446 



RESEARCH IN PROTOZOOLOGY 



error. Probable error may be briefly defined as that value on the 

 ;r-axis which when scaled off on either side of the mean will 

 include fifty per cent of the normal curve. Probable error is 

 therefore directly related to standard deviation and either unit of 

 variation may be used in any problem. The relationship between 

 them is given by the expression 



P. E. = .674490 



In the problem under consideration we would state that the 

 standard deviation of the individual measurements is 1.05 microns 



TABLE 2 



TABLE OF AREAS OF THE NORMAL CURVE 



and that the probable error of the individual measurements is 0.71 

 micron. Adding this probable error to and subtracting it from 

 the mean would give the statement that between the limits 12.30 

 microns and 13.82 microns, we would expect to find half of the 

 individual measurements. 



As a use of the table of areas of the normal curve, the following 

 computation of the theoretical frequency of lengths of trophozoites 

 is given : 



