Mutual Induction of Eccentric Coih 



453 



9. The formulae for unequal circles close together do not 

 readily admit of simplification even with the aid of tables. 

 The following calculations (Table III.) have been made to 

 test the range of the formulae. The ratio A/a — 2 has been 

 chosen so as to compare the results with the experimental 

 curves of Campbell (loc. cit.). Otherwise it is not a very 

 favourable ratio for the formulae. The curves obtained 

 (tig. 2) show very good agreement with the experimental 





1 















1 ! 

























\ 























1*0 











! 



\ 





















































i 







T 



x/fl 



= 















/ 





\ 















n 



xfa 



: O 



2 



M 









/, 







\i 







j J 









TTT 



x/n 





s 













n\ 









i 1 









W 



*/a- 



. 1- 



3 



0-5 



1 















\ 





I 



















1 











^s 





\\ 















































































1 







\ 









































s 





























| 

































! i 









Na p 

















| 















"VK 

















.. 

















i i r 













I p/a 2 3 4 



curves and give a[)proximately the same zero points. The 

 separate terms are tabulated so as to indicate their relative 

 importance. The labour involved in obtaining the third 

 term is altogether out of proportion with the importance of 

 that term, especially as in the cases where it is large the 

 fourth and succeeding terms are likely to have an appreciable 

 effect. It will be found that for most purposes the first 

 two terms only in the formulae need be used. It will also 

 be noticed that in the most important range of the curves 

 (viz., from p/a=l to M = 0) the curvature is slight, so that 

 after calculating a few points within this range from the 

 theoretical formulae, an empirical formula of the type 



M = «o + «iJ+V+ ... 

 a a 



should be sufficient to determine intermediate values. 



