*POPULATION OF THE UNITED STATES.*

THE POPULATION OF THE UNITED STATES DURING THE NEXT TEN CENTURIES. |

PRESIDENT OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY.

IS it possible to predict with any degree of certainty the population of a country like the United States for a hundred years to come?

Doubtless the average intelligent person would say *à priori* that the growth of population is not a matter which can be made the subject of exact computation; that this growth is the result of many factors; and that those factors are subject to such great fluctuations that an estimate of the population a hundred years hence can be, in the nature of the case, only a rough guess.

It is true that the growth of population depends on a number of factors. It is also true that these factors vary in accordance with laws which are at present not known. Nevertheless it does not by any means follow that because the law of these variations is unknown we cannot represent the variations themselves by a mathematical equation. The problem of representing mathematically the law connecting a series of observations for which theory furnishes no physical explanation is one of the most common tasks to which the mathematician is called. And it does not in the least diminish the value of such a mathematical formula, for the purposes of prediction, that it is based upon no knowledge of the real causes of the phenomena which it connects together.

To illustrate: The black spots on the sun have been objects of the greatest interest to astronomers ever since Galileo pointed the first feeble telescope at his glowing disc. These spots, as observed from the earth, seem to pass across the disc from east to west as the sun rotates on its axis.

Among the problems with which the possessors of the first telescopes busied themselves were the observation of these spots for determining the period of the sun's rotation. The observation is a very simple one and consists merely in noting the time which elapses between successive returns of a spot to the central meridian of the disc. The earlier observers were astonished to find that the different spots gave different results for the rotation period, but it was only within the last thirty years that the researches of Carrington brought out the fact that these differences follow a regular law showing that at the solar equator the time of rotation is less than on either side of it.

The explanation which is generally accepted to account for this peculiar state of affairs is that the spots drift in the gaseous body of the