Urinary excretion of a substance after a single dose.

THE method of Stern1 for representing experimental data seems to be useful. However, the equation of Haigh and Reiss2 has good theoretical justification, and it seemed worth while to see whether there was any simple relation between the two formulae. Stern derives the equation to represent the data where Q and t 0 are constants and x is the cumulative excretion as a function t. Haigh and Reiss's equation is where x max. and λ are constants. Plotting Haigh and Reiss's equation in the manner of Stern gives an effective straight line over the range t = 0.2/λ to t = 4/λ, and this curve then has a discontinuity and becomes the horizontal straight line x = x max. for greater times. This straight line yields values of Q = a x max. and t 0 = b/λ; tentative values of the constants a and b are a = 0.25 and b = 0.1. For values less than 0.2/λ, the curve tends to the straight line x = 0 as t tends to zero. This behaviour is more satisfactory than the straight line of Stern, as the latter will yield negative excretions for the period immediately after the injection. Thus it appears that in fact Stern's method is merely a convenient way of plotting a Haigh–Reiss formula.