RESIDUAL CHARGE OP THE LEYDEN JAE. 
601 
II. The following method of treating the question of residual charge was suggested 
to the author by Professor Clerk Maxwell ; it is essentially similar to that used by 
Boltzmann for the after-effects of mechanical strain (“ Zur Theorie der elastischen 
Nachwirkung,” aus dem lxx. Bande der Sitz. der k. Akad. der Wissensch. zu Wien, 
II. Abth. Oct. Heft, Jahrg. 1874). 
Let L be the couple tending to twist a wire or fibre about its axis, Q t the whole angle 
of torsion at time t ; then L at time t depends upon Q t , but not wholly on 0 t , for the 
torsion to which the wire has been submitted at all times previous to t will slightly 
affect the value of L. Assume only that the effects of the torsion at all previous times 
can be superposed. The effect of a torsion Q t _ w at a time a before the time considered, 
acting for a short time du, will continually diminish as a increases ; it may be expressed 
by —to t -uf{<»)dw, where f{eS) is a function of a, which diminishes as a increases. Adding 
all the effects of the torsion at all times, we have 
L =afl t — j* O t _ a j\co)dco. 
In the case of a glass fibre Boltzmann finds that f[co)—-, where A is constant for 
moderate value of co, but decreases when a is very great. 
The after-effects of electromotive force on a dielectric are very similar ; to strain cor- 
responds electric displacement, to stress electromotive force. Let x t be the potential at 
time t as measured by the electrometer, and y t the surface-integral of electric displace- 
ment divided by the instantaneous capacity of the jar ; then, assuming only the law of 
superposition already proved to be true for simultaneous forces, we may write 
y t -M a ) du ’ (i) 
where <p(a) is a function decreasing as a increases. This formula is precisely analogous 
to that of Boltzmann ; but in the case of a glass jar the capacity of which is too small 
to give continuous currents, it is not easy to measure y t ; hence it is necessary to make 
#*the independent variable. From the linearity of the equation (1) as regards x t y t and 
the value of y t _ a for each value of a, and from the linearity of the equation expressing 
x t _ a for each value of a>, it follows that 
y t =Xt+\ Xt-'Mtfdu, ( 2 ) 
Jo 
where decreases as a increases. 
The statement of equations (1) and (2) could be expressed in the language of action 
at a distance and electrical polarization of the glass, y t being replaced by the polariza- 
tion as measured by the potential of the charge which would be liberated if the polari- 
zation were suddenly reduced to zero, the jar being insulated. It should be noted that 
the view of this subject adopted by the author in the previous paper * can be included in 
equation (2) by assuming that ^(a) is the sum of a series of exponentials. 
* Vide Phil. Trans, vol. clxvi. pt. 2. 
4 q 2 
