The existence of these potentials applies generally to all fields of force, regardless of whether these fields are of the uniform or non-uniform variety.[78] It is, as we have said, the variations in value of these potentials from point to point that are associated with the existence of forces. When this variation is uniform in one direction and no variation exists in directions at right angles, we are in the presence of a uniform field of force. When the variation is irregular, we have a non-uniform field of force. When the potential has the same constant value throughout space, so that it does not change in value from place to place, no forces can be present; there is then no field of force. From this we see that a certain degree of indeterminateness surrounds the precise numerical value of a potential, since it is only its variation from place to place, and not its absolute value, that defines the force. This indeterminateness can be removed in the case of a non-uniform field of force by stipulating that in those regions of the field where the force vanishes (such as would be the case with the gravitational force at an infinite distance from matter), the [Pg 247] potential itself vanishes. A definite value having been attributed to the potential in one part of the field, we can determine its precise value from place to place in all other parts of the field. Let us now give a few concrete illustrations of fields of force and of potentials in classical science. We have already mentioned the field of force surrounding matter. This was the gravitational or Newtonian field, and the potential at every point derived therefrom was called the Newtonian Potential at the point. The distribution of the field of force was known in a perfectly definite manner when the potential distribution was known. In fact Newton’s law, which tells us how the field of force is distributed around matter, can also be expressed in an equivalent form by Laplace’s Equation, in which it is the potential distribution, and no longer the force distribution, that is described.