xxxii Trans. Acad. Sci. of St. Louis. 



Besolved, by the members of The Academy of Science of St. Louis, that 

 the property conveyed on the 18th day of March, 1903, by Edgar R. Hoad- 

 ley and Lavinia L. Hoadley, to The Academy of Science of St. Louis, which 

 property is the gift of Mrs. Eliza McMillan and William N. McMillan, shall 

 not be mortgaged or incumbered so long as it remains the property of The 

 Academy of Science. 



Besolvedj further, that the property shall not be sold except by a two- 

 thirds vote of the members of The Academy of Science of St. Louis by 

 letter-ballot in the manner prescribed by the Council, and that when sold, 

 the proceeds of the sale, or as much thereof as may be necessary, shall be 

 used to provide a suitable location and building for the uses of The Academy 

 of Science. 



Mrs. Eliza McMillan and Mr. William Northrop McMillan 

 were elected patrons of the Academy, on nomination of the 

 Council. 



Professor A. S. Chessin presented the following communi- 

 cation on the strains and stresses in a rotating thin circular 

 disc : — 



The problem of determining the strains and stresses in a 

 rotating disc or, as it is commonly known, the problem of the 

 fly-wheel, is still an open one so far as a general solution is 

 considered. The present paper deals only with very thin 

 discs but the method of obtaining a solution may be readily 

 extended to the more general problem. 



Let the axis of the disc be the axis of ^, and let r be the 

 radius vector to any point drawn perpendicular to this axis, 

 and 6 the angle between the direction of r and a fixed plane 

 through the axis ; also let u and w be the displacements in 

 the direction of the radius and the axis ; finally let p be the 

 density of the solid, « the angular velocity of its rotation 

 and 2,h its thickness. If the disc be isotropic the stresses 

 are 



(1) 



<9^ = XA 4- 2At - , 

 r 



'^ ^ 9w 



2;^; = XA + 2u ;r- » 



y-^ /Su 9w\ 



