402 i2. T, Patton: 



early, and therefore suggests that the value of r lies between 2 and 

 2.5, but it is certainly not greater than 2.5. It may be that the 

 expansion of the crown is a linear function of time, but towards 

 the end of the expansion the growth is slower, and hence the graph 

 is no longer a straight line. It may be, however, that the graph 

 is not linear, but during the earlier stages of crown expansion it 

 approximates to a straight line. It is probably true that the value 

 for r is the same for all close canopied pure forests. The difference 

 between forests is due to the time taken to pass from one crown 

 class to another. In other words, the forests differ in the intensity 

 of the struggle for existence, and this intensity reaches a maximum, 

 probably, in Mountain Ash forests. Since we know the number of 

 trees in each crown class, and the age of each crown class we can 

 plot the result. 



The curve for Mountain Ash is a theoretical curve, the curves 

 of Fir, Spruce and Cluster Pine are taken from tables, the sources 

 of which have already been indicated. Very few tables were avail- 

 able for comparison, as our forestry literature is extremely limited. 

 These curves, while giving the number of trees per acre at any 

 particular year, are in reality the curves of the struggle for exist- 

 ence. It will be seen that the number of trees at any future period 

 is equal to the present number of trees divided by the square of 

 the quotient of the future age and present age. Expressing as an 

 equation — ^ 



in 



Where ^ = future number of trees. 

 ?i = present number of trees. 

 y = future age. 

 ;: = present age. 



This seems to be the equation for the struggle for existence for 

 a,ny species competing for the same necessaries of life. The equa- 

 tion is only true until maturity is reached; after that the mortality 

 is due to other causes. 



From this view of the forest several suggestions stand out. 



Each given set of conditions determines the ultimate size of any 

 given species when grown in close canopy. Hence if the ultimate 

 size of the mature tree varies with the environment, then the 

 spacing of the trees when being planted out must be varied accord- 

 ing to the site. No arbitrary distances, for all classes of soils, can 



