1892.] and animal and vegetable life. 9 



vapour during the life of the tree, operation (4) will be the re- 

 verse of (2) (both being supposed reversible) ; and the quantity 



of heat absorbed and the value of 2 K for the two operations to- 

 gether, will both be zero. Hence since the total quantity of 

 heat absorbed in the complete cycle is zero, the heat absorbed 



in the first operation is q, and the value of X ^ for the whole 



u 

 q q 

 cycle is 5 — ^, , which is positive, contrary to Carnot's principle. 



The solution of this difficulty appears to be found in what 



botanists call ' transpiration/ or the exhalation of aqueous vapour. 



In consequence of this process the air in which the tree grows 



gradually comes to contain more aqueous vapour. Hence more 



vapour is deposited in (4) than absorbed in (2) ; and therefore, 



in the two operations together, a positive quantity of heat, x say, 



Q X 



is given out, and the corresponding value oi %— is — -^ , where 



9(, < 6. If therefore, as before, q be the quantity of heat given 

 out in (3), q-^ X will be the quantity absorbed in (1), and the 



value of 2 ^ for the complete cycle will be 



q + x X 



lil'D-^ik-l) 



This will be negative when x> -^, -. — ^ q, and therefore, a for- 



6 



tiori, when x> ^ ° ^ q. If, for example, d^ = ^6, 2-^ will 



^ 7 ^0. . 



certainly be negative if x > 9q. Now this appears to be actually 



the case. Thus we may safely put the quantity of aqueous 



vapour transpired by an oak-tree in 24 hours at 20 litres, or 



about 4^ gallons, of water [Sir J. D. Hooker's Primer of Botany]. 



Hence since the latent heat of one gramme of water at the 



freezing-point is a little over 600 calories, the value of x for 



one day's growth will be roughly 12 million calories. If we 



suppose 50 growing days in a year, the value of x for 20 years 



will be about 12 thousand million calories. Again, if we take 



the heat given out in the combustion of one gramme of dry wood 



to be 3000 calories, it will require 4 million grammes, or 4000 



kilogrammes, or about 4 tons of dry wood to be burnt to evolve 



12 thousand million calories of heat. Hence since we can only 



suppose the increase of the tree to amount to a small fraction 



of 4 tons of dry wood in 20 years, q will only be a small frac- 



