364 PRINCIPLES OF ANIMAL NUTRITION. 
are geometrically similar figures, the surface is proportional to 
the two-thirds power of the volume. If we let S=surface and 
V=volume, then S=kV3, in which & is a constant for any given 
form. Putting W=weight, if the bodies have the same specific 
gravity we may substitute W for V in the above equation, and we 
then have 
Ss 
S=kWi, k=, 
On the assumption that the bodies of animals of the same species 
constitute similar figures and have the same specific gravity, the 
value of k has been determined for several species, as follows (the 
weight being expressed in kilograms and the surface in square 
centimeters) : 
Man.......... 12.9  Meeh (Zeit. f. Biol., 15, 425). 
Wog.......... 11.2 Rubner (Jbid., 19, 548). 
Rabbit ....... 12.9 Rubner (Ibid., 19, 553). 
Hlorse........ 9.02 Hecker (Zeit. f. Veterinark., 1894). 
5 (2 10.45 Rubner (Zeit. f. Biol., 19, 553). 
paneer De .... 8.89 Rubner (Biol. Gesetze, p. 17). 
nee cov $03 brubner Zeit. £. Biol., 19, 558). 
The heat production per unit of surface in most of the foregoing 
experiments is computed by the use of these factors. The results 
of such computations, however, are necessarily approximations 
only. While animals of the same species are of the same general 
shape, we can by no means regard them as being exactly similar 
figures in the geometrical sense, nor can we safely assume them to 
be of exactly the same specific gravity, since changes in the 
amount of contents of stomach and intestines, and particularly in 
the quantity of fat in the body, would cause greater or less variations. 
Moreover, the state of fatness has, as Voit points out, still another 
effect. As an animal grows fat, the increase in size is mainly 
transverse and not longitudinal, the effect being like that of in- 
creasing the diameter of a cylinder of fixed length.* In such a 
case, however, the increase in the surface is not proportional to the 
two-thirds power of the volume, nor to the square root of the vol- 
* In the case of an animal, of course, we have the additional fact that the 
deposit of fat is not of uniform thickness over the whole surface of the body. 
