604 TRANS. ST. LOl IS ACAD. SCIENCE. 



of the Tenth Census said in his report in relation to the taking of the cen- 

 sus in South Carolina: "It follows as a conclusion of the highest autho- 

 rity, either that the census of 1870 was grossly defective in regard to the 

 whole of the State or some considerable parts thereof, or else that the 

 ■census of 1880 was fraudulent." Those, therefore, who believe in the 

 accuracy and honesty of the Tenth Census — and that was thoroughly 

 established — must accept the other alternative offered by General Walker, 

 namely, that the Ninth Census was " grossly defective." What was true 

 of South Carolina was also true, in greater or less degree, of all the 

 southern States. 



There is, of course, no means of ascertaining accurately the extent of 

 these omissions, but in all probability they amounted to not less than 

 1,500,000. There is but little question that the population of the United 

 States in 1870 was at least 40,000,000, instead of 38,558,371, as stated. 



The computed value just given is 39,316,000; but this is, of 

 course, affected to a certain extent by the error in the census of 

 1S70, which entered into the computation of formula (i). To 

 compute a value for 1S70 which shall be derived from data unaf- 

 fected by the deficit due to the war, it will be necessary to dis- 

 cuss the observations from 1790 to 1S60 alone. The data furnish 

 the following 8 equations of condition : 



V. 



A — 5 B -f 25 C — 125 D — 3.929 



A— 4B-f-i6C— 64 D— 5.30S 



A — 3B-I- 9C — 27 D — 7-240 



A — 2B-J-4C— 8D— 9.634 



A— B+ C— D — 12.866 



A — 17.069 



A+B-j- C+ D — 23.192 



A + 2B+4C+ 8D — 31.443 



Solving by the method of least squares for the value of A, B, 

 C and D we obtain the following function : — 



P = 17. 1S19 -t- 5.210279 / -f- 0-8201904 /'^ -f~ o-o623i82 t^ - - (2) 



How closely this equation fits the observed values will be seen 

 from the table of residuals. These residuals show that during 

 the 70 years from 1790 to 1S60 the growth of population followed 



