The mood Baroko gave much trouble to the old logicians, who could not *reduce* it to the first figure in the same manner as the other moods, and were obliged to invent, specially for it and for Bokardo, a method of Indirect Reduction closely analogous to the indirect proof of Euclid. Now these moods require no exceptional treatment in this system. Let us take as an instance of Baroko, the argument All heated solids give continuous spectra (1) Some nebulæ do not give continuous spectra (2) Therefore, some nebulæ are not heated solids (3) Treating the little word some as an indeterminate adjective of selection, to which we assign a symbol like any other adjective, let A = some B = nebulæ C = giving continuous spectra D = heated solids The premises then become D = DC (1) AB = AB*c* (2) Now from (1) we obtain by the indirect method the contrapositive proposition *c* = *cd* and if we substitute this expression for *c* in (2) we have AB = AB*cd* the full meaning of which is that “some nebulæ do not give continuous spectra and are not heated solids.” We might similarly apply the contrapositive in many other instances. Take the argument, “All fixed stars are self-luminous; but some of the heavenly bodies are not self-luminous, and are therefore not fixed stars.” Taking our terms A = fixed stars B = self-luminous C = some D = heavenly bodies we have the premises A = AB, (1) CD = *b*CD (2) Now from (1) we can draw the contrapositive *b* = *ab* and substituting this expression for *b* in (2) we obtain CD = *ab*CD which expresses the conclusion of the argument that some heavenly bodies are not fixed stars. *Contrapositive of a Simple Identity.* The reader should carefully note that when we apply the process of Indirect Inference to a simple identity of the form A = B we may obtain further results. If we wish to know what is the term not-B, we have as before, by the Law of Duality, *b* = A*b* ꖌ *ab* and substituting for A we obtain *b* = B*b* ꖌ *ab* = *ab*. But we may now also draw a second contrapositive; for we have *a* = *a*B ꖌ *ab*, and substituting for B its equivalent A we have *a* = *a*A ꖌ *ab* = *ab*. Hence from the single identity A = B we can draw the two propositions *a* = *ab* *b* = *ab*, and observing that these propositions have a common term *ab* we can make a new substitution, getting *a* = *b*.