lOO GROWTH PRINCIPLES AND THEORY 2 



since the surface rule also applies, and in fact is more accurately established, in 

 cold-blooded vertebrates and even in certain invertebrates where there is no 

 thermoregulation (Table 7). 



4. Another interpretation assumes that the surface rule is based upon the 

 anatomy and physiology of the circulatory system. The supply of oxygen and nutritive 

 materials to the tissues is a function of the intensity of the blood current. The 

 latter depends on factors such as the size and stroke volume of the heart, the 

 frequency of heart beat, the diameter of the blood vessels, the degree of capillari- 

 zation, etc. There are rather strict quantitative relations between body size, 

 metabolic rate, pulse rate, and other characteristics of the circulatory system. 

 For example, in interspecific comparison "from the mouse to the elephant", 

 pulse rate decreases approximately proportional to the 3/4 power of the weight 

 (Fig. 35, p. 233). So does basal metabolic rate in the interspecific comparison of 

 mammals, if adult specimens of corresponding species are plotted (Brody, 1945; 

 Kleiber, 1947). However, hemodynamics cannot offer a general explanation. 

 Examples to the contrary are clams, where the circulatory system is completely 

 different from that found in vertebrates, or ascaris, which has no blood circulation 

 at all — animals whose metabolic rate nevertheless follows the surface rule. 



5. Still another explanation of the reduction of metabolic rate is based upon 

 anatomical or chemical changes in composition with increasing body size. "Meta- 

 bolically active" organs such as the viscera, the brain, etc. are relatively larger 

 in small as compared to large animals. So it has been assumed that they consume 

 relatively more oxygen and are responsible for the higher weight-specific metabolic 

 rate in smaller organisms. However, the relative growth of inner organs is different 

 from one organ to the other, allometry constants being irregular and often higher 

 than 2/3 or 3/4 as would correspond to the reduction of metabolic rate (Table 16, 

 p. 242; Figs. 32, 33, p. 230, 231). So it is improbable that this can yield the simple 

 relation of the surface rule of metabolism [cf. Bertalanffy, 1951a). A quantitative 

 estimate (Bertalanffy and Pirozynski, 1953) shows that this factor is not sufficient 

 to account for the actual variations of metabolic rate. 



6. Recent investigations of the Ludwig laboratory (Ludwig, 1956; Kienle and 

 Ludwig, 1956; Sattel, 1956) give support to the hypothesis proposed by Ludwig 

 and by Bertalanffy (1951a, p. 252f.) that the "metabolic types" are connected 

 with types of respiratory apparatus. Gill-breathing and lung-breathing animals 

 appear to follow the surface rule; hence its validity in fish, certain invertebrate 

 classes, and mammals. On the other hand, the surface of tracheas in insect larvae 

 develops proportional to body weight, as was shown by Sattel (1956) in Bombyx 

 ?nori; hence the proportionality of metabolic rate to weight. With this corresponds 

 the fact that not only respiration (Table 8) but also transpiration in insects 

 {Gryllus domesticus : Jakovlev and Kriiger, 1954) is weight-proportional. Inter- 

 mediate cases would result from the presence of two types of respiratory apparatus, 

 as in the case of fresh-water pulmonates, belonging to the intermediate type and 

 possessing two types of respiratory mechanisms ( "lungs" and cutaneous respiration) . 



The explanation of the reduction of metabolic rate with increasing body size 

 is unsatisfactory at present. That the factors usually contemplated give no 

 sufficient explanation is shown by an example like Ascaris (Kriiger, 1940) which, 



