( 919 ) 
Fig. 1 
secutive layers, we get for the radii of the consecutive layers: 
a, =a, — da 
es MRE) 
=d 2da 
Am == a, — (m—1) da 
The mutual inductance between any two cylinders with radii a, 
and a, being M,,., the self-inductance of the solenoid is given by 
the equation : 
P= G=-m™m 
Be eh hte My Pe A vir a 
== 
Substituting the value of « given by (3) in the equation (2) and 
taking provisionally, in order to facilitate the survey of the derivation, 
3 
only’ the two first terms of « with omission of the term —, we 
x 
obtain : 
M=4 n°n?a? | Vac Bea eae | Aes EEE |) 
2 8A 
In this expression we replace a and A by their above values, 
a,, A, — da ete. and expand the terms within the square brackets 
according to ascending powers of da. We neglect all terms in which 
da occurs to a higher degree than the second, and for the above 
mentioned reason we also omit the terms with da’ resulting from 
the expansion of the form under the radical. 
Moreover putting Va,?+?—=r we find for the terms of the 
integral (4): 
60 
Proceedings Royal Acad, Amsterdam. Vol. XIII. 
