100 THE PRINCIPLES OF SCIENCE. 



The mood Baroko gave much trouble to the old lo- 

 gicians 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 

 processes in this system. Let us take as an instance of 

 Baroko, the argument 



All heated solids give continuous spectra, (i) 



Some nebulae do not give continuous spectra ; (2) 

 Therefore some nebulae 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 = nebulae 



C = giving continuous spectra 

 D = heated solid. 

 The premises then become 



D = DC (i) 



AB = ABc. (2) 



Now from (i) we obtain by the Indirect method the 

 Contrapositive 



c = cd, 

 and if we substitute this expression for c in (2) we have 



AB = ABcd; 



the full meaning of which is that ' some nebulae do not 

 give continuous spectra and are not 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 



