ipoS.J JENNINGS— HEREDITY IN PROTOZOA. 397 



water, then these must be overwhelmed with a considerable quantity of the 

 fluid. If the infusoria are in a larger quantity of water, the killing takes 

 place more slowly, the animals have time to contract, and distortion results. 



The measurements were made on the slide, the organisms being either 

 still in the killing fluid or in ten per cent, formalin. Transference to the 

 latter has no efl'ect on the form of 4:he fixed animals. Most of the meas- 

 urements were made directly with an ocular micrometer. In the case of 

 cultures of large individuals, however, the form was projected on paper w-ith 

 the camera, in the way described by Pearl (1907), the extremities of length 

 and breadth marked with the pencil, then these were measured with a scale 

 made by projection of the ocular micrometer. 



Such combinations of lenses were used that one division of the microm- 

 eter scale was equal to 4 microns (or in a few cases, which will be expressly 

 noted, to 3J microns). The measurements were thus recorded in units, each 

 of which was equal to 4 microns, so that the recorded units are multiplied 

 by four to give results in microns. When the measurements fell between two 

 lines of the micrometer, the line nearest the actual measure was that re- 

 corded; if the measurement fell just half way between two lines, the higher 

 line was recorded. Thus, the recorded unit 45 included all measurements 

 beginning with 442, and less than 452. In the tables, the measurements, 

 given in microns, are therefore grouped about such values that each group 

 includes values from two microns below to two microns above the one 

 recorded. Thus, in Table i, the length 180 includes all the specimens meas- 

 uring from 178 up to (but not including) 182. 



It will be well to summarize here, once for all, the method of treating 

 the data obtained in the measurements. For most of the tables the con- 

 stants computed (and recorded below the tables) were the following: the 

 mean, standard deviation, and coefficient of variation, for length and for 

 breadth ; the mean index or ratio of breadth to length ; and the coefficient 

 of correlation. The computation of the constants was based on the well- 

 known formulae that have been brought together by Davenport (1904) and 

 others. I used as a rule the actual methods set forth so clearly by Yule 

 (1897). The computations w^ere made by the aid of seven-place logarithms 

 and of Crelle's and Barlow's tables. Two independent computations, at 

 considerable intervals of time, were made in each case. While I cannot 

 hope that errors in computation are excluded, I believe that such as may 

 exist do not in any way affect the conclusions to be drawn. 



Certain points of detail should be mentioned. While, as will appear, 

 most of the tables do not give symmetrical curves, I have used only the 

 simple statistical methods applicable in strictness to such curves ; the methods 

 are quite sufficient as a basis for the comparisons we wish to make. 



In computing the standard deviation, Sheppard's correction of the 

 second moment was used throughout. That is, if we employ the method 

 of Yule (1897), 



a=-i/5:(/^2)_,/2_. 08333, 

 or using the signs employed by Davenport (1904) 





