J. A. Harris 
13 
the seed planted and number of pods per plant, can be determined. The corre- 
lations between weight of seed planted and number of pods produced are com- 
parable from variety to variety or from cultural condition to cultural condition. 
To render the results more intelligible, the straight line regression equations 
have also been calculated and represented in a series of diagrams. These show by 
the slope of the lines the (smoothed) change in mean number of pods per plant 
associated with changes in the weight of the seed planted. 
The reader unacquainted with higher statistical methods need only remember 
that the coefficient of correlation describes the degree of interdependence between 
two variables on a scale of — 1 to + 1. This measure of interdependence is, there- 
fore, quite independent of the magnitude and of the variability of either or both 
of the characters in question. The regression coefficient, on the other hand, shows 
the absolute amount of change in a second character y consequent upon a change 
of one unit on the scale of the first character x. Concretely, in our present case, 
the regression coefficient shows the absolute increase (or decrease) in number of 
pods per plant associated with an increase (or decrease) of one unit in the weight 
of the seed planted. " Increase " or " decrease " is measured from the average 
condition in the population as a whole. 
The correlation coefficient is fully justified as a measure of interdependence 
only when regression is linear, that is to say, when the mean value of y increases 
at a uniform rate throughout the whole range of x. Where regression is not 
strictly linear, the coefficient of correlation still furnishes in many cases a very 
satisfactory measure of the intensity of relationship between two variables. This 
is true in the present case. 
All the weighings were made on seeds which had dried for several months at 
laboratory temperature. Drying at high temperatures was of course precluded by 
the fact that the seeds were to be used for planting. Drying in a vacuum over 
sulphuric acid could not be undertaken because of the excessive labour involved 
where each seed had to be followed individually throughout the whole work. 
The weight unit adopted was "025 gram. Hence to obtain means and standard 
deviations of weights in grams deduct '5 from values in tables and multiply by "025. 
The correlation tables showing the relationship between the weight of seed 
planted and the number of pods produced are entirely too bulky for publication. 
It is possible, however, to present the essential data by showing the total number 
of pods produced by each grade of seed weight (Tables III — VI). A convenient 
method of calculation for such cases has been suggested elsewhere*. 
In deducing the correlations from such tables, the means and standard devia- 
tions for the two characters involved are required. The distributions of numbers 
of pods per plant for the twenty series have already been published f for a quite 
* Harris, J. Arthur : " The Arithmetic of the Product Moment Method of Calculating the Coefficient 
of Correlation." Amer. Nat. Vol. xliv. pp. G93— 699, 1910. 
t Amer. Nat. 1912. In press. 
