( 925 ) 
The accurate determination of these constants is practically equi- 
valent with including in the integration a very great number of the 
not mentioned terms of (3). 
That in formula (14) m represents the finite number of layers, 
whereas for the integration m is supposed to be infinite, depends 
upon the fact, that the self-inductance, for the case the current is 
uniformly distributed over the ercss section of the coil, is proportional 
to the square of the number of layers. 
For moderate values of 9, which quantity in most cases is consi- 
derably smaller than 1, the mutual proportions of the coéfficients 
Cv, CU, and C, are very nearly represented by the mutual proportions 
of the constants 6, 10 and 15 appearing in these coëfficients. As 
the terms with g and go? for long coils are always very small in 
comparison with the first term we may put approximately : 
Dota RE 
TETE C,.= 543 
substituting these values in (14), we obtain;: 
2 | dar 
Li rd RE [p‚(e) — 0.8488] + a [y,(v, + 9.0848] o + 
r 
ue 5 [p‚(e) + 0.11] 9? }. . (15) 
9 
Putting in this formula @ =O the terms with @ and o? vanish 
ann ‘C= 6. 
We then get the formula for the self-inductance of a cylinder or 
single layer coil: 
fee aoe na (Pp, (2) 0.8488). in fB 
The method of testing the degree of accuracy obtained in the 
computation of self-inductances by means of the formulae (14) and 
(15) is based on the same principle, as used by Rosa in his above 
mentioned method. 
tosa') begins with the calculation of the self-inductance of a 
cylindrical current sheet, which has the same mean radius and length, 
as the solenoid with depth of winding t. He takes the total number 
l 
of windings of this cylinder equal to —, where /is the common length. 
: 
Afterwards he considers the solenoid of length / and depth of winding 
¢ as to be formed by one single layer of square conductor, so that 
the cross section of this conductor is {<t and the total number of 
windings is also equal to 
1) E. B. Rosa. Bull, of the Bur. of St. IV 369, 
