The metabolic rate of an organism per unit weight. The metabolic rate of an organism divided by the organism's weight. (If it were physics it would be called specific metabolism, but biologists perhaps fear confusion with species.)
In biology great stress is traditionally laid upon a warm blooded (homoiothermic) animal having to get rid of much of its body heat through its surface. Since the amount of heat it produces increases with the cube of its linear dimension (volume) and its surface increases with the square of its linear dimension the larger it gets the more difficulty it has cooling itself. (See Bergman's Rule.) If this factor determines its metabolic rate - i.e. if homoiotherms keep their heat output per square centimeter constant - then simple mathematics reveals the intrinsic metabolism should be inversely proportional to their linear dimension. Inversely proportional to the cube root of the body weight. In fact it is inversely proportional to the fourth root of the body weight.
(This even prompted a paper, in the Journal of Theoretical Biology, claiming that animals are 4-dimensional.)
Hence plotting a graph of the logarithm of the intrinsic metabolisms of birds against the logarithm of their weights yields a good straight line without too much scatter. Another type of form, say snakes, would give another straight line of different intercept upon the weight axis.
The relationship between metabolism and body size applies, as far as Sporus knows, to all animals including microorganisms, independently of whether they are homoiothermic.
It follows that the intrinsic metabolism of smaller things is greater than that of a larger. For example the metabolic output of a mouse is greater than that of a mouse sized chunk of elephant. A small thing's fires burn more fiercely than those of a large