The quantity of a given matter can only be estimated in general according to its force, and its force can only be known in its _expression_. Now when we are considering matter only as regards its quantity, not its quality, this expression can only be mechanical, _i.e._, it can only consist in motion which it imparts to other matter. For only in motion does the force of matter become, so to speak, _alive_; hence the expression _vis viva_ for the manifestation of force of matter in motion. Accordingly the only measure of the quantity of a given matter is the _quantity of its motion_, or its _momentum_. In this, however, if it is given, the _quantity_ of matter still appears in conjunction and amalgamated with its other factor, _velocity_. Therefore if we want to know the quantity of matter (the mass) this other factor must be eliminated. Now the velocity is known directly; for it is _S/T_. But the other factor, which remains when this is eliminated, can always be known only _relatively_ in comparison with other masses, which again can only be known themselves by means of the _quantity of their motion_, or their _momentum_, thus in their combination with velocity. We must therefore compare one _quantity of motion_ with the other, and then subtract the velocity from both, in order to see how much each of them owed to its mass. This is done by weighing the masses against each other, in which that _quantity of motion_ is compared which, in each of the two masses, calls forth the attractive power of the earth that acts upon both only in proportion to their _quantity_. Therefore there are two kinds of weighing. Either we impart to the two masses to be compared _equal_ velocity, in order to find out which of the two now _communicates_ motion to the other, thus itself _has_ a greater quantity of motion, which, since the velocity is the same on both sides, is to be ascribed to the other factor of the _quantity of motion_ or the _momentum_, thus to the mass (common balance). Or we weigh, by investigating how much _more velocity_ the one mass must receive than the other has, in order to be equal to the latter in _quantity of motion_ or _momentum_, and therefore allow no more motion to be communicated to itself by the other; for then in proportion as its velocity must exceed that of the other, its mass, _i.e._, the quantity of its matter, is less than that of the other (steelyard). This estimation of masses by weighing depends upon the favourable circumstance that the moving force, in itself, acts upon both quite equally, and each of the two is in a position to _communicate_ to the other directly its surplus _quantity of motion_ or _momentum_, so that it becomes visible.