POPULATION OF THE UNITED STATES. 49 



THE POPULATION OF THE UNITED STATES DUEING 

 THE NEXT TEN CENTUEIES. 



By H. S. PRITCHETT, 



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 a priori that 

 the growth of population is not a matter which can be made the sub- 

 ject 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 knowl- 

 edge 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 tele- 

 scopes busied themselves were the observation of these spots for de- 

 termining the period of the sun's rotation. The observation is a very 

 simple one and consists merely in noting the time which elapses be- 

 tween 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 



VOL. LVIII.— 4 



