198 Dr. J. Prescott on the 



occurs on the right of (72). Thus 



EcJ=Gt+M-%, 



(76) 



the term liy being the bending moment in Euler's theory of 

 struts. 



Case 8. — Beam of length I under a pair of balancing 

 couples, each G, at the ends, together with a thrust II 

 (fig. 11). 



Fig. 11. 



B 



Eievatson 



B 



D 



Plan of Central Line 



It is understood that the section of the beam has at least 

 one symmetrical axis which is assumed to be vertical, and 

 the length of this axis is several times as long as the greatest 

 horizontal breadth of the section. The end couples men- 

 tioned in this problem are in a vertical plane parallel to the 

 length of the beam. 



It should be noticed that the direction of G, and therefore 

 of t, are contrary to their directions in Case 1 in the first 

 paper. 



In this case M is zero. Then the equations applying to 

 this case are (71) and (76). 



Since G is constant (71) gives 



(77) 



or 



T— Gg + N, 



ax ax 



(78) 



But at the middle of the beam r and y have both maximum 



or 



minimum values, and consequently -*- and -~ are both 



.zero. It follows that the constant N is zero, 



