144 METHODS OF ABBREVIATION. [cHAP. IX. 



ceive that such applications would possess any independent va- 

 lue. They would, for instance, throw no light upon the true 

 principles of classification in the science of zoology. For the 

 discovery of these, some basis of positive knowledge is requisite^, 

 some acquaintance with organic structure, with teleological adap- 

 tation ; and this is a species of knowledge which can only be de- 

 rived from the use of external means of observation and analysis. 

 Taking, however, any collection of propositions in natural his- 

 tory, a great number of logical problems present themselves, 

 without regard to the system of classification adopted. Perhaps 

 in forming such examples, it is better to avoid, as superfluous, 

 the mention of that property of a class or species which is im- 

 mediately suggested by its name, e. g. the ring-structure in the 

 annelida, a class of animals including the earth-worm and the 

 leech. 



Ex. 4. 1. The annelida are soft-bodied, and either naked or 

 enclosed in a tube. 



2. The annelida consist of all invertebrate animals having 

 red blood in a double system of circulating vessels. 



Assume a = annelida ; 



s = soft-bodied animals ; 



n = naked ; 



t = enclosed in a tube ; 



i = invertebrate ; 



r = having red blood, &c. 



Then the propositions given will be expressed by the equations 

 a = vs {n (1 - t) + t (1 - n)} ; (1) 



a = ir ; (2) 



to which we may add the implied condition, 



nt = 0. (3) 



On eliminating v, and reducing the system to a single equation, 

 we have 



a {l-sn(l- t)-8t(l-n)} + a(l- ir) + ir(l - a) +nt= 0. (4) 



Suppose that we wish to obtain the relation in which soft- 

 bodied animals enclosed in tubes are placed (by virtue of the 



