=119. Law of Machines.=--When a body receives energy, work is done upon it. Therefore work is done upon a machine when it receives energy and the machine does work upon the body to which it gives the energy. In the operation of a machine, therefore, two quantities of work are to be considered and by the principle of the conservation of energy, these two must be equal. _The work done by a machine equals the work done upon it, or the energy given out by a machine equals the energy received by it._ These two quantities of work must each be composed of a _force_ factor and a _space_ factor. Therefore two forces and two spaces are to be considered in the operation of a machine. The force factor of the work done on the machine is called the _force_ or _effort_. It is the force applied to the machine. The force factor of the work done by a machine is called the _weight or resistance_. It is the force exerted by the machine in overcoming the resistance and equals the resistance overcome. If _f_ represents the force or effort, and _D_{f}_ the space it acts through, and _w_ represents the weight or resistance, and _D_{w}_ the space it acts through, then the law of machines may be expressed by an equation, _f × D_{f} = w × D_{w}_. That is, _the effort times the distance the effort acts equals the resistance times the distance the resistance is moved or overcome_. When the product of two numbers equals the product of two other numbers either pair may be made the means and the other the extremes of a proportion. The equation given above may therefore be expressed _w: f = D_{f}: D_{w}_. Or the resistance is to the effort as the effort distance is to the resistance distance. The law of machines may therefore be expressed in several ways. One should keep in mind, however, that the _same_ law of machines is expressed even though the form be different. What two ways of expressing the law are given? =120. The Simple Machines.=--There are but six _simple machines_. All the varieties of machines known are simply modifications and combinations of the six simple machines. The six simple machines are more easily remembered if we separate them into two groups of three each. The first or _lever_ group consists of those machines in which a part revolves about a fixed axis. It contains the _lever_, _pulley_ and _wheel and axle_. The second or _inclined plane group_ includes those having a sloping surface. It contains the _inclined plane_, the _wedge_, and the _screw_.