Researches in the Theory and Calculus of Operations. 



[Read before the Albany Institute, January 1872.] 



FIRST RESEARCH. 



Physical Operations. 

 1. The cosmical universe consists of a continuous succes- 

 sion of operations, performed by forces conspiring together 

 in space and time. The complete description of an operation 

 requires the enumeration of five things or elements : 1° The 

 Time occupied in the performance of the operation; 2° The 

 Space taken up by the operation ; 3° The Force, or the forces 

 which conspire in the operation ; 4° The Phenomena, the re- 

 sults or resultants of the operations; and 5° The Ratio, or the 

 relations of simultaneous and successive operations, referred 

 each to a homogeneous arbitrarily chosen unity, and re- 

 cor4ed by the observer as the coefficient or intellectual 

 measure of the operation on hand. Time and Space, then, 

 in a logical thesis, constitute the container or containing 

 member of the Cosmos; the field and stage in and upon 

 which the forces of the universe, the contained member of 

 the dichotomy, deploy themselves in eternal unrest. En- 

 wrapt among these changes, stands the humble observer, 

 man, whose highest terrestrial duty is to unravel the web of 

 concealed modes and habits which underlie the outward 

 appearance of things. 



" Man is the measure of the universe." 



The statical division of the universe into the container and 

 the contained having served its momentary purpose, a more 

 » fertile arrangement is found in the dynamical classification 



