We have now to express in a still more general manner the important principle that is here involved. Let us consider any system of attracting particles, no matter what their masses or whether their movements be restricted to a plane or not. Let us start them into motion in any directions and with any initial velocities, and then abandon them to the influence of their mutual attractions, withholding at the same time the interference of any forces from bodies exterior to the system. Draw any plane whatever, and let fall perpendiculars upon this plane from the different particles of the system. It will be obvious that as the particles move the feet of the perpendiculars must move in correspondence with the particles from which the perpendiculars were let fall. We may regard the foot of every perpendicular as the actual position of a moving point, and it can be proved that if the mass of each particle be multiplied into the area which the foot of its perpendicular describes in a second round any point in the plane, and then be added to the similar products from all the other particles, only observing the proper precautions as to sign, the sum will remain constant, _i.e._, in any other second the total quantity arrived at will be exactly the same. This is a general law of dynamics. It is not a law of merely approximate truth, it is a law true with absolute accuracy during unlimited periods of time. The actual value of the constant will depend both on the system and on the plane. For a given system the constant will differ for the different planes which may be drawn, and there will be some planes in which that sum will be zero. In other words, in those planes the areas described by the feet of the perpendiculars, multiplied by the masses of the particles which are moving in one way, will be precisely equal to the similar sum obtained from the particles moving in the opposite direction.