BIOLOGY: L. J. HENDERSON 
655 
minute canalization of the body, and the prodigious jumps of the flea, 
as well as the variation in metabolism with the size of the organism. 
Yet even this subject is by no means exhausted. For example (a fact 
which appears to be of some importance in describing the internal 
regulation of temperature) the difference in temperature between center 
and surface of a sphere which is producing heat uniformly throughout 
its whole mass, when equilibrium has been established with a sur- 
rounding liquid medium of constant temperature, is proportional to 
the square of the radius.^ 
But apart from this great principle and certain superficial discussions 
of the nature of oedema and similar phenomena, the regulation of vol- 
ume has remained without any physico-chemical analysis. Yet, from 
the standpoint of physical science, this is perhaps the most universal 
and fundamental of all organic regulations. I believe that this strange 
neglect may be traced to three facts. In the first place, the chemist is 
accustomed to vary the volume of his systems to suit his convenience. 
This is a justifiable practice, because, if the phases are so large that 
capillary phenomena may be disregarded, and so small that gravity 
need not be taken into account, the division of a phase into two parts 
does not change its energy. Thus, volume hardty enters into our cal- 
culations except as an indirect expression for that which is regarded as 
the true variable, viz., concentration. This, however, is to disregard 
the real question as it presents itself in biology. Secondly, when equilib- 
rium has been established in a heterogeneous system, as Willard Gibbs 
rigorously proved, the volume of the phases — capillary and gravitational 
phenomena being absent — is not relevant to the state of the system. 
But it may be at once observed, first, that until equilibrium has been 
attained the volume is of great moment, and, secondly, that equi- 
librium is never attained within the organism. Finally, the ordinary 
conception of the process of diffusion is based upon a mathematical 
discussion, which, though leading to a consistent description of the 
phenomena, is nevertheless a false representation of the actual occur- 
rences. And nearly all physiological changes of volume depend upon 
diffusion. 
Contrary to a general though vague belief, the regulation of volume 
is theoretically independent of osmotic pressure regulation . For exam- 
ple, if a kidney produces a liter of urine of the same freezing point 
as blood, it must have diminished the volume of the body and left the 
osmotic pressure sensibly unchanged. 
For the purpose of discussion, the activity of the kidney may be 
reduced to the following fiction: First there must be an excretion of all 
