# Calendar: 1874-1875 Page 570

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570 APPLIED SCIENCES pieces of the roof ABC where the pitch of the roof is 45 and where AF and FB are each inclined at an angle of 15 to the rafter AB The whole roof weighing 000 lbs Prove that the volumes of the solid generated by the com- plete revolution of right-angled triangle having the sides each V2 7r equal feet about its hypothenuse Show that the direction of the smallest force which will make body slide either up or down an inclined plane makes an angle with the plane equal to the limiting angle Show how to determine the resultant of any system of forces acting in one plane on point and to infer the conditions of equilibrium of such system of forces In the third system of pulleys with three pullevs each in in radius on rough axles each £ an inch in radius find the relation between the power and weight sin φ 16 Also determine at what point of the horizontal rod AB the weight iV should be attached wall of brickwork is to be built round reservoir its slope is inward at an angle of 45 and it is foot thick at the top find its depth so that when the reservoir is full the line of

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