CHAP. XII] INDUCTANCE OF WINDINGS 215 



With certain simplifying assumptions he arrived at the same 

 formula for inductance as eq. (146) in which approximately 



Because of the simplifying assumptions made in the deduc- 

 tion of this formula, the values of k calculated from the results 

 of tests on actual transformers differ slightly from those given 

 by the formula. Let k' be an empirical correction coefficient, 

 then 



(147) 



In Dr. Rogowski's experiments the actually measured induct- 

 ance was on the average 6 per cent higher than the calculated 

 one. Until more experimental data are available it is therefore 

 advisable to use in eq. (147) the value of '=1.06. Eq. (147) 

 is applicable to transformers of all the three types (Figs. 12 to 

 14), though in the case of a shell-type or cruciform transformer, 

 the presence of iron outside the coils tends to increase the value 

 of k'. However, Dr. Rogowski states, that with the space usually 

 allowed for insulation between the coils and the iron, the influence 

 of the iron in increasing the leakage reactance is negligible. Eq. 

 (147) holds approximately true for cylindrical coils also, though 

 there are as yet no conclusive tests for the value of the cor- 

 rection factor to be used with such coils. 



The general similarity between the equations for leakage induct- 

 ance given above raises the question, as to what clement they 

 possess in common. This is found in the conception of a leakage 

 coil, which is the " fictitious coil " spoken of above. An inspec- 

 tion of Figs. 50 and 51 will show that the successive lines of 

 force converge upon lines which may be called the " hearts " 

 of the flux system. These hearts are located in places where 

 tin- net m.m.f. is zero. This is at the edge of the half-coils and 

 at the center of the whole-coils, in the two figures m< -nti<>n< >1. 

 In deriving eq. (144) for the case where the coils are not split, 

 ihf heart is assumed to be at the edge of both coils. If we 

 define a leakage coil as that part of the winding between two 

 successive hearts, thru <j. (144) will always apply to it. In 

 eq. (143) ^ and l> 2 refer to the \vi<!th of the double leakage coil. 

 hence if we substitute in eq. (144) J6 l and i^ for 61 and 62, 



