BY R. M. JOtlNSTON, F.L.S. 3 



Then let A= Total area in acres = 77*80 million acres. 



H=Tlie number of hands required to cultivate 

 each 100 acres according to existing 

 conditions=5*35 hands. 



E= Average natural rate of increase of Eural 

 Population = say 1-2.5 per year. 



C=The actual area already in cultivation in 

 (1840) =43-80 million acres. 



N=The number of hands already employed in 

 1840 in cultivating the land = 3-400 

 million hands. 



]SI*=Ditto ditto in 1881 = 2-561 million hands. 



The answers to queries 1, 2, 3, and 4 would be as follows : — 



AH 



Query (1.) .-. -,-7^ = X or max. number of hands or 



=Ans. (1) =4*162 millions. 



= T or max. number of hai 

 or = Ans. (2) = 3-122 millions. 



(2.) .'. ^ 100 J X H = T or max. number of hands, 

 100 



(3.) 



(4.) 



log.X-log.N _ log. 4-162-000 - log. 3-400-000 

 log. R ~ log 1-25 



= 16*28 years or year 1856. 



•. log.Y-log.N^ log. 3-122-000-log.2-561-0QO 

 log K ~ log. 1-25 



= 15*94 years, or year 1896. 



•. log.X-log.N log. 4*162*000-log. 2-561-000 

 log. R ~ log. 125 



= 39-09 years, or year 1929. 



It has thus been demonstrated that the ordinary growth 

 by natural increase of the agricultural population of the 

 United Kingdom of 1841 (if migration was prevented by 

 placing them on the land still uncultivated) would fully 

 stock the whole of its land area of every description in 16*28 

 years later ; that is in the year 1856, or 36 years ago. 

 Starting with the agricultural population of 1881, the same 

 rate of natural increase, under similar conditions, would fully 

 stock 75 per cent, of its land surface in the year 1896, or four 

 years hence; and even if we conceive what is impossible, 

 that its total area was open to cultivation, this same natural 



