(918 ) 
Epwarp B. Rosa?) describes in the same part of the above mentioned 
annual, a method for the accurate computation of the self-inductance 
of a coil of any length wound with any number of layers, which 
he presumes to be absolutely correct and which is used by him to 
check the results obtained by other formulae, especially STErAN’s. 
This method, though based on a correct principle, will, if applied 
in the manner used by Rosa, only then lead to very accurate results, 
when the total depth of the windings on the coil is very small 
compared with the mean radius. 
In the following pages I propose to give the derivation of a new 
formula, which, in a simple and for numerical computation very 
convenient form, represents the self-inductance of multiple layer coils 
with a high degree of accuracy in all cases in which the formulae 
for short coils fail. 
For the mutual inductance between two coaxial cylinders of equal 
length Maxwerr®) has derived the following expression : 
ML oF in? a Bee ee en 
wherein 
l—r+A a A’ a‘ l BAe 5A! 
(a | = Bape ee a 
2A 16A? r 64A4\ 2 7° 2r7 
35 a° (1 BAS AA TO. 5 
EK Q vid I TEN ——— Pe o 
2048A°\7 Tr! 9 RT (3) 
r=V A? +, A=radius of outer cylinder, a = radius of inner 
cylinder, 7/= length, „== number of windings per cm. 
Te last term of « has been added to the derivation by E. B. Rosa *), 
Generally the self-inductance of a coil is found by integrating the 
expression for the mutual inductance between two elements of the 
section twice over the whole area of this section. 
In order to obtain this integral we suppose the solenoid to be 
formed by a very great number m of layers. Indicating by a, the 
radius of the outer layer and by da the distance between two con- 
1) Epwarp B. Rosa, Bull. of the Bur. of St. IV 369. 
2) Maxwett, Electricity and Magnetism, Il, § 678. 
3) E. B. Rosa and L. Conen, Bull. of the Bur. of St. III 305. 
