590 Prof. J. A. Fleming on the Measurement 
found that a very simple formula enables the inductance to 
be calculated very approximately. 
If D is the mean diameter of the axis of one circular turn 
of the wire forming the solenoid, and if / is the length of the 
solenoid, and N the total number of turns on the solenoid, 
then it is clear that the magnetic force per unit of current in 
the central portions of the interior of the coil is equal to 
ArN/l, and the total self-linked flux is 47N’aD?/4/. Hence, 
if we neglect the variation of flux at the ends and consider 
that all up the coil it has the same value as at the centre, 
the inductance L of the coil is given by the formula 
eee Darts 
where ¢ is written for the turns per unit of length of the 
solenoid =N/1. 
Hence the above equation may be written 
L=(7Dt) (DN). 
The first factor wD¢ is the length of wire wound on one 
unit of length of the cylindrical rod used as a core. This 
factor is of no dimensions and is a mere numeric. 
The second factor wDN is the total length of wire used. 
Hence, we have for such a solenoid :— 
_( length of wire per total length of wire 
Tnducaee ce length of solenoid usedto form solenoid )* 
Applying this rule to the above mentioned long Seibt coil, 
we have for the total length of wire used 
3°1416 x 4:096 x 5000 cms. = 64340 ems., 
and the length wound on per centimetre of the rod is 
3°1416 x 4096 x 5000+ 200°3=321 cms., 
and hence 
L=20°6 x 10° ems nearly, or 20°6 millihenrys. 
It will be seen from Table I. that the average observed 
value of L for this coil, as calculated from nine bridge- 
readings made with the telephone method, is 19°9 x 10° ems. 
nearly ; and hence the inductance calculated by the above 
rule agrees within 3°5 per cent. with that obtained by actual 
measurement. 
This rule affords a very simple and convenient guide for 
constructing small known inductances. All that it is 
necessary to do is to wind silk-covered copper wire in one 
layer and in closely adjacent turns on a glass rod of measured 
diameter, and make the length of the solenoid at least 50 
times the diameter. The inductance can then be predetermined 
