1. In a compound apposition eye the acuity may be limited by the inter-ommatidial angle or by the optical performance of each ommatidium. In the honeybee the performance of the ommatidia must approach the theoretical limit set by diffraction if the whole eye resolves points separated by twice the inter-ommatidial angle.
2. The eyes of twenty-seven other species of Hymenoptera were measured, and the results show that in eyes of different sizes the number of ommatidia is adjusted so that inter-ommatidial angle is just below the limiting resolving power of the ommatidia; this is the condition for optimum acuity in a compound apposition eye.
3. When this condition is fulfilled the minimum resolvable angle is inversely proportional to the square root of the linear dimensions of the eye. Acuity increases with size more rapidly in the simple type of eye.