, 8 PROCEEDINGS OF THE AMERICAN ACADEMY 



differences between the several divisions in man and in many 

 of the lower animals ; divisions too marked to be deemed 

 simply varieties, and yet not sufficiently great to constitute a 

 proper basis for a classification into different species. They 

 might, with more propriety, be termed races. The differ- 

 ent kinds of dogs, breeds of cattle, &c. were instances of 

 this sort of difference. Animals, differing only in race, form 

 more frequent connection with one another than those differ- 

 ing specifically, and the fruit of connections of the latter 

 kind, like the mule, the mulatto, or the mongrel, were inter- 

 mediate between the two parents, and still capable of pro- 

 ducing to a certain extent. 



, Three hundred and sixty-fifth, meeting'. 



July 13, 1852. — Monthly Meeting. 



The President in the chair. 



Professor Peirce presented a communication upon the Solu- 

 tion of Equations by the Means of Geometric Diagrams. 



Professor Peirce also presented a communication upon the 

 form assumed by an elastic sac containing a fluid. 



The positions of unstable equilibrium he found to divide 

 themselves into four special forms, the annular, cylindrical, 

 that of the cylinder with a bilateral character, and the double 

 or multiple cylinder. The ultimate form of the first case is 

 a sphere. 



He also alluded to the interest of this fact to those who 

 were not themselves mathematicians. For the primitive forms 

 which Professor Agassiz had found to be the four types of the 

 animal kingdom were the same, the Radiata being represented 

 by the sphere, the Mollusca by the cylinder, the Articulata by 

 the bilateral, and the Vertebrataby the double cylinder. Now, 

 as all animal forms begin as elastic sacs, containing fluids, 

 these forms seem the necessary ones for the condition of equi- 

 librium. 



This led to a discussion, in which Messrs. Eustis and Peirce 

 took part. 



