346 The Ohio Naturalist. [Vol. VIII, No. 7, 



habitat. In selecting one character for measurement it must 

 not be forgotten, of course, that the organism is a correlated 

 unit or whole. Change of environment may alter therefore a 

 great variety of characters. Whatever the species, its differences 

 constitute a distribution of deviations extending sometimes 

 through a considerable range. Points such as these the system- 

 atist above all, must necessarily consider. 



Another conception of the character and the amount of 

 wood-accretion and its distribution is possible through the 

 arithmetical average or mean. Multiplying the value of each 

 variate by its frequency, adding the results and dividing the 

 sum by the total number of rings, we thus get a determination 

 of the mean or average length. In this case the mean length 

 is 3.42 mm. and 1.70 mm. respectively for each of the habitats 

 under consideration. These values differ very sensibly from 

 the most common length or mode. It will be seen at once, that 

 the deviations in excess of the mode are in the case of the bog 

 habitat larger and in the woodlots smaller. The mean is in the 

 latter case less and in the former greater than the respective 

 mode. Such distributions are termed skew, — the mode and the 

 mean are separated from each other by a certain measurable 

 distance. The relative breadth of the curves exhibits to the 

 eye the great variability and the prominent skewness. 



There have been various interpretations of skewness, but 

 it is evident that we are dealing here with the results of direct 

 physiological reactions to the changes in the environment. 

 On an average the annual accretion in woodlot conditions is 

 by far less than in the bog habitat. Not all individual trees are 

 alike sensitive to changed conditions, but the greater value of 

 the positive skewness in the bog habitat indicates that only a 

 small proportion of the variates is conservative. It is plain, 

 therefore, that the position of the mode and the negative skew- 

 ness in the woodlot forms has resulted from physiological varia- 

 tion, i. e. from the prevailing edaphic conditions of that place, 

 and that the differences in the environment have changed the 

 type, the variability and even the sign of the skewness. 



The frequency curves enable us to perceive still another 

 relation. It will be observed that some of the rings deviate 

 but little from the mode or the mean, while others deviate more 

 and some even very much. For instance, the deviations from 

 the mean in the frequencies of the woodlot samples are —.70, 

 — .20, -H .30, -f.SO, and 4-1.30. The average deviation is 

 omitted here as having no particular significance. Usually a 

 standard deviation is derived in the following manner. The devi- 

 ation of each frequency from the mean is squared and then multi- 

 plied by its corresponding frequency ; the products are added and 

 then divided by the total number of variates, and the square root 



