PHILOSOPHICAL SOCIETY OF WASHINGTON. 



143 



Mr. Todd's paper is published in full in the Proceedings of the 

 American Academy of Arts and Sciences, 1880, page 270 ; also iu 

 the Monthly Notices of the Royal Astronomical Society for June, 1880. 



The second paper was by Mr. Thomas Craig on 



VORTEX MOTION IN ORDINARY FLUIDS. 



This paper is to be published in full in the Proceedings of the 

 London Mathematical Society. 



The third communication was by Mr. Edgar Frisby 



ON MAGIC SQUARES. 

 [Abstract.] 



The ordinary idea of a magic square is a square divided up inta 

 a smaller number of squares, with the successive integers placed in 

 each square in such a way that the sum of the numbers, whether 

 counted horizontally, diagonally, or vertically, will always be the 

 same — many very ingenious such squares have been constructed 

 also squares of squares, magic cubes, and magic circles. I pro- 

 pose to simply show what I consider the most convenient way of 

 constructing them when they can be constructed, and pointing out 

 some of their remarkable properties. 



The two which follow are remai"kable illustrations of what I will 

 call unsymmetrical squares : 



Fig. 2. 



Fig. I. 



The first square counts 34 the ordinaiy 10 ways, each small 

 square of 4 at the corners also counts 34, or the whole square can 

 be divided into 4 squares each of which counts 34, and the 4 



