+) 
MATHEMATICAL FORMULAS AND ACID EXCRETION. 
By GEORGE D. BARNETT. 
(From the Medical Division of the Stanford University Medical School, 
San Francisco.) 
(Received for publication, December 5, 1917.) 
The application of mathematical formulas in the attempt to 
elucidate biological processes has lately furnished us with laws, 
quantitative relationships, constants, and indices which might 
seem to leave little to be desired. Some of us, however, have 
been inclined to question the value of certain of these laws, par- 
ticularly as applied to the excretion of a variety of substances 
by. the kidney, not only on account of the positive contrary evi- 
dence brought forward, but also on the ground that we believe it 
improbable that our present knowledge is sufficient to permit us 
to express the complexities of kidney activity with mathematical 
accuracy. 
An analysis of the data presented in the recent paper of Fitz 
and Van Slyke! on acid excretion affords a specific basis for crit- 
icism of one such mathematical relationship. In this paper the 
authors search for a “‘quantitative relationship . . . .  be- 
tween the alkali reserve of the blood plasma, as measured by the 
combining power for COs, and the rate of acid excretion by the 
kidneys,” and arrive at the conclusion that the combined formula 
developed by Ambard for urea and for chloride excretion is 
applicable here in the form 
Plasma CO, = 80 — 2 VC 
where D is the excretion rate for acid plus ammonia, C’ their 
concentration in the urine, and W the weight of the individual. 
They adopt this form as an expression of the true quantitative 
relationship only after trials of various modifications, concluding 
1Fitz, R., and Van Slyke, D. D., J. Biol. Chem., 1917, xxx, 389. 
267 
