  In this paper, we employ the peak count rate{\bf \}$C_p$ and the total count
$C_{total}$ of light curves to study in the corresponding aspects the
relationship between different channel light curves. To make a direct
comparison between count rates of different channel light curves we introduce a
plot of $C(\tau)$ versus $C_H(\tau)$, where $C(\tau)$ is the count rate of a
channel and $C_H(\tau)$ is the count rate of a definite cannel, channel H (see
the text). According to the plot we define $\Delta C_{\max}$ as the maximum
deviation of the two count rate values of $C(\tau)$ associated with a same
count rate value of $% C_H(\tau)$ and define $\Delta S$ as the area confined by
the close curve of $C(\tau)$ in the plot to measure the difference of the
rising and decaying portions of a light curve relative to the count rate of
channel H. Under the assumption that some GRBs observed are in the stage of
fireballs which expand relativistically, predictions on the relationships
between the four quantities{\bf (}$C_p$, $C_{total}$, $\Delta C_{\max}$, and
$\Delta S$) and energy within a wide band, calculated with different rest frame
radiation forms and two typical Lorentz factors ($\Gamma =20$ and 200), are
made and presented, which would make the test of our model with the coming
Swift data easier. Interpretations to the relationships within the mechanism of
fireballs are also presented.
