Page:American Journal of Sociology Volume 2.djvu/97

 THE SOCIAL FORCES 83

modern doctrines in mechanics discussed under the general name of the "theory of units." The three ultimate elements in this theory are mass, space, and time. Motion being assumed, the rate, or velocity is equal to the space divided by the time. When the mass, or quantity of matter is taken into the account there arise four manifestations of force. The simplest of these is mere momentum, which is equal to the product of the mass into the velocity. The next simplest stage is force proper, which is the mass into the rate of change of velocity, or acceleration. The third is energy, as now understood by physicists, *'. e., kinetic energy, which is half the product of the mass into the square of the velocity. The fourth stage represents the power, or rate at which energy is produced or consumed. The distinction between these fundamental quantities is clearly shown by the following algebraic statement, showing how the units of mass, space and time enter them. Denoting these units by m, s, and /, respec- tively, we have :

Momentum = > or mv

ms mv Force = > or

ms 3 Energy = > or mv 3

ms 9 m?' 3 Power = > or

The theory of units is applicable to every true science in proportion as it can be reduced to exact measurement. In mechanics, astronomy, and physics the phenomena can, for the most part, be thus reduced, but in the more complex sciences, at least in their present state, this can be done only to a limited nt. It must not, however, be inferred from this that exact laws do not prevail in these domains. They are as rigid here n the simpler ones, and the only imperfection is in our knowledge of them. The acceptance of this statement is what constitutes scientific faith. Those who do not accept it and doubt tin uniformity and invariability of natural law in the fields of