Calendar: 1859-1860 Page 440

GENERAL LITERATURE AND SCIENCE 441 inclination of the section to the axis in order that the cone may so stand ball whose elasticity is projected from the floor of room 12 feet high strikes the ceiling and floor and just rises to the ceiling again find the velocity of projection Find the positions in which square lamina may float in fluid with one angle out of the fluid the plane of the lamina being vertical An uniform rod Β turns about smooth hinge at at the bottom of vessel containing fluid the depth of which is equal to half and of which the density is three times that of the rod find the inclination of the rod to the vertical when there is equilibrium and determine what weight must be suspended at Β in order to depress the rod through 15 sphere touches each of two straight lines which are at right angles to one another but do not intersect find the locus of its centre body whose weight is 12 lbs is fastened by string yard long to fixed point in smooth horizontal table The string being kept stretched velocity of feet second is com- municated to the body perpendicularly to the string find the tension body revolving in circle about centre of force which varies inversely as the square of the distance has an impulse given to it in the direction of the centre which increases its velocity one-half Find the new orbit described Ill-Stffmnttal ra1rtl integral Calculus Jlciuton'S Prinrt'pta If 11 tan show that -l eos given volume of metal is to be formed into rectan- gular vessel without lid the sides of which are to be of given thickness Determine the shape of the vessel so that it may have maximum capacity