A perturbation calculation on the eikonal equations by Bergmann [Phys. Rev. 70, 486 (1946)] is extended to apply to acoustic transmission in a medium with a single horizontal layer in which the deviation of the index of refraction from unity is very small. Numerical calculations for the sound level deviation for transmission in such a medium are presented. A temperature layer about 2 yd thick with a maximum temperature deviation from the surrounding water of 0.02°C can produce sound level variations of 2.2 db at 500-yd range. Excellent agreement is obtained in a comparison between these results and direct acoustic transmission measurements in an underwater medium closely approximating these assumptions. (This work was supported by the Bureau of Ordnance, U. S. Navy, under Contract NOrd 12937.)