xliv Trans. Acad. Sci. of St. Louis. 



Messrs. A. F. Ewers, Benjamin G. Shackleford and 

 Charles H. Slater were elected to membership. 



November 17, 1913. 



President Engler in the chair; attendance 18. 

 The following donations to the Museum and Library 

 were reported : 



C. H. Turner Six pamphlets on entomology. 



H. L. Webb Biography and Unparalleled Discoveries of T. J. J. 



See. 

 H. M. Whelpley...A Flying Fox from the Philippine Islands. 



Professor F. E. Nipher called attention to the well 

 known equations for uniform motion of a load upon an 

 inclined plane. 



Some of the conditions which follow from the equations had never 

 suggested themselves to him until recently, and inquiry had revealed 

 the fact that they appeared new and interesting to his associates. 



Let R = mg be the weight of a block which is drawn uniformly up 

 a plane making an angle a with the horizontal. Let / be the coeffi- 

 cient of friction. Let R' be the component of R down the plane, and 

 R" the component at right angles to the plane. 



The force which will produce uniform motion up the plane is 



P = R> + fR" = R( S m a + /cos a) (1) 



Assuming R constant and a variable the force P will be a maximum 



when 



1 dP 



or when 



— = cos a — /sin a = 0. 



R da 



cot OL = / 



This angle is the complement of the angle which the plane would 

 make with the horizontal if P were made zero, and the block slides 

 uniformly down the plane. 



For this condition of maximum p 



fi 

 Sin a = .» h — r— fit cos « = 



~\1+. 



p =p i/T+7~ 2 



When / = 0.42, which is the value for an oak block upon an oak 

 plank, P= 1.085 R. This force is therefore greater than that required 

 to lift the load R by about 8%. 



