We report the second study from the FUSE survey of molecular hydrogen in translucent clouds , for the line of sight toward HD 110432 . This star lies beyond the Coalsack dark nebula , and with E ( B - V ) = 0.40 , and A _ { V } = 1.32 this line of sight bridges the gap between less extinguished diffuse cloud lines of sight with A _ { V } \sim 1 , such as \zeta Oph , and the translucent clouds with A _ { V } \gtrsim 2 such as HD 73882 . Through profile fitting and a curve-of-growth analysis , we have derived rotational populations for H _ { 2 } for J = 0–7 . The line of sight has a total molecular hydrogen column density , log N ( H _ { 2 } ) = 20.68 \pm 0.05 cm ^ { -2 } , nearly identical to that toward \zeta Oph , but a factor of three less than HD 73882 . The ratio of N ( J =1 ) to N ( J =0 ) yields a kinetic temperature T _ { kin } = 63 \pm 7 K , similar to other lines of sight with A _ { V } \gtrsim 1 . The high- J lines show considerable excitation above this temperature . However , the high- J lines can not be well-fit to a single excitation temperature , and the even- J lines of para-hydrogen appear slightly enhanced relative to the odd- J lines of ortho-hydrogen . The high- J excitation is similar to that toward \zeta Oph , but much smaller than that toward HD 73882 . Chemical modeling indicates that the physical conditions in the cloud ( s ) are very similar to those in the cloud ( s ) toward \zeta Oph . An analysis of IUE spectra of the Lyman- \alpha line gives log N ( H i ) = 20.85 \pm 0.15 cm ^ { -2 } . Combined with N ( H _ { 2 } ) , we derive a hydrogen molecular fraction , f _ { H 2 } = 0.58 \pm 0.12 , statistically identical to that found for the lines of sight toward \zeta Oph and HD 73882 . From the FUSE data , and a curve-of-growth analysis using the same component structure as H _ { 2 } we find log N ( HD ) = 15.2 ^ { +0.7 } _ { -0.4 } cm ^ { -2 } , between the values found for \zeta Oph and HD 73882 . Profile fitting suggests smaller b -values for HD than for H _ { 2 } and a value log N ( HD ) = 16.0 ^ { +0.2 } _ { -0.3 } cm ^ { -2 } . From FUSE and IUE data we derive log N ( CO ) \approx 14.3 cm ^ { -2 } assuming the same component structure as CH , or log N ( CO ) \approx 14.8 cm ^ { -2 } if all the observed CO is co-spatial with the strongest CH component . From the combined measurements of hydrogen and carbon-containing molecules , the line of sight toward HD 110432 appears quite similar to the diffuse cloud line of sight toward \zeta Oph , and quite dissimilar to the translucent cloud line of sight toward HD 73882 . Upcoming FUSE observations will further explore the transition between diffuse and translucent clouds .