452 JENNINGS— HEREDITY IN PROTOZOA. [April 24, 



fission; this decrease continues till the length is just twice the original 

 length. Now the constriction appears, so that the animal may be 

 looked on as two; the length, therefore, drops in a straight line to 

 the original length found at the beginning of the curve. The 

 breadth decreases from the beginning till about an hour after fission ; 

 then slowly increases ; it shows in the course of the twenty- four 

 hours many fluctuations which are doubtless mainly due to differences 

 in the environment — especially to differences in the amount of food 

 taken. In preparation for fission the breadth increases at the same 

 time that the length decreases. 



The curve of length is much the more interesting of the two, since 

 it is the one which represents mainly the actual growth. It is of 

 great interest to find that this curve of growth in a single cell is of 

 essentially the same form and character as those which have been 

 obtained for the growth of many higher organisms, composed of 

 many cells. A number of such curves are brought together in the 

 recent interesting paper of Robertson (1908). Inspection shows at 

 once that the curve of growth in Parniecium closely resembles that 

 for growth of the rat, as worked out by Donaldson (1906); for 

 growth of m.an, and for growth in various other organisms. 



The curve of growth, as is well known, is a logarithmic curve 

 in the cases where it has been worked out mathematically. While 

 the growth in Paramecium has merely been plotted empirically, it is 

 evident that it is essentially a similar logarithmic curve; this could 

 doubtless be worked out from the data given. 



The fact that the curve of growth is essentially the same in the 

 unicellular organism as in the animal composed of millions of cells 

 is in some respects surprising. In the brain of the rat, or in its body, 

 the curve of growth is the resultant of the growth of many different 

 groups of cells, some groups growing at one period, some at another ; 

 yet the resultant curves are of the same character as when there is 

 growth in but a single cell. 



The temporal relations shown in the curves are likewise of much 

 interest. As our diagram shows, that portion of the curve showing 

 the greatest curvature, requires in Paramecium about four hours 

 from the beginning. In the rat the corresponding part of the curve 

 takes several months, while in man it requires several years. It 



