V GROWTH IN TIME OF THE TOTAL ORGANISM ibl 



etc. ; on the other hand, energy which, in aerobic animals, is provided by oxidative 

 processes. Both can be contemplated as limiting factors. Experimental results 

 indicate that the first factor is effective in unicellulars and primitive metazoa 

 while in higher animals, in connection with the development of inner surfaces 

 and a circulatory system providing the body with nutrients, there are correlations 

 between respiration, anabolism, and growth. 



These considerations lead to the establishment of several ''metabolic'' and 

 ''growth types'' as summarized in Table 6. In this respect, the relations between 

 metabolic rate and body size have first to be discussed. 



(<?) Dependence of metabolic rate on body size 



The relation between metabolic rate and body size belongs to the classical 

 topics of physiology. It goes back over more than a hundred years to the time 

 when Sarrus and Rameaux (1837-39), Bergmann and Leuckart (1855), and 

 Richet (1883) noticed that the intensity of metabolism systematically decreases 

 with increasing body size. 



According to Rubner's classical surface rule (1902), weight-specific metabolic 

 rate, that is, the intensity of metabolism as measured by oxygen consumption or 

 calorie production per kilogram, decreases with increasing body weight. If, how- 

 ever, metabolism is calculated per unit of body surface, approximately constant 

 values appear. Rubner explained the surface rule in terms of homeothermy. Since 

 all warm-blooded animals heat their bodies to a temperature of ca. 37°C and heat 

 output takes place through the body surface, the same number of calories {ca. 1000 

 kcal/m2/day) must be produced per unit surface in order to maintain the body 

 temperature constant. 



It is difficult to measure exactly the outer surfaces of animals, and it is questionable 

 whether these are responsible for the reduction of metabolic rate with increasing 

 body size. If, however, two bodies are geometrically similar, any surface can be 

 expressed as the 2/3 power of weight multiplied by a constant because the cubic 

 root of the volume or weight is a linear dimension, and therefore its square has 

 the dimension of a surface. Hence, the surface areas of geometrically similar 

 bodies can be obtained by multiplying the 2/3 power of the weight by a suitable 

 constant. This is expressed in the formula of Meeh : 



s = bup-'^ (5-2 1 ) 



The surface rule of metabolism accordingly states that basal metabolic rate is 

 proportional to the 2/3 power of weight. In the case of man where determination 

 of basal metabolism is clinical routine, the somewhat more complicated Dubois 

 formula is applied. Dimensionally, however, the Dubois formula is identical 

 with the surface rule. The Dubois formula is: j- = kup-'^-^ ■ f'"^'^. As, pre- 

 supposing geometrical similarity, length / = cw^^'^, this can be written : s = kup-^^^ x 



^^0.725.0.33 =^^2/3_ 



The relation between metabolic rate and body size can be studied either 

 inter specifically, i.e. comparing adult animals of different species and body size; 

 or intraspecifically, i.e. comparing animals of the same species and different size, 



Literature p. 253 



