A very remarkable feature in this discussion is the use made of the idea of "ignoration of coordinates." The variables made use of in the Lagrangian equations must be such as to enable the positions of the parts of the system which determine the motion to be expressed for any instant of time. These parts, by their displacements, control those of the other parts, through the connections of the system. They are called the independent coordinates, and sometimes the "degrees of freedom," of the system. Into the expressions of the kinetic and potential energies, from which by a formal process the equations of motion, as many in number as there are degrees of freedom, are derived, the value of these variables and of the corresponding velocities enter in the general case. But in certain cases some of the variables are represented by the corresponding velocities only, and the variables themselves do not appear in the equations of motion. For example, when fly-wheels form part of the system, and are connected with the rest of the system only by their bearings, the angle through which the wheel has turned from any epoch of time is of no consequence, the only thing which affects the energy of the system is the angular velocity or angular momentum of the wheel. The system is said by Thomson and Tait in such a case to be under gyrostatic domination. (See "Gyrostatic Action," p. 214 below.) Moreover, since the force which is the rate of growth of the momentum corresponding to any coordinate is numerically the rate of variation with that coordinate of the difference of the kinetic and potential energies, every force is zero for which the coordinate does not appear; and therefore the corresponding momentum is constant. But that momentum is expressed by means of the values of other coordinates which do appear and their velocities, with the velocities for the absent coordinates; and as many equations are furnished by the constant values of such momenta as there are coordinates absent. The corresponding velocities can be determined from these equations in terms of the constant momenta and the coordinates which appear and their velocities. The values so found, substituted in the expressions for the kinetic and potential energies, remove from these expressions every reference to the absent coordinates. Then from the new expression for the kinetic energy (in which a function of the constant momenta now appears, and is taken as an addition to the potential energy) the equations of motion are formed for the coordinates actually present, and these are sufficient to determine the motion. The other coordinates are thus in a certain sense ignored, and the method is called that of "ignoration of coordinates." Theorems of action of great importance for a general theory of optics conclude this chapter; but of these it is impossible to give here any account, without a discussion of technicalities beyond the reading of ordinary students of dynamics.