. 140 (2nd 

 edition) , 



