Extreme helium stars (EHe) with effective temperatures from 8000K to 13000K are among the coolest EHe stars and overlap the hotter R CrB stars in effective temperature. The cool EHes may represent an evolutionary link between the hot EHes and the R CrBs. Abundance analyses of four cool EHes are presented. To test for an evolutionary connection, the chemical compositions of cool EHes are compared with those of hot EHes and R CrBs. Relative to Fe, the N abundance of these stars is intermediate between those of hot EHes and R CrBs. For the R CrBs, the metallicity M derived from the mean of Si and S appears to be more consistent with the kinematics than that derived from Fe. When metallicity M derived from Si and S replaces Fe, the observed N abundances of EHes and R CrBs fall at or below the upper limit corresponding to thorough conversion of initial C and O to N. There is an apparent difference between the composition of R CrBs and EHes; the former having systematically higher [N/M] ratios. The material present in the atmospheres of many R CrBs is heavily CN- and ON-cycled. Most of the EHes have only CN-cycled material in their atmospheres. There is an indication that the CN- and ON-cycled N in EHes was partially converted to Ne by $alpha$-captures. If EHes are to evolve to R CrBs, fresh C in EHes has to be converted to N. If Ne is found to be normal in R CrBs, the proposal that EHes evolve to R CrBs fails. The idea that R CrBs evolve to EHes is ruled out; the N abundance in R CrBs has to be reduced to the level of EHes, as the C/He which is observed to be uniform across EHes, has to be maintained. Hence, the inferred [N/M], C/He, [Ne/M], and the H-abundances of these two groups indicate that the EHes and the R CrBs may not be on the same evolutionary path.
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