32 AFFINITY OF THE TIIILOBITES , 



I have endeavoured in various ways to meet this obstaele, and liave ah'eady laid down the 

 fundamental features of my system, which I have rendered as much as possible independent 

 of every subjective mode of consideration, in my ' Hand-book of Natural History,' (Berlin, 

 1837-8, 2d division.) It would lead me too far here if I were now to communicate similar 

 results, and it would also be unnecessary, since I have already published the principal 

 facts in the work alluded to, and am even now engaged in carrying out the subject more 

 in detail.* I will therefore merely state that the conceptions of the homonomous, and 

 hc.teronomom systems of the articulated fundamental type are the characteristics which, 

 according to my view, principally determine that type : the former notion intimating an 

 always fluctuating, indefinite numerical proportion, the latter an immutable, constant nume- 

 rical proportion either in all, or in some of the heteronomous divisions of the body. This 

 numerical proportion in the latter case generally exhibits itself in the multiple of a simple 

 combination, consisting either of the number three or five, the former being generally 

 applicable to the lower heteronomous Articulata; the latter, on the other hand, to the 

 higher. The class of Crustacea certainly exhibits an heteronomous type throughout, having 

 no generally equal number of body rings, but a varying one corresponding, to its character 

 as a transition group of the Arlleulaia. The separation of the body into caput, thorax, 

 and abdomen, of which each ought to be treated as an independent whole, according to 

 peculiar laws, justifies the assumption of their heieronomity, which I consider as the most 

 essential class-characteristic of the Crustacea. The two typical numbers, and as it appears 

 generally, always the maximum number, predominate among the Crustacea in the thorax, 

 which here, as among all other Articulata, presents the best systematic characters for the 

 determination of the class. But the presence of these typical numbers, owing to the 

 frequent absence of so many thoracic rings in the shape of isolated divisions, and also 

 by the conversion of the organs of motion into accessory parts of the mouth, for the service 

 of the head and of its organs, is frequently obscure on the first superficial observation. 

 We must therefore, if we wish correctly to recognize the typical number of the thorax, 

 always consider the accessory parts of the mouth as organs of motion, and these must 

 add to the true organs of motion of the thorax, and then divide the total by 3 or 5, in 

 order to arrive at the fundamental number and its multiple. This mode of proceeding 

 soon leads us to the interesting result that all the higher Crustacea together with a constant 

 type of antennae, eyes, mouth, and organs of motion, also possess an equally unchangeable 

 numerical proportion with regard to the rings of the thorax, which is always 2 x 5 or 10, 

 and is therefore the simple multiplication of the second higher typical number ; while, on 

 the other hand, all the other Crustacea with fluctuating typical character of antennre, eyes, 

 parts of the mouth, and organs of motion, never exhibit the fundamental number of 5, 

 but either possess no fundamental number which can be considered as generally peculiar 

 to them, or at least as far as I have been able to convince myself by exact personal 

 investigation, and in the majority of cases possess the number 3 in a formula of multiplication 

 which fluctuates from 1 to 4. 



Tiie typical coincidence of both groups, already suggested in point of several charac- 

 teristics, renders it possible to define them with still greater certainty than this can be done 



* I intend to puljllsli tliis ^vork sLortly, under tLe title of 'An Attemiit at a Rational Zoology.' 



