### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 еМЭТГТА 1 1 еМЭТГТА 2 18
 еМЭТГТА 3 31 еМЭТГТА 4

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 14 - ... paraboloid. 12. A slender rod suspended horizontally by two equal parallel strings attached to two points equidistant from its ends oscillates round a vertical line; find the time of a small oscillation. If in the position of equilibrium the strings are inclined at equal angles to the vertical, show that the time of oscillation is the same as it would be if the strings were parallel, of a length equal to the projection of either of them on a vertical line, and at a distance equal to a mean proportional...
сЕКъДА 23 - When a body is placed on a horizontal plane, it will stand or fall, according as the vertical line, drawn from its centre of gravity, falls within or without its base.
сЕКъДА 13 - Find the limiting value of xt~x3 jt*dx when x = oo . 4. A regular octahedron is inscribed in a cube, so that the corners of the octahedron are in the centres of the faces of the cube; prove that the volume of the cube is six times that of the octahedron. 5. A bucket partly filled with water is attached to a weight by a string which passes over a fixed pulley ; supposing the water to revolve with a given angular velocity as the bucket is ascending or descending, find the form of the free surface....
сЕКъДА 6 - Shew that the surface generated by the revolution of a plane curve about an axis in its plane is equal to the rectangle of which the sides are the length of the curve and the length of the path of its centre of gravity. How must the enunciation be altered if the curve lie on both sides of the axis ? a.
сЕКъДА 23 - If two forces acting perpendicularly on a straight lever in opposite directions and on the same side of the fulcrum balance each other, they are inversely as their distances from the fulcrum ; and the pressure on the fulcrum is equal to the difference of the forces.
сЕКъДА 23 - Prop. 8. When a body of uniform density floats on a fluid, the part immersed : the whole body :: the specific gravity of the body : the specific gravity of the fluid. Prop.
сЕКъДА 12 - ... 15. The radius vector of any point in the surface of a solid differs from a constant by a small quantity of the order a, and the angle which it makes with the normal is of the same order; prove that if small quantities of the order a2 are neglected the sphere which has the same volume as the given solid is also that which has the same surface. 16. A uniform flexible and inextensible heavy string AB is laid in the form of a circular arc on a smooth horizontal plane; a given impulsive force being...
сЕКъДА 5 - ... pencil parallel to ap and capable of producing normal vision in an eye placed to receive them. The image seen is magnified and erect. This arrangement of lenses is used in opera and field glasses, which consist of two such telescopes, one for each eye. Its magnification is, it may be shewn, measured by the ratio of the focal length of the object glass to that of the eyepiece. Since the distance between the lenses is the difference between their focal lengths instead of as in the Astronomical...
сЕКъДА 23 - If a body floats on a fluid, it displaces as much of the fluid as is equal in weight to the weight of the body ; and it presses downwards and is pressed upwards with a force equal to the weight of the fluid displaced.
сЕКъДА 12 - P ; prove that __ ^ dxdy dxdy dx dy ' 15. The radius vector of any point in the surface of a solid differs from a constant by a small quantity of the order a, and the angle which it makes with the normal is of the same order; prove that if small quantities of the order a2 are neglected the sphere which has the same volume as the given solid is also that which has the same surface. 16. A uniform flexible and inextensible heavy string...