  The diffuse far-ultraviolet (FUV) continuum radiation "longward" of Ly-alpha
(1216A) is well known to correlate with the dust emission at 100 um. However,
it has been claimed that the FUV continuum background "shortward" of Ly-alpha
shows very weak or no correlation with the 100 um emission. In this paper, the
observational data of the diffuse FUV radiation by the Far Ultraviolet
Spectroscopic Explorer is reexamined in order to investigate the correlation
between the diffuse FUV radiation shortward of Ly-alpha and the 100 um
emission. Large fluctuations were confirmed in the linear-linear correlation
plots, but good correlations were found in the log-log plots. The large
fluctuations in the linear-linear plots, and thus poor correlations, between
the FUV and 100 um intensities were attributed to the lognormal property of the
FUV intensity distribution. The standard deviation of the intensity
distribution of the FUV radiation shortward of Ly-alpha was found to be
sigma_log I = 0.16-0.25. The result is consistent with that obtained not only
for the FUV radiation longward of 1216A, but also with the dust column density
measurements of various molecular clouds. This implies that most of the diffuse
FUV radiation shortward of Ly-alpha is dust-scattered light in the turbulent
interstellar medium. The diffuse FUV data obtained from the Voyager missions
was also investigated. However, much wider random fluctuations were found
compared with the FUSE data, which is most likely due to the systematic
difficulties in data reduction of the Voyager data.
