An equation for the diffusion of oxygen along a plastron of uniform thickness was provided by Thorpe and Crisp in their classical work on plastrons. Since then it has been discovered that some plastrons are tapered, e.g. those of many spiracular gills, in which the thickness of the plastron becomes less as the distance from the spiracle increases. Here a differential equation is provided for calculating the efficiency of a uniformly tapered plastron. A series of curves is also given that show the efficiency of the tapered plastron as a function of the distance from the spiracle, thickness, and degree of taper. Using these curves the efficiency of the plastron can be estimated immediately without the necessity of solving the differential equations. © 1976.
Hinton, H. E., & Jarman, G. M. (1976). A diffusion equation for tapered plastrons. Journal of Insect Physiology, 22(9), 1263–1265. https://doi.org/10.1016/0022-1910(76)90104-9