From the data of experiments with bees in which threshold response is employed as a means of recognizing visual discrimination between stripes of equal width alternately illuminated by intensities I1 and I2, it is shown that the detectable increment of intensity ΔI, where ΔI = I2 - I1, is directly proportional to σI2 (I1 being fixed). From tests of visual acuity, where I1 = 0 and the width of the stripes is varied, σI2 = kI2 + const.; here I2 = ΔI, and ΔI/I2 = 1. When the visual excitability of the bee is changed by dark adaptation, λI ≡ kΔI (= k' σΔI) = k'' I + const. For the measurements of critical illumination at threshold response to flicker, σI2 (= σΔI) = k I2 = k' ΔI + const. The data for critical illumination producing threshold response to flicker in the sun-fish Lepomis show for the rods σI2 = K I2 for the cones σI2 = K'(I2 + const.). The data thus indicate that in all these experiments essentially the same visual function is being examined, and that the recognition of the production of a difference in effect by alternately illuminated stripes takes place in such a way that d (ΔI)/d (σI2) = const., and that ΔI is directly proportional to I (or "I2," depending on the nature of the experiment). It is pointed out that the curve for each of the cases considered can be gotten equally well if mean I or σI is plotted as a function of the independent variable involved in the experiment. Certain consequences of these and related facts are important for the treatment of the general problem of intensity discrimination.