Numerical System of Nature qfM. E. Fries. 87 



ated, of which the first and second, and the third and fourth, are 

 in affinity ; but the first and third, and the second and fourth, are 

 in analogy. 



But when this method of division becomes circuitous, a more 

 direct path is undoubtedly to be discovered : hence other num- 

 bers are admitted, especially the quaternary (or double dicho- 

 tomy), and also others in which dichotomy is understood. 



There are other and most acute observers (Oken, MacLeay), 

 who contend for other fixed fundamental numbers. Care must 

 be taken, however, that no cabalistical or occult virtues are at- 

 tributed to any particular number ; in the higher spheres a higher 

 number is, on account of the multiplicity of organs, admissible 

 than can be used in the lower spheres ; the only object of such a 

 contrivance being to explain in what direction rays pass off from 

 their centre, and at what points the rays of different spheres im- 

 pinge upon each other. To do this a determinate number is re- 

 quired. 



We must, moreover, avoid extending too precipitately any 

 system whatever to specialities. We can proceed in no direction 

 further than the power of arrangement acquired by what we po- 

 sitively know of nature, admits. I certainly am not of the num- 

 ber of those who assume that infinity is to be circumscribed within 

 strict limits ; although I may be of opinion that infinity and uni- 

 versal harmony are better explained by them than according to 

 any arbitrary rules of arrangement. 



In the formation of sections and genera it is most especially 

 necessary to beware that they do not depend upon characters 

 alone ; so that if the character should hereafter prove defective, 

 the section or the genus may still remain unchanged. In this 

 lies the difference between an artificial and natural arrangement ; 

 the former depending upon characters, the latter upon affinity. 

 Hence Linnaeus did not characterize his families of plants, nor 

 Ehrenberg those of fungi, rightly perceiving that affinity is of the 

 first importance, characters of secondary. 



It is occasionally necessary to admit into a particular section a 

 genus or species in which the most important character of such 

 section does not exist, but then its truly essential character can- 

 not have been detected. Thus when we say that Rosacea? are di- 

 cotyledoneous, perigynous, polypetalous, &c, and refer to them 

 Alchemilla, it will be easily seen that the really essential charac- 

 ter of Rosacea? remains to be discovered. 



§ 14. Every sphere (section) expresses a particular idea; 

 thence its character is best expressed by a simple notion. 



But to effect this, it is necessary that the character which is 

 really most essential shall have been detected. For if a section, 

 of which the primary character is unknown, be circumscribed by 

 a simple notion, the most arbitrary and artificial arrangement 

 possible would be the result. 



When the essential character is once detected, all others will 

 be wholly dependent upon it (for when this character is changed 



the 



