20 PLANT PHYSIOLOGY 



paper ruled in faint-colored cross lines; the abscissae, or hori- 

 zontal lines, are used for the degrees of the external factor which 

 alters steadily (as, e.g., temperature), and the ordinates, or 

 vertical lines, express .the degree of the effect upon the plant. 

 The joining of the tops of the ordinates, by carefully ruled lines, 

 gives the polygon showing the relation existing between factor 

 and effect, especially the rate of rise or fall of the effect under 

 influence of the factor. In general the polygon is preferable, 

 because more true to observation, than the curve, which is made 

 by drawing a sweeping line through the tops of the ordinates; 

 but the curve has its use for generalized or demonstration pur- 

 poses. In the construction of the graphs there is no necessary 

 relation between the values of the abscissae and of the ordi- 

 nates, but these may be so established as to give the most expres- 

 sive result. As a rule the most striking form of graph is one 

 in which the height does not exceed the spread of the base. 

 The principles of their construction are well illustrated by the 

 accompanying example (Fig. i), made in the course of regular 

 work by my own students. The average curve provides, on the 

 principle earlier described, a standard of comparison and meas- 

 ure of probable error in the results of the individual. In illus- 

 trating a scientific paper by graphs, it is a good rule to give also 

 the figures upon which it is based, all very compactly and neatly 

 tabulated; for the reader may thus test for himself the accuracy 

 of the graph, or he may wish to make other use of the figures. 



The form of graph just described, which may be termed 

 the rate-graph, is the one most used in Plant Physiology. There 

 is, however, another form, called the frequency-graph, which is 

 very useful wherever variability of any units is concerned. It 

 is constructed by marking off the degrees, or classes, of the 

 variable quantity along the abscissa, or horizontal line, and then 

 reckoning one ordinate, or vertical, space for each individual 

 falling under the respective degrees, or classes, after which the 

 joining of the tops of these ordinates will give a curve, or polygon, 

 of frequency. Such a curve is a refined substitute for a mean, 

 for while the latter lumps together all the data regardless of 



