412 CALCULATIONS OF POPULATION IN JUNE, 1900 



four. Perhaps this may be taken as an indication that the 1830 

 census gave a somewhat excessive total, while the others were 

 fairly close to the truth. Calculation C gives a near agreement 

 with all these ante-bellum results, while B and D show system- 

 atic divergences. To those since the war, on the contrary, B 

 and D are both nearer than C. The agreement of A for every 

 census but 1870 is strikingly close. 



No attempt has been made to compare these results by aggre- 

 gating the residual corrections and so computing a probable error 

 of quantities found, because this work could only be misleading. 

 It is plain that the results of calculation A would come out best 

 and C worst by such test, residuals in parentheses being omitted ; 

 and yet it is the belief of the writer that the result under C for 

 1900 is nearer the truth than that under A. He does not believe 

 that the rate of natural increase has really reached a maximum 



and is now diminishing, as both A and D require (for - / - = 56 



by A and 53 by D). He does not believe that the discordance 

 of the 1870 census is altogether due to omissions in taking it, or 

 that it can really be a million and three-quarters short. A cal- 

 culation in the preface to the population volumes for 1890 made 

 the deficiency a little over a million and a quarter, and even that 

 figure is probably too high, because it depends upon a supposi- 

 tion that the southern section of the country, which had suffered 

 most in the war, yet increased during that decade correspond- 

 ingly with other sections. The writer believes that three-quar- 

 ters of a million is a fair estimate for war losses in the 1870 

 census, and that the official figures were little, if any, over a 

 million too small — about as calculation C makes them. It is 

 more probable that the eleventh census, or both the tenth and 

 eleventh, were largely in error, than that such a theory of the 

 ninth census as is shown under calculation A is true. 



Final Result for 1900. — The final figures under the four calcu- 

 lations have a range of two million and indicate a correspond- 

 ing uncertainty in the prediction. The highest of them is two 

 million less than the Treasury Department's calculation would 

 give : the estimates of population which accompany the monthly 

 financial reports point to a value of 77,676,000 for June, 1900. 

 Those estimates show substantially uniform third differences, 

 and therefore appear to connect i^opulation with time by an 

 algebraic equation of the third degree. There is no evidence 

 of an attempt to take separate account of immigration in the 



