224 Proceedings of Indiana Academy of Science 
I, Is In 
From this «T =log.-=log.—=log. 
: This is the same as the 
is I; In+1 
usual logarithmic decrement used in ballistic galvanometer work, except 
in ballistic galvanometer work we follow the English fashion of taking the 
ratio of the two successive swings in the opposite direction instead of the two 
successive in the same direction. Or the decrement in U. S. wireless is two 
times the value determined by the English method. The determination of 
I,, I., ete., or successive amplitudes of the current is impossible where the 
frequency is in the order of 1 million, as it is in wireless work. 
nie Sl R? 
In the above equation the frequencyn=—, | —- — : 
aN LC 41 
If Ris small or zero, this becomes n=—-———._ This is the same value for n 
TEE naa 
2xV LC 
obtained from the equation of alternating current in a circuit containing re- 
sistance, inductance and capacity, with an alternating e.m.f. 
1D) 
i=—= a The value of I is a maximum when 1/Cw—Lw 
V R2+ (1/Cw-— Lw)? 
1 
=0,ie.1[=E/R. If Lw=1/Cw, then (2xn)?=1/CL or era 
22 LC 
2 
9 
The above equation for I can be written I[?= 
R2+ (1/Cw- Lw)? 
When the reactance term 1/Cw-—Lw=0 the circuit is in resonance with the 
K2 E z 
e.m.f. Then I?, =——----- ——— =— where Cy is the value of the capacity 
R? 24 (1) lise eae: R2 
which makes the circuit in resonance uae the e.m.f. Then Lw=1/Cr w. 
If the capacity is changed until I?=1/2 I* , I’, being the resonance value, 
ace IY PAl, Sea ————— and 2R?=R?+(1/Cw-1/Cr w)? since 
R?2+ (1/Cw-1/C, w)? 
doubling the denominator will halve the value of I’. Then 
R?=1/w?((Cr —C]CC,r )? or R=1/w(C, —C/CC, ) 
ae ae and decrement d=aT=R/2L T. 
(= ale (= = 
=a te ——-- r 
CCn Jw2L. Cc. Jw? 2CL 
a, 
nee —— where Cy is the value of the capacity at resonance and C is the 
’ 
r 
value of capacity which reduces the mean square of the current to 1/2 its 
value. In this manner the decrement is measured by determining the re- 
sistance in terms of a capacity. 
