If it should happen that a series is known to follow the law of error or any other law, and if the number of individuals in the series is known, it would be always possible to reconstruct the whole series when a fragment of it has been given. But I find no such method to be applicable in the present case. The doubt as to the number of plants in each row is of minor importance; the real difficulty lies in our ignorance of the precise law followed by the series. The experience of the plants in pots does not help us to determine that law, because the observations of such plants are too few to enable us to lay down more than the middle terms of the series to which they belong with any sort of accuracy, whereas the cases we are now considering refer to one of its extremities. There are other special difficulties which need not be gone into, as the one already mentioned is a complete bar."]
Mr. Galton sent me at the same time graphical representations which he had made of the measurements, and they evidently form fairly regular curves. He appends the words "very good" to those of Zea and Limnanthes. He also calculated the average height of the crossed and self-fertilised plants in the seven tables by a more correct method than that followed by me, namely, by including the heights, as estimated in accordance with statistical rules, of a few plants which died before they were measured; whereas I merely added up the heights of the survivors, and divided the sum by their number. The difference in our results is in one way highly satisfactory, for the average heights of the self-fertilised plants, as deduced by Mr. Galton, is less than mine in all the cases excepting one, in which our averages are the same; and this shows that I have by no means exaggerated the superiority of the crossed over the self-fertilised plants.
After the heights of the crossed and self-fertilised plants had been taken, they were sometimes cut down close to the ground, and an equal number of both weighed. This method of comparison gives very striking results, and I wish that it had been oftener followed. Finally a record was often kept of any marked difference in the rate of germination of the crossed and self-fertilised seeds,--of the relative periods of flowering of the plants raised from them,--and of their productiveness, that is, of the number of seed-capsules which they produced and of the average number of seeds which each capsule contained.
When I began my experiments I did not intend to raise crossed and self-fertilised plants for more than a single generation; but as soon as the plants of the first generation were in flower I thought that I would raise one more generation, and acted in the following manner. Several flowers on one or more of the self-fertilised plants were again self-fertilised; and several flowers on one or more of the crossed plants were fertilised with pollen from another crossed plant of the same lot. Having thus once begun, the same method was followed for as many as ten successive generations with some of the species. The seeds and seedlings were always treated in exactly the same manner as already described. The self-fertilised plants, whether originally descended from one or two mother-plants, were thus in each generation as closely interbred as was possible; and I could not have improved on my plan. But instead of crossing one of the crossed plants with another crossed plant, I ought to have crossed the self-fertilised plants of each generation with pollen taken from a non-related plant--that is, one belonging to a distinct family or stock of the same species and variety. This was done in several cases as an additional experiment, and gave very striking results. But the plan usually followed was to put into competition and compare intercrossed plants, which were almost always the offspring of more or less closely related plants, with the self-fertilised plants of each succeeding generation;--all having been grown under closely similar conditions. I have, however, learnt more by this method of proceeding, which was begun by an oversight and then necessarily followed, than if I had always crossed the self-fertilised plants of each succeeding generation with pollen from a fresh stock.