HEAT 



107 



homoiotherms, and they affect such impor- 

 tant ecological phenomena as the time span 

 of the life history or the length of any given 

 stage. 



A number of mathematical formulae have 

 been used in attempts to express accurately 

 the relation between temperature and the 

 velocity of biological processes. These are 

 of two main types; the first type is based 

 on the chemical "law of mass action," 

 which, in its simplest form, states that the 

 rate at which any chemical reaction pro- 

 ceeds is directly proportional to the concen- 

 tration of substances actually taking part in 

 the reaction. According to this law, tem- 

 perature influences can be expressed by an 

 exponential curve. This means that the ve- 



whatever the location on the effective tem- 

 perature scale.* 



Reaumur suggested in 1735 (see p. 18) 

 that the sum of average daily temperatures 

 during the growing season bears relation to 

 the time at which fruits ripen. This idea 

 can be expressed by the equation 



in which y represents time, t, temperature, 

 and k is a. constant. The velocity (u) of the 

 process in question can be calculated, since 



v = -; therefore, v = tk. As stated pre- 



y ^ 



viously, the ecological zero (see p. 110) of 

 a given process usually fails to coincide with 



° ° o ^ , 



-o 



o 



o 



o 



o 



35 4 36 



(l/-^,0 



ABC 



Fig. 15. Velocity of ameboid movement in relation to temperature. A, Log of velocity plot- 

 ted against inverse of absolute temperature. B, Three straight lines fitted to the same points. 

 C, Log of velocity plotted against log of temperature. (Redrawn from Belehradek, after 

 Pantin. ) 



locity constant is an exponential function of 

 effective temperature, which, in turn, means 

 that the effect of an increase of 1 degree 

 in temperature differs, depending upon the 

 location of the increase on the temperature 

 scale. Van't Hoff's rule (1884) and the 

 formula of Arrhenius (1915) are exponen- 

 tial expressions of this type, while the more 

 empirical catenary formula of Janisch 

 (1932) and the equally empirical one of 

 Belehradek (1935) are also exponential. In 

 the second type, the relationship is based 

 on the observation that in many biological 

 processes, the product of temperature and 

 time to a given end point is a constant. 

 Sanderson and Peairs (1914) state this 

 generalization, and the formula of Krogh 

 (1914) gives the usual form of expression. 

 According to this idea, the effect of an in- 

 crease in temperature of 1 degree is similar. 



the freezing point of water. It is a variable 

 quantity and depends on the process and 

 the organism. The last equation must, 

 therefore, be modified by the parameter c, 

 which, practically speaking, shows the loca- 

 tion of the intercept of the straight-line por- 

 tion of the velocity curve on the tempera- 

 ture axis (Belehradek, 1935; Powsner, 



" Roughly approximated, the overworked 

 Van't Hoff rule, often known as the Qio rule, 

 states that the rate of reaction is often doubled, 

 or more, for each 10° C. increase in tem- 

 perature in the median range. The use of these 

 temperature coefficients is not a subject for the 

 unwary. Accounts by Shelford ( 1929 ) and 

 Chapman ( 1931 ) contain helpful discussions 

 of general temperature relations. Readers with 

 stronger physiological inclinations can consult 

 such references as Kanitz (1915), Belehradek 

 (1935), Barnes (1937), and Heilbrunn (1943). 



