we obtain the following forecasts:
Since one of the factors used in the formula is a square, it is noticeable that the increase is quite a rapid one as the years go on. In the year 2270, which is not so very remote, the estimate is 1,557 millions, which is about the population of the globe at the present clay. The predictions reached by this formula are somewhat smaller than those given by the formula of Dr. Pritchett in the article referred to. An interesting point in the curve is noticed for the year 1870. It will be observed that the population for this year differs more widely from that of the predicted population than that for any other year. This is probably due to two causes. In the first place, the effects of the civil war are shown in the reduction of the population, and, secondly, it is probable that the census of 1870 was not so accurately taken as that of any other decade. This latter reason is given by Mr. Robert Porter in the Census Bulletin No. 12, 1890.
There is another method of forecasting the census, which depends upon reported estimates of the population in various centers. "The World Almanac," for example, secures the best available data from government and other officials, and each decade estimates the census which is to be taken. In January, 1900, this estimate was 79.4 millions, while the census enumeration showed 76.3 millions. This was about 4 per cent, too high. In January, 1910, the estimate is given as 92.3 millions. If this is reduced in this ratio, it gives a result of 88.8 millions for the year 1910.
In conclusion, it may be stated that the results of empirical formulæ, unlike those of the mathematical formulæ, are never perfectly reliable or correct. It is, therefore, impossible to predict the population for 1910 with any such degree of certainty as one can predict the free fall of a body in a given interval of time. It is to these empirical formulæ, however, that science owes much of its progress, and the governments of civilized countries are spending thousands of dollars in order to bring the constants in these various formulæ a little nearer the truth. In its application to the problem before us, it may be stated that if the population for 1910 shall be found to conform to the general trend of increase in the population since the first census was taken, we may feel certain that it will come out about 89.7 millions. If, on the other hand, it shall be found to conform more nearly to the growth made in the last few decades, it will be about 91.3 millions. Of course, there