so AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE. 



Bumber, its potential equivalent, a varying number, — usually 8, but at times 8 and 

 a fraction, 9, and so on ? Far from this tlie number is as fixed as the universe. 

 There are no indefinite blendings of elements. There are combinations by multi- 

 ples or sub-multiples but these prove the dominance and fixedness of the com- 

 bining numbers. 



But further than this, even numbers, definite in value and defiant of all destroy- 

 ing powers, are well known to characterize nature from its basement to its top- 

 stone. We find them in combinations by volume as well as weight, that is in all 

 the relations of chemical attraction ; in the mathematical forms of crystals and 

 the simple ratios in their modifications, — evidence of a numerical basis to a cohe- 

 sive attraction ; in the laws of light heat, and sound. Indeed the whole constitu- 

 tion of inorganic nature, and of our minds with reference to nature, as Professor 

 Peirce has well illustrated, involves fixed numbers ; and the universe is not only 

 feased on mathematics, but on finite determinate numbers in the very natures of all 

 i%3 elem-ental forces. Thus the temple of nature is made, we may say, of hewn 

 and measured stones, so that, although reaching to the heavens, we may measure 

 and thus use the finite to rise toward the infinite. 



This being true for inorganic nature, it is necessarily the law for all nature, for 

 the ideas that pervade the universe are not ideas of contrariety but of unity and 

 universality beneath and through diversity. 



The units of the inorganic world, are the weighed elements and their definite 

 compounds or their molecules. The units of the organic are species which exhibit 

 themselves in their simplest condition in their germ-cell state. The kingdoms of 

 life in all their magnificent proportions are made from these units. Were these 

 units capable of blending with one another indefinitely, they would no longer be 

 units, and species could not be recognized. The system of life would be a maze 

 of complexities; and whatever its grandeur to a being that could comprehend the 

 infinite, it would be unintelligible chaos to man. The very beauties that might 

 charm the soul would tend to engender hopeless despair in the thoughtful mind 

 instead of supplying his aspirations with eternal and ever-expanding truth. It 

 would be to man the temple of nature fused over its whole surface and through its 

 structure, without a line the mind could measure or compreLead. 



Looking to facts in nature, we see accordingly every where, that the purity of 

 species has been guarded with great precision. It strikes us naturally with won- 

 der, that eTen in senseless plants, without the emotional repugnance of instinct, 

 and with reproductive organs that are all outside, the free winds being often the 

 means of trnnsmission, there should be rigid law sustained against intermixture. 

 The supposed cases of perpetuated fertile hybridity are so exceedingly few as al- 

 most to condemn themselves, as no true examples of an abnoi'mity so abhorrent to 

 the system. They violate a principle so essential to integrity of the plant-king- 

 dom, and so opposed to nature's whole plan, that we rightly demand long and 

 careful study before admitting the exception. 



A few words will explain what is meant by perpetuated fertile hybridity. The 

 following are the supposeable grades of results from intermixture between two 

 species : — 



1. No issue whatever — Ihe usual case in nature. 



2. Mules (naming thus the issue) that are wholly infertile whether among them- 

 selves or in case of connection with the pure or original stock. 



