396 JENNINGS— HEREDITY IN PROTOZOA. [April 24, 



with the sphere of indefinitely numerous small causes — amenable 

 only to the calculus of chance, and not to any analysis of the indi- 

 vidual instance." Such treatment is a most valuable instrument for 

 precisely such analysis as will bring out the effects of individual 

 factors when we are unable to experimentally disengage them com- 

 pletely from others ; it aids us most essentially in the " analysis of 

 the individual instance." Of this I hope the present paper may fur- 

 nish iUustrations. As Johannsen (1906, p. 98) has well expressed 

 it, the mathematical treatment must, to give valuable results, be 

 " based upon an accomplished sorting of the special facts and a 

 biological setting out of the premises which are to be treated." 

 Davenport (1899) states that "the statistical laws of heredity deal 

 not with the relations between one descendant and its parent or 

 parents, but only with the mean progeny of mean parents." The 

 object of the present work is precisely to discover so far as possible 

 the relation between one descendant and its parent (or other rela- 

 tives) ; for this, statistical methods show themselves most useful. 



2. A Typical Culture, 



We will then first examine a typical culture of Param^«Mm, made 

 in the usual way with pond water and decaying vegetation, in a 

 circular glass vessel about nine inches across and three inches deep. 

 This culture we will call Culture i. 



Inspection showed that Paramccia of markedly different size 

 were found in this culture, so that it seemed a favorable one for a 

 study of inheritance in size. Cursory examination seemed to indi- 

 cate the existence of two sets of individuals, those of one set being 

 nearly double the length of the others. 



Of this culture a large number were killed on April 10, 1907, and 

 four hundred specimens, taken at random, were measured as to 

 length and breadth. 



3. Methods of Measuring and Recording. 



The animals were killed with Worcester's fluid, which is known to cause 

 practically no distortion when properly used. Worcester's fluid consists of 

 ten per cent, formalin saturated with corrosive sublimate. In using it, a 

 large number of the infusoria must be brought into one or two drops of 



