484 Prof. C. A. Carus Wilson on the Influence of 



case in point, and one which will be found to agree closely 

 with the experimental results I had previously arrived at, and 

 which are given later on. 



Suppose there to be a uniform pressure p exerted over every 

 element du of bearing-surface between two extremities A, A' 

 (see figure), having abscissse u=—NA=—a, ?^ = NA'= + «, 

 and let p = J*du, calling P the constant exterior pressure per 

 unit of length AA / = 2a. 



The total pressure over unit of surface of an element E E' 

 will be, from equation (3), 



2 27rr 5 



3px* _ CaVaPdu _ 3IV f+ a du 

 "J 2vrr 5 ~"~2iTj_ a ^ 



3P.r 3 f" du rA ™ n 



x dot, we gel 

 unit of area on E E', 



Putting — = a, du = xdot, we get as the normal pressure per 



— \ (1 + * 2 ) V«; 

 or, very nearly, if a is much smaller than a, 



The value of the integral is — - 3 or % — -„ which, 



3(i+^ 3(i+i 2 y 



2 

 between the limits a =0 and a = oo , becomes ~. Thus 



o 



2P 



the pressure per unit of area on an element E E' becomes — , 



7TX 7 



or 



0-64- (4) 



x 



This expression has the form of that given below, though, 

 inasmuch as the problem is not altogether the same as that 

 treated experimentally*, a difference in the coefficients is only 

 what might have been expected. 



* The mathematical solution assumes the length of bearing A A' on an 

 infinite surface. 



