450 JENNINGS— -HEREDITY IN PROTOZOA. [April 24, 



the curve of length shows the actual proportion of growth to the 

 original length. The distance from the base to the curves is 357 

 times the actual dimension at the given time. 



In order to sliow changes due to growth alone all the data for such a 

 curve should be measurements from a single uniform culture on a single day; 

 otherwise environmental differences complicate the matter, as we shall see 

 more clearly in the next division of this paper. Now, it is impracticable to 

 obtain from a single culture on a single day measurements of all the required 

 stages. We are compelled therefore to make certain corrections in some of 

 the measurements, to compensate so far as we can for environmental differ- 

 ences. As Table X. shows, the mean dimensions of random samples differ 

 much in (for examples) lots i (row 3) and 6 (row 12). It will not do, 

 therefore, to compare directly the young of these two lots. Since we have 

 from lot 6 the greatest number of different stages, it is best to make the 

 measurements from this the basis for the curve, correcting others, so far as 

 possible, to compare with this. In lot 2 the mean length (Table X., row 6) 

 is almost exactly the same as for lot 6, so that we may use the measurements 

 of lot 2 without correction, so far as length is concerned. On this account 

 we shall employ lot 2 for the earliest stages, in place of lot i, though the 

 latter is based on a larger number of specimens. 



Since the mean breadth of the sample of lot 6 is 64.880 microns, while 

 that of lot 2 is but 46.020 microns, it is necessary to correct the breadth for 

 lot 2. At first thought it would seem that the proper method of making 

 this correction would be by multiplying the breadths of the different sets of 

 lot 2 by the ratio 64.880/46.020. This would be the proper method of pro- 

 cedure if we were dealing with the same stages of growth in the two lots ; 

 the specimens of lot 2 would be made plump, like those of lot 6. But the 

 stage with which we are dealing is that of the beginning of fission. Now, 

 we have already seen that when the specimens not dividing are plump, the 

 breadth does not increase at the approach of fission nearly so much as 

 when the specimens not dividing are thin. Indeed, if the specimens are very 

 plump, there is an actual decrease, instead of an increase, at the approach 

 of fission. Our problem is : What would be the breadth of specimens be- 

 ginning fission, in which the length is 82.600, and the animals are very plump, 

 as in lot 6? This problem can best be solved by asking what is the ratio 

 of breadth to length in specimens beginning fission, in a very plump culture? 

 In lot 3 (row 7, Table VIII.) we have such a plump culture, and we find that 

 the ratio of breadth to length is, in the earliest stage of fission, 78.563 per 

 cent. We therefore take this as the ratio of breadth to length for the 

 earliest stage of lot 2, from which the corrected breadth is found to be 64.893. 

 If this decreases at the same relative rate as actually occurred in lot 2, then 

 the breadth 15 minutes after the beginning of constriction would be 64.493 

 microns. 



We are compelled to use, further, lots 9 and 10 (Table X.). In lot 9 

 both length and breadth require correction to make them comparable with 

 the measurements of lot 6. The correction is made by multiplying the 



