4. AiiT. 6. — II. nagaoka: tiij: inductance 



Looking iit the tablu^'^ of q, we lind tliat q varies from to 

 0,15 as r increases from 0° to 73°. 1 ; similarly the range of q^ 

 is from to 0.01, as r diminishes from 90° to G7°.4. 



For the calculation of the nnitiud inductance of coaxal coils, 

 it is therefore convenient to use (4) for values of q from to 

 0.15, and (4') for q^ from to 0.0 1. When q^ is very small, 

 we can write (4') in the form 



-i^- = ^ \ loqn (-' ) ( 1 + 8 ^, + £/) - 4 \ 



7T-/Aa 2(1- 2(71)- I -^ \qj^ ^ ' ) 



A.71 ^ 



where 



:/= _8r7,- + 32r7;'-40r/i-' + 48^i^+ {\") 



§ 4. For facilitating the calculation of mutual inductance, 

 it would be convenient to construct the tables of the following 

 quantities. 



I. Table of q- ^ from ^' = 0.02 to 0.15, und of £ and 



/o^io ('^ + 2) for the same interval- 

 II. Table of £1 and -^/-Sr/f-^i for ry-O.Ol to ^y, = 0.00. 



These tables cover all values of r from 10°.2 to 90°, thus 

 enabling us to calculate M for any value of J, a and 6', without 

 using the tables of elliptic integrals, which by ordinary methods 

 of calculation must always be resorted to. The special advantage 

 of the formuhe (4), (4') or (4") lies in their rapid convergence ; 

 we may also dispense with the calculation of /', which is a great 

 disadvantage of the method usually employed. 



The following tables have been calculated by Mr. C. Harada. 



(1) See Jucubi, Werke, 1, \\\k oüL!-^ü8. 



