These pipes, being in the smoke-box, are exposed to great changes of temperature, and are therefore subjected to expansion by heat and contraction by cold. The joints are therefore constantly subject to disturbance by the contraction and expansion of the pipes and so are difficult to keep tight. It is also practically impossible to construct the boiler, the cylinders and the pipes with perfect accuracy, and therefore a small amount of adjustability and flexibility is necessary in the joints of the pipes. If, for example, the opening _x_ in the cylinder, fig. 40, were either too near or too far from the cylinder of the engine, it would be necessary to move the end of the pipe _o_ either to the right or to the left in order to connect it with _x_. If the joint of the upper end of the steam-pipe were attached to the T-pipe with a flat joint like that shown at _a b_, fig. 87, it would be impossible to move the lower end of the steam-pipe either to the right or to the left without disturbing the joint and causing it to leak. For this reason these pipes are connected with what are called _ball joints_, fig. 88, that is, the end _a b_ of one of the pipes is turned into the form of a part of a sphere,[43] and the other end into a corresponding concave form. It is known that a sphere will fit into a corresponding socket in any position; for example, an acorn in its cup or the bones at the hip or shoulder joints. If, therefore, the pipes are joined with such spherical or _ball-joints_ as they are called, the lower end can be moved sideways several inches either way, and the joint will still be steam-tight if it is then firmly bolted together. Even after it is bolted together it will have so much flexibility that the expansion and contraction of the pipes will not cause it to leak. [43] The dotted lines indicate what would be the form of the sphere if the pipe was solid instead of hollow.