The address of the author is: The Congressional, 100 East Capitol Street, Washington, D. C.
EQUATION OF THE DEMOGRAPHIC LAW OF INTERDEPENDENCE OF NATIONS.
As already noted, our demographic law of the interdependence of nations is, that increase in the means of communication between States causes increase of their interdependence but decrease in their sovereignty. Just as a physical body consists of molecules of various kinds, so the State may be regarded as a psychological entity with citizens of various characteristics, and just as the density of a body is equal to its mass divided by its volume, so the density of citizenship is equal to the population divided by the land area.
If, therefore, we consider the States' adult population, as its mass (m) and the resultant aggregate increase of its means of communication as its velocity (v), and (t) as the time, then the psychological force (F) or interdependence of the State can be expressed by the familiar equation in physics F=mv/t; that is to say, the interdependence of a State is equal to its adult population (mass) multiplied by the resultant aggregate increase of its means of communication (velocity) and the product divided by the time (t).
The poundal unit of physical force is such a force as will move 1 pound (mass unit) at a velocity of 1 foot per second in one second of time.
Now, assuming the unit of citizenship of a State to be one citizen and the unit of the resultant aggregate increase of means of communication per annum in one year of time to be K, then
The statal unit of psychological force is such a force as will give one citizen (mass unit) one K unit (for convenience the K unit of annual aggregate increase of means of communication can be expressed in per cents. Taking some of the principal means of communication, and working out their annual average per cents of increase, we have for the United States during the census periods (1900-1910); annual average increase of passengers on railroads, 7 per cent; on street and electric railways, 3 per cent (1907-1912); of telegraph messages sent, 6 per cent; of telephone stations, 10 per cent. Combining these, the per cent of annual average aggregate increase will be 6.5 per cent, as value of K, assuming the percentages are equally weighted) of resultant aggregate increase of means of communication per annum in one year of time.
As yet there is no exact way to measure the sovereignty and means of communication of the State, but the psychological side of this physical equation may suggest a working hypothesis for our demographic law of the interdependence of States which may some time be useful in the realm of international psychology.
To measure the aggregate influence upon citizens of the many means of communication in a State (also, for illustration merely, let us take one of the principal means of communication, as steam railroads, and we find that the annual average increase in passenger-train-car miles for one citizen of the United States, from 1908 to 1914, to be 4.45, which is the value of K for steam railroads alone for period mentioned. In a later article the author will consider in detail the practical application of the equation) as steam, street and electric railways, telegraph and telephones, will require exact detailed knowledge of the mental, moral, and physical power of the individual citizen, the unit of the social organism. Such measurements might be made when psychology and sociology become sciences in the rigid sense. The underlying hypothesis in this equation is that both the psychological and physical mechanism of the world are under one fundamental law.[7]