1902.] I. H. BnrkiW— Flower of Ranunculus arvensig. 103 



If we take three absolutely symmetrical dice and toss them the 

 probable scores obtained in 240 throws mathematically calculated are 

 as follows:— 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 

 1 3 6 10 15 21 28 36 36 28 21 15 10 6 3 1 * 



If we take another three dice of distinguishing colour absolutely 

 symmetrical, and throwing them with the others record the association 

 of numbers, the resulting table will be as symmetric as the binomial 

 curve just given, but in two dimensions, and out of 14,400 throws there is 

 one chance of 3 + 3 being the score of the two sets of dice and one of 18 -f 18, 

 one of 3 + 18 and one of 18 -|- 3; there are three chances of the score 

 being 4 + 3, and three of its being 17 ^- 3, i.e , equal chances as far as 

 the extremes are concerned of there being a close similarity between 

 the figures and a wide dissimilarity. A glance at the tables just given 

 will satisfy that this is not the case in them and that the tendency to 

 similarity is evident; that in the mutual relationship of mood to mood 

 the adjustment is not a question of chance but, as is indicated by 

 the averages in the last column and lowest line of each table, is due 

 to some loosely coercing force which will be discussed. 



As I have foregone the publishing of tables to give for the Kew 

 New plants and the Bonn and Heidelberg races my exact observations 

 on adjustment of moods, I place below the averages found omitting 

 those derived from fewer flowers than ten. 



I will briefly call attention to the chief points in the averages. 

 Table XI shows that fewer sepals mean fewer of all other organs and 

 it is to be noted that the reduction is greatest in the organs furthest 

 away from the sepals. Table XII shows for the Kew race a consider- 

 able reduction of both stamens and carpels when the petals are reduced ; 

 it shows for the German races a much slighter reduction of carpels 

 and an insignificant reduction of stamens. It shows further that re- 

 duction in the number of petals does not act as a reflex on the number 

 of sepals in anything like the way in which reduction of sepals may be 

 said to promote reduction of petals. Table XIII shows that with a 

 reduction or increase of stamens the reduction or increase of the carpels 

 is much greater than the reduction or increase of the organs which pre- 

 ceeded them. Table XIV shows that reduction or increase of carpels is 

 accompanied by a more nearly corresponding reduction or increase in 

 the organs closest to them. Consequently, admitting that there is an 

 exception in the relation of petals to stamens in the German races, we 

 may broadly state that the influence producing correlative increase or 

 decrease chiefly acts forwards from the preceding mood to the moods 

 which follow and that correlative increase and decrease is closest 

 in neighbouring moods. 

 J. II. 14 



