TJ. Three :heres hang in C'.nt:icf from a fixed 



point by three eqiul strings: find the heaviest sphere of 

 radius that may be placed upon them without causing 

 to separate. 



>i1t. Let Tl'be tin- V. ; i of the equal 



the anirle which each string makes with the vertical, </> the 



which the line joining the o ntre of one of the three 

 equal spheres with the, centre <>f the upper sphere makes with 

 the vertical ; then the weight of the upper sphere must not 



, SWtantf 

 ed - 2, . 



tan p tanp 



13. ABCD is a tetrahedron in wliicli th< Ml. AC, 

 AD are at right angles to each other; forces are represented 

 in magnitude and direction by AB, AC, AD, BC, CD, l>tt\ 

 determine their resultant. 



14. Three equal hollow spheres rest symmetrically in>M< 

 a smooth paraboloid of revolution, whose axis is vertical ; a 

 solid sphere of equal radius is placed upon them : shew that 

 the equilibrium will be destroyed if the radius of the 8]>!. 



is less than - ,- , where I is the latus rectum ; the weight of 



- \ 



the hollow spheres being neglected in comparison with that 

 of the solid one. 



