Mathematical Contributions to the Theory of Evolution. 3 



material grew, it seemed desirable to separate the vegetable and 

 animal kingdoms, and the present paper deals only with the former. 

 In this field I have had the aid of a number of competent helpers. To 

 collaborators who have long aided me, like Dr. Alice Lee, Miss C. D. 

 Fawcett, and Mr. Leslie Bramley-Moore, I have been able to add, for 

 the present purpose, Miss Agnes Fry, Dr. E. Warren, Dr. W. R. 

 Macdonell, Miss M. Barwell and others, who have taken part in the 

 labour either of collection, of measurement, or of computation. The 

 result of this united labour is that twenty-two series, with upward of 

 twenty-nine correlation tables, are here dealt with.* Small in number 

 as this may seem, when we think of the vast variety of the vegetable 

 kingdom, it means an immense amount of work— special series, which are 

 in the memoir represented by a page of table and a few lines of 

 numerical constants, have often cost one or other of us weeks of steady 

 work. Hence I cannot strongly enough express my gratitude to my 

 co-workers ; they have more than ever convinced me of the great im- 

 portance of co-operation for the future of scientific research, and the 

 desirability, if possible, of organising the labour of isolated scientific- 

 workers. I will now indicate the general results we have reached. 



(2.) The following series were dealt with : (1) to (3). The leaflets of 

 the compound leaf of the Ash were counted in upwards of 300 trees 

 from Buckinghamshire, Dorsetshire, and Monmouthshire. The results 

 were in good agreement, and show homotyposis as a racial character of 

 considerable constancy. (4) to (5) The veins in the leaf of the Spanish 

 Chestnut were counted in 100 trees from Buckinghamshire and 100 

 trees of mixed character. Homotyposis was found to increase with 

 heterogeneity of age and locality. (6) The veins were counted in the 

 leaves of 100 Beech trees from Buckinghamshire. (7) and (8) The 

 prickles were counted on the leaves of 100 Holly trees from Somerset- 

 shire and 100 from Dorsetshire. This completes the series of homo- 

 types for trees. The tree results are in fair accordance, when we allow 

 for the disturbing factors of environment, age, and personal selection. 

 (9) to (13) We next investigated five series of Poppies, counting the 

 stigmatic bands on the seed-capsules ; Papaver Bhoeas for three series,, 

 from top of Chilterns, bottom of Chilterns, and the Quantocks ; Shirley 

 Poppies for two series from Great Hampden and Chelsea. The results 

 were again in fairly reasonable accordance with each other and with 

 those for trees. (14) and (15) The segmentation of the seed vessels 

 was counted vnNigella Hispanica and Mai 'va Botundifolia ; the homotyp- 

 osis was found to be much weakened, but actual differentiation was 

 observed between the seed vessels on the main stem and on the side 

 shoots of the former, and the 127 plants of the latter had principally 

 arisen by stolons from a single clump, and were not thus entirely in- 

 dependent individuals. (16) The members of the whorls were counted 



* In the Appendix an additional fifteen scries will be found. 



B 2 



