INTRODUCTION. 9 



put on this work. To her are due the determinations of the raw material 

 of Series V and VI, and an independent verification of the computations 

 for Series I, II, and III. The rest of the work and the arrangement of 

 the material for publication is due to the writer. 



To the Carnegie Institution I am greatly indebted for a grant in aid 

 of this and other biometric work now in progress. Without this aid it 

 would have been quite impossible to have brought the work to comple- 

 tion at this time. To Prof. Karl Pearson I am very grateful for valuable 

 suggestions and advice, especially on the mathematical side of the work. 



A word should be said regarding the arrangement of the paper. On 

 account of the number of topics dealt with and the consequent length 

 of the paper as a whole, it has seemed best to include a brief summary 

 and discussion of the results of a particular section in that section itself 

 rather than reserve all discussion for the end. This I believe will con- 

 duce to clearness. 



MATERIAL AND METHODS. 



The plant on which this work is based, Ceratophyllum demersum,^ is 

 a submerged aquatic which has a wide distribution. It is usually found 

 in quiet rather than running water, and under favorable conditions 

 forms great masses of vegetation. It commonly occurs in shallow water, 

 frequently extending to the very edge of the pool where it is growing. 

 The plant consists of a main axis, which may attain a length of 5 or 6 

 feet, from which spring a varying number of lateral branches. At more 

 or less regular intervals along the main axis and the branches are whorls 

 of leaves. These leaves are elongate and very narrow, being reduced 

 practically to the form of rods. This shape of leaf is undoubtedly to be 

 regarded as an adaptation to aquatic conditions. (Cf. Schenk, '86, and 

 Henslow, '95.) At their outer ends the leaves divide, leading to the 

 form of whorl shown in fig. 1. This division of the leaves at the 

 outer end is the usual condition for Ceratophyllum. The plant has no 

 root in the strict sense, but, as has been shown by the excellent physio- 

 logical study of Pond (:05), probably absorbs all its nutrition directly 

 from the water. It thus exhibits a practically perfect adaptation to 

 aquatic conditions of existence. The lower end of the main axis of the 

 plant is usually embedded for a distance of several inches in the layer of 

 soft mud and plant debris which forms the substratum of a Ceratophyl- 

 lum bed. This portion of the axis which is embedded is more or less etio- 

 lated and usually bears only the broken remnants of leaf -whorls. There 



ij follow Pieters (:01) in designating the species of Ceratophyllum found about 

 Ann Arbor demersum. I have not myself been able to get plants in flower. 



