I894-] BAKER GRAPHIC I.MAGIXARIKS. 155 



To recapitulate, when the number concept was appHed to con- 

 crete objects only, a negative number was unintelligible and imaginary, 

 but when the number concept was applied to a more extended object, 

 one where the sense of mutual opposition held, as in the case of debit 

 and credit, the negative lost its unintelligibility and became real. But 

 here the y^i-i) was still unintelligible and imaginary, to become in its 

 turn real as soon as the number concept was applied to strokes, where 

 the stroke representing |/(-i) is a real stroke though an imaginary 

 number, just as — i may be a real debt, but a purely imaginary 

 number of inhabitants. 



On this system of strokes hangs all the enormous modern devel- 

 opment of the Theory of Functions, a development which has 

 increased the volume of mathematical literature more in the last half 

 than in the previous forty centuries, with a corresponding increase of 

 power and extension of grasp. 



The paper was discussed by several members. 



December id, 1894. 



The President in the chair. Forty persons present. 



The Council report was adopted, which recommended : (i) The 

 payment of certain bills ; (2) The appropriation of a sum not to 

 exceed $50.00 to defray the expenses of the Popular Lecture Course 

 for 1895. 



Professor Charles Wright Dodge read a paper 



ON PROTOPLASM. 

 Illustrated by Microscopical Preparations. 



January 14, 1895. 

 sixteenth annual meeting. 



Vice-President J. M. Davison, in the chair. Forty-five persons 

 present. 



The Council recommended the appropriation of $10.00 to pay for 

 lantern illustrations of the paper on the Geology of the Pinnacle Hills. 

 The recommendation was adopted. 



