Machines are composed of parts connected together by rigid and movable joints; rigid joints are necessary because of the expense, and in most cases the impossibility, of constructing framing and other fixed detail in one piece.
 
All moving parts must of course be independent of fixed parts, the relation between the two being maintained by what has been called running joints.

It is evident that when the parts of a machine are joined together, each piece which has contact on more than one side must have specific dimensions; it is farther evident that as many of the joints in a machine as are to accommodate the exigencies of construction must be without space, that is, they represent continued sections of what should be solid material, if it were possible to construct the parts in that manner. This also demands specific dimensions.

In arranging the details of machines, it is impossible to have a special standard of dimensions for each case, or even for each shop; the dimensions employed are therefore made to conform to some general standard, which by custom becomes known and familiar to workmen and to a country, or as we may now say to all countries.

A standard of lineal measures, however, cannot be taken from one country to another, or even transferred from one shop to another without the risk of variation; and it is therefore necessary that such a standard be based upon something in nature to which reference can be made in cases of doubt.

In ages past, various attempts were made to find some constant in nature on which measures could be based. Some of these attempts were ludicrous, and all of them failures, until the vibrations of a pendulum connected length and space with time. The problem was then more easy. The changes of seasons and the movement of heavenly bodies had established measures of time, so that days, hours, and minutes became constants, proved and maintained by the unerring laws of nature.

A pendulum vibrating in uniform time regardless of distance, but always as its length, if arranged to perform one vibration in a given time, gave a constant ............