A survey of HCO~+ and N_2H~+ has been conducted in the 11 cirrus cloud cores and 28 Clemens-Barvainis translucent objects whose structures and chemistry have been studied earlier in this series. HCO~+ (J = 1-0) emission is seen in all objects and emulates ~(12)CO in its distribution. By contrast, J = 3-2 emission requires exceptional excitation conditions, is seen in only a few cases, and is generally much more localized. In several objects HCO~+ (J = 1-0) is also seen in emission from associated diffuse gas. HCO~+ emission appears to trace a wide range of physical conditions, including diffuse, translucent, and shocked gas. Observations are modeled in terms of our previous hydrostatic equlibrium and n ～ r~(-α) structures together with other chemical and physical properties derived earlier. We find that the abundance ratio HCO~+/~(12)CO is ～10 times higher toward regions with extinctions A_(v0) approx< 1 mag than toward regions where A_(v0) approx> 1.5 mag, at which dense-cloud chemistry appears to onset. This behavior is well described by a chemistry which combines the diffuse cloud formation process C~+ + OH → CO~+ + H for HCO~+ and CO with the dense-cloud processes H_3~+ + CO → HCO~+ and HCO~+ + e → CO. The transition region between these regimes is precisely that of the translucent objects comprising the bulk of this study. By contrast with HCO~+, N_2H~+ (J = 1-0) is detected in only two translucent objects of 16 searched. This is expected, since there is no analogous diffuse-cloud formation process for N_2H~+, but only the "dense-cloud" process H_3~+ + N_2 → N_2H~+ + H_2. Significant amounts of N_2 can form only when photoprocesses are minimal, so only the regions with highest A_(v0) exhibit detectable N_2H~+. Conventional N_2H~+ astrochemistry is consistent with all present N_2H~+ observations. The unusual source CB 17, exhibiting very strong lines of both HCO~+ and N_2H~+, is explained as having an unusually large column density together with a strong external radiation field, consistent with previous analyses of the object.
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