PART THREE. 



METHODS OF EXPERIMENTATION AND CALCULATION. 



1. Theory of Thresholds .\nd Rates of Development. 



Calendars of periodic events have been used in connection with agri- 

 cultural practice for thousands of years. Becquerel (18.53) published a 

 Chinese calendar of TOO B. C. which does not differ in its essential features 

 from various published spray calendars. For several centuries attempts 

 have been made to predict development by summing temperatures. 

 According to Becquerel, Reaumur (17:55) was one of the early investiga- 

 tors who contended that the mean daily temperature multiplied by the 

 number of days should be used. De Candolle made important contribu- 

 tions and is most often quoted, but one of the outstanding investigations 

 in the last century is that of Von Oettingen (18T9) on the Dorpat woody 

 plants, who used the term, "threshold" (perhaps first) for the tempera- 

 ture at which development begins and made his sums from that. De Can- 

 dolle also recognized the threshold but made his sums above zero 

 Centigrade. 



Thresholds. This summing of temperatures has been done on the 

 assumption that the time-temperature relation is accurately represented by 

 an equilateral hyperbola and that the hyperbolic zero marks the actual 

 threshold development.* This assumption is false. The velocity of 

 development does not always bear a fixed ratio to the temperature. Only 

 a portion of the velocity curve, that for medial temperatures, is a straight 

 line. Valuable as this straight-line portion is — it is the only proper basis 

 for beginning any accurate calculation of the effects of temperature and 

 other factors influencing the rate of development of organisms — it alone 

 does not tell the whole story. The complete velocity curve shows a "lag 

 phase" at lower temperatures and falls off at higher temperatures. The 

 hyperbolic zero {alpha value) does not mark the actual threshold of 

 development ; in fact, the threshold is not a fixed point hut varies for 

 different individuals of the same species and for dift'erent sp>ecies. It is, 

 therefore, no simple matter to derive a velocity value for any given tem- 

 perature. The problem involves the establishment of an absolute unit of 

 development in which to express the effects of all weather phenomena, and 

 the determination of a normal total of developmental units required for 

 the completion of each stage in the life-history of the organism. Ideally, 

 the developmental unit, defined with reference to the straight-line limits 

 of the velocity curve under conditions normal to the habitat of the species 



• The product of the ordlnates and abscissas establishing any point on an equi- 

 lateral hyperbola is a constant ; and the reciprocals of the ordinates, when multiplied 

 by the constant and plotted on their abscissas, eive a straight line which crosses the 

 temperature axis at a point called the hyperbolic zero (represented by the Greek let- 

 ter aliyha) and which exactly bisects the angle between the two axes. 



357 



