It would be highly desirable to have a mathematical analysis of the normal functions and interrelationships of accommodation and convergence. These two functions seem to behave mathematically, i. e., they follow with absolute constancy (of unit measure) certain predetermined patterns; therefore, with a "physiologically ideal" relationship between his accommodation and convergence, for a given patient there can be only one mathematically correct value for each function. Although this would seem obvious, I have been unable to find a specific treatise on these mathematical identities and interrelationships. The probable reason is that accommodation has been treated as an algebraic and convergence as a nonalgebraic function. Using constant units of measurement it is impossible to express in a simple equation the coordinate roles of an algebraic function (accommodation) and a transcendental or nonalgebraic function (convergence).
It is my purpose to describe how this problem can be solved by changing the transcendental function
HILL RV. The Hyperbolas of Accommodation and Convergence. AMA Arch Ophthalmol. 1957;57(2):259-265. doi:10.1001/archopht.1957.00930050269017