  This paper derives a prediction for the variation of the amplitude of the
dielectric loss from isomorph theory, and presents an experimental test of the
prediction performed by measuring the dielectric-relaxation behavior of the van
der Waals liquid 5-phenyl-4-ether (5PPE). The liquid is studied at isochronal
states in the temperature range $266-333$ K and pressure range $0.1-300$ MPa,
for relaxation times around $10^{-3}$ s and $10^{-4}$ s. From the isomorph
statement that there is structural and dynamic invariance of isomorph states in
reduced units for Roskilde simple liquids we derive four equivalent
isomorph-invariant terms, one of which is used in analyzing our data. It is the
frequency-dependent term $\chi_{e}(f) \rho^{\gamma-1}$, with electric
susceptibility $\chi_{e}$, density $\rho$, and density-scaling factor $\gamma$.
Due to the unique design of our experimental setup, we obtain dielectric loss
data where the amplitude is reproducible $\pm 0.1 \%$. We moreover find that
the empty capacitance of the capacitor cell is stable within $\pm 0.3 \%$ in
our measuring range and can be assumed to be constant. Using this we predict
for two isomorph states there is $-C_{2}"(f)= -C_{1}"(f) \left(\rho_1 / \rho_2
\right)^{\gamma-1}$ to scale the negative imaginary capacitance, where $C_{1}$
is the capacitance measurement at ambient pressure and $C_{2}$ is the predicted
capacitance at elevated pressure. We visually compare the predicted and
measured plots and there is good match between the two plots among the 42 pairs
of isochronal states from the measurement.
