544 
Journal of Agricultural Research 
Vol. XXIV, No. 7 
The differences in the dimensions given by the various workers in 
the case of P. graminis could readily be explained on the basis that 
more than one biologic form of this species was involved. However, 
other factors, such as host plant, habitat, personal element, number of 
measurements made, etc., might have played a part in causing the 
variation. From Table I, it will be noticed that the size of the uredinio- 
spores of timothy rust as given by Sydow differed slightly from those 
recorded by Eriksson and Henning and by Saccardo. This difference 
perhaps might be explained as due either to experimental error, va¬ 
riation in the environmental conditions under which the spores were 
developed, or the number of measurements made. It must be borne 
in mind, however, that the differences in the dimensions of any of the 
spores indicated in the table may or may not be really significant. The 
significance of the difference could not be proved on account of the im¬ 
possibility of applying a biometric test to the limited data available. 
In order to determine the value of numerical differences it is necessary 
to calculate the probable error of these differences and then establish the 
relationship between the differences and their probable errors. Rietz 
and Smith (9) and Pearl and Miner (< 5 ) state that a difference may be 
considered as “certainly significant'^ only when it exceeds its probable 
error by more than three times, since a difference which is less than 
three times its probable error “may reasonably be attributed to random 
sampling” (9), and “that as the ratio, Dev.: P. E., passes 3 the odds 
against the deviation increase rapidly, reaching a magnitude at 8, which, 
practically speaking, is beyond any real power of conception” (d). 
The biometric constants obtained in this study were calculated accord¬ 
ing to the methods given by Davenport {2) and Babcock and Clausen (j). 
Table II represents a summary of the measurements of all of the biologic 
forms studied, in their different spore stages, when grown under normal 
conditions. This table gives the classes according to width and length 
in microns (each class differing from the next by a single micron), and 
the number of spores falling into each class both for length and width. 
In Tables III and IV, in addition to the variations in the spore meas¬ 
urements, the constants with their probable errors for the different spores 
of the various biologic forms are given. Table III represents spore lengths 
while in Table IV spore widths are given. The classes for width differ by 
one micron (ju) in all cases, whereas the classes for length vary with each 
spore type. In the measurements of aeciospores the classes differ by i /i, 
in those of urediniospores by 3 ju, and in those of teliospores by 5 fi. 
The probable errors of the differences in the statistical results obtained 
in this study are given in Tables V, VII, and VIH. The bearing they have 
on the dimensions of the different spore studies is brought out in the 
discussions of each of the spore types. 
In figures i to 6, curves are plotted for spore dimensions in microns. 
These graphs represent the variation in the spore sizes of the biologic 
forms when the rust was grown on highly susceptible hosts and under very 
favorable conditions. In each of these graphs the number of spores 
falling into each class was plotted according to the data contained in 
Tables III and IV. 
