CALCULATION OF DATA 195 



way, but so far nothing has appeared in biology with the beautiful sim- 

 plicity and profound generality of E = mc^. Nonetheless, on a lower 

 level, experimental results and theoretical interpretations of the data can 

 fit simple equations quite well. 



Analytic geometry presents a variety of equations for geometrical fig- 

 ures. For example, if a graph is plotted on rectangular coordinate paper, 

 the values of y on the vertical axis bear some natural relationship to the 

 values of x on the horizontal axis. If y = mx -[- h, the graph is a straight 

 line, m is the constant slope, and intercept h is the value of y when x is 

 zero. The slope can be positive or negative. 



The straight line or linear relationship is very common in the labora- 

 tory. A verbal expression indicating the same relationship is "y is directly 

 proportional to x." The data in Fig. 14-1 can be used as an example. At 

 zero time, the manometers contained some amount, h, of oxygen, al- 

 though we were not concerned about this amount. After some time, it 

 was apparent that the amount of oxygen produced in each five-minute 

 interval was about the same. The slope, then, is the average change per 

 five minutes, or 24.3 jA O2/5 min. The total amount of oxygen in the 

 vessel at the end of the measurement is 



' ^ " X 6 (5 min intervals) + l7Atl02 at start = 146 + 1? /t^l02 



5 min interval 



m X -^h =y 



In our previous calculations, we assumed that h was unimportant and 

 measured only the change since the beginning. This assumption does 

 not change the equation; it merely assigns a value of zero to h, so 

 y = mx + 0. 



Sometimes the actual expressions for which x, y, m, and h stand are 

 exceedingly complex. A part of the genius of the theoretically-minded 

 biologist lies in the ability to recognize simple equations in these com- 

 plex expressions or to convert some more complex relationship into a 

 straight line. 



The straight line is probably the most common relationship, partly 

 because many experiments are set up to test for such a relationship. Per- 

 haps the next most common equation is that for the hyperbola. The basic 

 equation for the hyperbola 



iL_Zl- 1 



