This paper attempted to define the approximational function of the swimming form of the rainbow trout. Undulatory movements of the swimming fish staying at the same posittion in a steady flow were recorded by a 16mm movie camera. Two axes were set up to measure the positions of the center of the cross-section. X-axis was in the direction of the steady flow. H-axis was in a direction perpendicular to the x-axis. The measured points were determined by x-coordinate. Mainly, the transformation of the spinal column was measured.
The amplitude was minimum near the posterior edge of the operculum, and increased in proportion to distance from that point, maximum at the tip of caudal fin. The function of the change of amplitude was indicated by the sum of two exponential functions. The approximational function could be indicated by the product of that function and the function of traveling wave.