PRITCHETT — FORMULA FOR POPULATION. 



6c'; 



B, C and D including the data of 1S90. This would yield the 

 following II equations of condition : — 



A — 5 B 4- 25 C — 125 D — 



A — 4 B + 16 C — 64 D — 



A - 3B + 9 C 



A — 2 B -f- 4 C 



A — B + C 



A 



A + B + C 



A + 2 B -f- 4 C 



A + 3B + 9 C 



3.9292 



5-3085 



27 D — 7.2399 



8 D — 9.633S 



D — 12.S660 



— 17.0695 



D — 23.1919 



8 D — 31.4433 



27 D - 3S.55S4 



A + 4B-|-i6C^ 64 D- 50.1558 

 A + 5 B -f- 25 C + 125 D — 62.6222 



= o 



:= O 



= O 



= O 



= O 



= O 



= o 



= o 



= o 



= o 



= o 



+ 0.083 



— 0.041 



— 0.I8I 



— 0.065 



-f O.I 19 



+ 0.415 



+ 0.05S 



— 0.975 

 + 0.754 



— o.iSi 

 + 0.012 



These yield the following normal equations : — 



-f ii.o A -}- 0.0 B -\- iio.o C -\- 0.0 D — 262.017 = o 



0.0 A + IIO.O B -|- 0.0 C -\- 1958.0 D — 620.753 = o 



-\- IIO.O A -f- 0.0 B -I-195S.0 C -\~ 0.0 D — 3163.765 = o 



0.0 A -|- 1958.0 B -\- 0.0 C -\- 41030.0 D — 11237.254 = o 



From which result the following values of A, B, C and D : — 

 A = 17.4841 B = 5.1019363 C = + 0.6335606 D = -j- 0.0304086 



and the population (P) at any decade (/) after 1840 will be given 

 by the equation, 



17.4841 -\- 5.1019363^' -\- 0.6335606,^' 4- 0.0304086/3 



(3) 



This formula, being the most probable result deducible from 

 all the data, forms the best basis at hand for predicting the popu- 

 lation of the future. In the course of time it is to be expected 

 that this will depart more and more from the observed values, 

 but for the next hundred years will doubtless represent the 

 growth of population within a small percentage of error. Carry- 

 ing forward the computation, we obtain to tlie nearest thousand 

 the following values for subsequent dates : 



