1919] Boeck: Studies on Giardia Microti 103 



mode of those curves having three or more modes lies on the ordinate 

 line in the region of points 19 and 20 on the abscissa, while the fourth 

 mode of the curves which have four modes is seen to lie on the ordinate 

 line at points 25 or 26 on the abscissa. 



In all cases these ordinate lines determined above were selected 

 because the majority of the modes of all the curves fell on these four 

 lines. Thus ten curves had at least two modes, and of these ten six 

 fell on the ordinate line in the region of points 11, 12, or 13 on the 

 abscissa. Five curves showed a distinct mode in the region of points 

 19 and 20 on the abscissa, and eight curves showed definite modes on 

 the ordinate line in the region of points 25 and 26 on the abscissa. 

 From this evidence it is justifiable to conclude that there is a common 

 interval between the modes of all the curves when they are placed 

 one above the other so that their first modes lie upon a common 

 ordinate line. This interval is approximately equal between all the 

 ordinate lines. The intervals between the ordinate lines are 6, 7, and 

 7 days; their average interval is 6% days. 



The average interval of 6% days as obtained from the super- 

 imposition of the curves, is almost identical with the average interval 

 of 7 days obtained by plotting the frequency of all the modes (see 

 ^g. 15). Thus by two different methods approximately the same 

 interval has been obtained, setting the interval between the maximum 

 numbers of cysts ejected in the faeces at about every seven days. 

 In other words, the cycle of encystment of Giardia occurred about 

 every seven days in the rats under observation during a period of 

 nearly one month. 



In the superimposition of the curves and in the consequent study 

 of the data to determine the common ordinate lines no consideration 

 was taken of the terminal point of all the curves, because the curve was 

 in the process of forming another mode in most cases when our obser- 

 vations were suspended. Therefore, because of its incompleteness this 

 portion of the curve was useless in the determination of the cycle of 

 encystment. 



In order to substantiate the evidence for these common ordinate 

 lines which mark the days when the maximum number of cysts 

 occurred in the faeces of most of the rats examined I plotted the 

 occurrence of the average number of cysts for each day when the 

 curves were thus superimposed. This is the average nujuber of cysts 

 that occurred on each ordinate line in figure 17. For example, on 

 ordinate line 4 in figure 16 two cysts were found twice, three cysts 



