To those who have followed the fluoride story, the comparatively narrow margin between health-conferring amounts in the drinking water and mottled enamel-producing amounts is well known. By a happy coincidence, the fluoride concentration associated with a beneficial reduction in caries is a concentration producing little or no injury. There are several remarkable aspects of this coincidence. First, the amounts of fluoride involved are extremely small; only 1 ppm. apparently confers a low incidence of cavities, and only 2 to 5 ppm. is associated with endemic mottled enamel. Second, fluorides provide an unusual example of a substance which may be healthful in small amounts, but in slightly larger amounts is harmful. Third, both of these fluoride effects show up in the same structure in the body; the benefit of small amounts of fluoride is exhibited in the teeth and the injury by slightly larger amounts is exhibited, as far as we know, only by the teeth.
If a patient comes into the office with a series of questions about fluorides, the busy practitioner may not have at his fingertips a quick, easily grasped answer. Suppose the patient asks how much good fluorides will do if they are put in the drinking water, and how we know that they are safe. Answers can be given briefly and convincingly accompanied by a little sketch made of two straight lines. The purpose of this paper is to describe these two straight lines, to tell how they were obtained and to discuss their significance.
To start with, it should be recognized that many functions of the body can be expressed mathematically. It is through this approach that the two straight lines have been found. There is something appealing about any straight line relationship; the regularity and simplicity of a linear change makes such a relation easy to grasp. Many of the body functions may be described as linear processes when the effect under study is expressed in terms, not of stimulus, but of the logarithm of the stimulus…
Professor of Pharmacology Division of Dental Research, University of Rochester School of Medicine and Dentistry, Rochester,