872 
period. Applying the wellknown formula of Hermnortz: 
R 
Di =< 
Sl L 
[= R (1--e ) 
we compute the current strength in the magnet at every moment. 
The current strength being known we try to calculate the number 
of lines of force through the armature, assuming it to be proportional 
to the current strength and inversely proportional to the length of 
the airgap. We may do this as, practically, the total reluctance in 
the: magnetic circuit is to be looked for in the airgaps. With small 
magnetizing forces the permeability of the iron is so great that this 
assumption is permittable. As an example we may take the moment 
just before the breaking of the current. Using HerMmnoLtz’s formula 
and supplying the real valne of the constants, we find /=1.13 
ampere, whilst from the oscillographie record we find /=1.17 
ampere. This makes the magnetising force: 0.42 X 400 X 1.17 = 
590. As the airgap has a length of 0.48 cm we get 590 « 0.48 = 
1225 lines of force through 1 cm? air-section. These lines start from 
the pole pieces, which have a surface of 0.7 cm’; hence we find 
for the magnetic density in the iron not more than 1750 lines per 
em’?. This means that we may expect a permeability u of the order 
of 3000. Taking u — 3000 we find that to force 1225 lines through 
16.4 cm of iron of a section of 0.7 cm’, not quite 5 ampere turns 
are needed. Consequently we have an error of not more than.1°/,, if 
we consider the airgap only and disregard the ironpath. 
In order to calculate the number of lines during the make-period, 
we assume that the armature vibrates in such a way as to vary the 
length of the airgaps periodically, according to the expression 
a+bsin2 ant. Then we get as an approximate expression for the 
number of lines of force: 
E aes 
Ord NE: 
R 
a+ 6b sin2 ar nt 
B= for SEG 
in which N is the number of turns of the magnetising coils, Z the 
voltage of the galvanic battery, R the resistance of the circuit, L 
the mean selfinduction, n the frequency of the interruptions, a the 
mean length of the air-path, and 5 half the amplitude of the armature. 
If we put in this formula the value already given for each of the 
constants, we get as a result the curves in fig. 3, where [ represents 
the current strength, IL the length of the airgap and III the number 
of lines of force during the make period. If this last curve be 
