248 re;ports on investigations and projects. 



The complete paper on this work will appear soon in Biometrika. 



(2) A study of variation in relation to differentiation and growth in 

 Ceratopln^llum. It is impossible in an abstract to give an adequate summary 

 of the results of this study. Some of the more important of the general 

 results are the following : 



(a) A thorough analysis of the facts of variation in the plant as a whole 

 and in its constituent axial elements was made. From this analysis it was 

 possible to work out the biological factors concerned in the genesis of charac- 

 teristic frequency curves of variation more completely than has hitherto 

 been done for any organism. 



(Jf) The analysis led to the establishment of two laws of growth, which 

 serve to describe very exactly and completely the observed phenomena of 

 variation and differentiation in leaf whorls, branch production, etc., in the 

 plant. 



{c) The first of these laws has been designated the " logarithmic law of 



growth." For Ceratophyllum it states that the size of parts on any axial 



division of the plant increases as we pass toward the distal end of that 



division, but the rate of this increase steadily diminishes the farther distad 



we go. As a general law of growth, this may be stated as follows : The 



increase by growth of a part or character is quantitatively expressed by an 



equation of the form 



y^=A-{-C\o% (a'— «) 



or some closely related logarithmic equation. In this equation y denotes size 

 of the growing part or character, x stands for the time factor, and A, C, 

 and a are constants. 



(d) The second of these laws is that in accord with which the variability 

 of an organism or its parts steadily diminishes with growth. 



The complete paper on this work will appear shortly as Publication No. 58 

 of the Carnegie Institution of Washington. 



(3) A study of the relation of variation and correlation to morphological 

 differentiation and homology in the appendages of the crayfish. This work 

 led to the general result that physiological and ontogenetic factors are rela- 

 tively much more important in influencing the degree of variation or correla- 

 tion of parts than are morphological and phylogenetic factors. I^ack of space 

 forbids a general summary of the results of the paper, which is now in press, 

 and, it is hoped, will appear shortly. 



(4) Experimental studies on variation and correlation in Protozoa. The 

 work on Paramecia of known ancestry reared under controlled environmental 

 conditions has been practically completed, but the results are withheld from 

 detailed publication until further experiments along similar lines have been 

 made. A prehminary paper dealing with a portion of the results has 

 appeared during the year. In this paper it is shown that while under normal 

 circumstances rigid selection of ancestry markedly reduces the variability of 



