PHILOSOPHICAL SOCIETY OF WASHINGTON. 65 



(2), but the mode of obtaining it is not so elegant as that em- 

 ployed in our first solution. 



The problem is proposed as an exercise in Bonnj-castle (John). 

 An Introduction in Algebra, etc., revised and enlarged, by James 

 Ryan, 4th edition, 12mo., New York, 1829, p. 310. In the key 

 to the second edition. New York, 1822, pp. 250-251, is a solution 

 essentially the same as the first one given here. 



The problem extended to any triangle was proposed by the 

 writer in the Analyst, vol, iii., No. 5, Sept. 18Y6, p. 163, and 

 solved in the next number, pp. 188-189, by Prof. J. Scheffer. It 

 was also solved by Henry Gunder, William Hoover, and the 

 writer. 



The problem not extended was proposed in the Educational 

 Times of January 1, 18'79, p. 22, question 5866, by Mr, N, H. 

 Capel; and in the following number proposed by the editor for 

 construction, question 5885. In the May number, p. 150, a, 

 construction by Mr. R. Tucker was given, which we have here 

 incorporated verbatim as our second construction. 



For the fourth solution I am indebted to my classmate, Prof. 

 W. W. Beman, of the University of Michigan. 



At the conclusion of Mr. Baker's communication the Society 

 adjourned. 



lUsT Meeting. ' December 19, 1879. 



Vice-President Taylor in the Chair. 



Thirty-four members present. 



The order of exercises for the evening consisted of the follow- 

 ing communications : — 



1. A paper by Prof. Chickering on the Luray Cave. 



2. A paper by Prof. William Harkness. 



3. A communication by Capt. Button on the Permian Forma- 

 tion in North America. 



The paper of Mr. Chickering was reserved for publication. 



The paper of Mr. Harkness was on 



THE number op LENSES REQUIRED IN AN ACHROMATIC OBJECTIVE, 



