rr SUTAIILK Kgrii.niKirM. 



Q denote tiic -lie beam; ! ? I'M 



be perpendiculars on the low 

 : 



beam above this direct 



V + Q\) ; for stu . ibrium this height should be * 



be the exccntricity of the ellipse we hare 



Proust be a minimum. Hut SP + SQ 

 is always arc:' opt when S in in tin- Mi-night 



/'<J. Therefore the position of stable equilibrium is that 

 PQ passes through the f< 



e the beam is in equilibrium uiM. -r tl, f its own 



weight aii'l the normal resistances of the curve, it follows that 

 the straight line u of inter- 



nals at the ends of a focal chord of an ellipse with the n\ 



parallel to the major axis: this result 

 may be verified geometrically. 



II. ay be applied to a liquid 



- regarded as a collection of indefinitely small 

 smooth heavy particles. 



pose a set of rectangles, all of the same length, but 



i long their lengths bj 



smooth hinges, so as to form a hollow prism v tids ; 



.1 smooth horizontal plane. 

 Let x l>c poured into the vessel thus formed. 



stable equilibrium the centre of gravity of the 

 1 b At a minimum ix'ight above tne horizontal 



area of a horizontal section c>: 

 will then have a maximum value. 



But .rojitntics the rectangles w: 



of the vessel are acted on by pressures 



i a system of forces like thn 

 ;t the end of Chap, iv.: and therefore when there is 

 equilibrium the horizontal sect he prism must form a 



'i can be inscribed in a circle. 



