( 917 ) 
Physics. - 4 new accurate formula for the computation of the 
self-inductance of along coil wound with any number of layers.” 
By F. L. Brre@anstus (Communicated by Prof. W. H. Junius). 
For the accurate computation of the self-inductance of multiple 
layer coils, different formulae are available in the case the cross 
section ot the coil is a square, a circle or a rectangle. All these 
formulae only give results of a high degree of accuracy, when the 
cross section is not too large in comparison with the mean radius, 
and besides for the rectangular section restriction is made, that the 
length of the coil shall not considerably surpass this mean radius. 
For the ease of a long coil or solenoid wound with many layers 
of wire, to my knowledge no formula has been derived, which, 
either in a closed form or in the form of a converging series, represents 
the value of the self-inductance with a high degree of accuracy. 
Louis Conex*) has derived for this case an approximate formula 
of the following form: 
2a, +a,7l? Sa,’ 
eS a ee ——— cal cna 
n>m Vigan TP 5 | ae 
: 5 7 
+ Barn? ge + (m—2)a,* +... (vn Jl — a «) de 
+ L[m ( 1) tL ( 1) ( 2) a,2-4 a, da : (1) 
4 m— (ml) (madl == — da | — 
- . Var tf? 
p da 
— £[m(m—1)a,’?+- (m—2)(m—3)a,* +] 3 
wherein «,== mean radius of coil a,,a,...= radius of the first, 
second layer reckoned from the axis of the coil; da = distance 
between two consecutive layers; /== length, 7 = number of windings 
per cm. m= number of layers. 
Conen says that the results obtained with this formula are accurate 
to within one half of one percent for a solenoid, whose length is 
twice the diameter, the accuracy increasing as the length increases. 
Apart from this moderate accuracy, this formula (which, moreover, 
contains errors in the third and fourth terms) is very laborious for 
numerical computations, when the number of layers m is large. 
1) Louis Conen, Bulletin of the Bureau of Standards IV, 385, 
