J. A. Harris 
465 
the line connecting these shows the difference between the two samples for each 
individual. The transverse lines show the position of the means for the whole 
population, the broken one being for the eliminated and the continuous one for 
the matured ovaries. 
The diagram sliows one further point — the great difference in the means of the 
individuals. The two transverse lines may be regarded as in a way smoothing 
these irregularities. The solid line is really the mean position of the solid dots on 
the scale while the broken line shows the mean position of the circles, each indi- 
vidual being weighted with the number of ovaries which it furnished. I think the 
differences shown on the diagram are conspicuous enough to carry considerable 
weight. 
Let us now consider tlie significance of the constants from the individual trees. 
We shall not expect this to be very high as judged by a comparison of the probable 
errors, because of the smallness of the samples of material taken. Unfortunately 
the excessive labour of the dissection and the counting of the ovaries, even in the 
mature state, precluded the examination of more extensive collections. 
The trustworthiness of the difference between any two constants is indicated 
by its probable error. The probable error of the difference between any two 
uncorrelated* constants, say x and y, may be calculated by the formula 
E {x -y) = ^E'j? + Ef. 
Conventionally, a constant is not considered significant unless it is 2'5 or more 
times its probable error. This is the degree of divergence from 0 demanded in the 
following discussion. For convenience of comparison the ratio 
Difference 
Probable Error of Difference 
has been tabled for the three comparisons for each tree (see the third column. 
Table IV.). 
For the comparison B — A it appears that there are 13 significantly positive 
and 5 significantly negative differences. For the comparison C — B there are 22 
significantly positive and 3 significantly negative differences. 
Finally for the most critical test of selective elimination, C — A, there are 25 
significantly positive and 1 significantly negative differences. 
The thing which strikes one particularly about these conclusions is the high 
number of cases in which the differences between the constants are significant with 
* I am afraid that here our constants are not perfectly independent. As Professor Pearson suggested 
to me, this is certainly not true where the size of samples is at all large as compared with the total 
number of ovaries produced, for a random excess in a first sample would be associated with a random 
deficit in the second. 
I do not believe that all of my samples combined equal one-tenth of the total ovaries produced, and 
I suspect that the influence of the correlation of the samples would not be large, but I have no statistical 
proof of this. Indeed in a form like Staphylea it would be difficult to get suitable data for the correction 
of the probable error of the differences in two constants, even if the formulae were available. I think 
these constants affect in no way the validity of the conclusions drawn in this paper, but they may 
render some of the probable errors somewhat questionable. 
