l62 ROCHESTER ACADEMY OF SCIENCE. Qail I4, 



ELECTION OF OFFICERS. 



The annual election of officers for the ensuing year was held and 

 resulted as follows : 



For President, Herman L. Fairchild. 



For Fb'st Vice- President, J. M. Davison. 



For Second Vice-President, J. Eugene Whitney. 



For Secretary, Arthur Latham Baker. 



For Corj-esponding Secretary, Charles Wright Dodge. 



For Treastwer, F. W. Warner. 



For Libj-arian, Miss Florence Beckwith. 



For Cojmcil/ors, C. C. Laney, //// i8g8, 



Dr. G. W. Goler, till i8g8. 



The President had been announced to present a paper upon The 

 Geology of the Pinnacle Hills, but was absent on account of illness. 



The Secretary presented an informal paper upon the subject of 



DIRECTED MAGNITUDES. 



fundamental operations in mathematics. 

 By Professor Arthur Latham Baker. 



Empty space may be considered as a continuum of positions. A 

 number of neighboring positions taken together we will consider as 

 locating a point in space and will designate as d. point, and the number 

 of positions composing it, its weight. 



The characteristics of points are weight and location. 



I. 



Considering for the present only the weights, ivhat operations can 

 be performed ? Obviously we can combine the weights, either in their 

 normal condition (addition), or we can reverse the operation (sub- 

 traction), or we can consider the weight of one point as the symbol 

 of an operation to be performed on the weight of the other. The 

 weight has only one characteristic : the manner in which it differs from 

 unity. As a symbol of operation, this manner of difference is either 

 its evolution from unity, or its conversion into unity. 



If we take the first manner of difference as the process which is 

 to be repeated, we call it multiplication, or the doing to the operand 

 whatever was done to unity to produce the operator. 



