curve on which the variations of any character in reference to a standard unit fall. This curve of probability is found by taking as the ordinates the coefficients of the binomial (a + b)n and arranging these ordinates at equal distances.
The second test is by hybridization according to the Mendelian formula. Starting with a contrasting pair of characters, one, say, a mutation, it is found that in the second generation and afterward these differentiating characters reappear in their purity and according to the mathematical law that each separates in each of these generations in one fourth of the progeny and thereafter remains true. A new character having appeared, it can in this way be shown to be a permanent acquisition.
Lectures XVI-XXIV. Although the author tested many species, only one, the evening primrose, Œnothera, gave positive, mutating, results. He finds that the various mutations obtained from this species take place with a great degree of regularity. Very simple rules of general validity, he assumes, govern the whole phenomenon:
I. 'New elementary species appear suddenly, without intermediate steps.' This is contradictory to the usual conception of very slow changes. 'No series of generations, no selection, no struggle for existence are needed for this.'
II. 'New forms spring laterally from the main stem.' There is neither a slow nor a sudden change of all the individuals; the vast majority remain unchanged. A species like Œnothera Lamarckiana will not die out from mutating. This is in contrast with the current conception that the slow conversion of one species into another affects all the individuals in the same direction and degree, and that the birth of the new species involves the death of the old one. Again, 'mutation' gives several new species from one parental form; according to the other view, only one was given.
III. No elementary species attain their full constancy at once. Constancy is a quality of its own, the result of neither selection nor improvement.
IV. ' The same new species are produced in a large number of individuals.' Obviously there must be some common cause which has lain dormant during many successive generations.
V. Mutations are not extreme fluctuations. In the latter there is a heaping up of slight deviations around a mean, and an occurrence of continuous lines of increasing deviations, linking the extremes with this group. Nothing of the kind is found in the case of mutations.
There is no mean for them to be grouped around ; the extreme
