ACADEMY OF SCIENCES. 291 



VII. Having subdivided the hollow square as in problem VI, 

 to determine, in terms of the two given sides, the consecutive sides 

 of the hollow squares inside the given hollow square, and having 

 equal areas with the prescribed subdivisions.' 



Let r, ?, a;, y, etc., represent quantities as before, /, i\ i"\ 

 etc., the consecutive sides of the inner hollow squares, and suppose 

 the given hollow square is divided into p hollow squares ; and there 

 are required n inner hollow squares, then, 



.1 __ {n + p) n — nl"^ 



VIII. Having subdivided the hollow square as in problem VI, 

 to determine, in terms of the two given sides, the consecutive sides 

 of the hollow squares outside the given hollow square, and having 

 equal areas with the previous subdivisions. 



Let Z', I, X. y, etc., represent quantities as before, o', o", o"\ 

 etc., the consecutive sides of the outer hollow squares, and sup- 

 pose the given hollow square is divided into p hollow squares ; and 

 there are required n outer hollow squares, then, 



n 



P 



Eegular Meeting, November 18th, 1872. 

 President in the Chair. 



Twenty-nine members present. 



H. F. Teschmacher, Ezra S. Carr, and J. A. Hoffman were 

 elected resident members. 



Donations to Library: Am. Naturalist, Oct. and Nov., 1872. 

 Overland Monthly. Am. Jour. Science and Arts, Oct. and Nov., 

 1872. Fifth Ann. Rep. Peabody Acad. Sci. White Coffee-Leaf 

 Miner, Pamph. Report of Geological Survey of N. H. Memoirs 

 of Boston Society Nat. History. Proc. Phil. Acad. Nat. Sci. 

 Proc. Boston Society Nat. His. On the Transit of Venus in 1874, 

 Paraph. 4to. Observations Encke's Comet in 1871, Pamph. 4to. 



