1. The ontogenetic allometry of radii of curvature and the tube radii of the semicircular canals of approximately 85 juvenile (2–20 g) centrarchids of the species Lepomis gibbosus (L.) was investigated. The radii of curvature of the semicircular canals have different allometries; these arefor the anterior vertical, posterior vertical and horizontal canals respectively. The differences in growth exponents between the anterior and posterior vertical semicircular canals and between the anterior vertical and horizontal semicircular canals were statistically significant (P < 0·02 and P < 0·05 respectively).
2. Body mass and standard length were almost equally good predictors of the radii of curvature of the anterior vertical semicircular canals, but body mass was the better predictor of the radii of curvature of the posterior vertical and horizontal semicircular canals, as judged by the magnitude of the mean squares about the logarithmic regressions of radii on length and mass.
3. By measuring and estimating the area moments of the fins of the fish, the moments of inertia about various axes and the allometry of the characteristic swimming velocity of the fish, we attempted to account for the magnitude and direction of the differences in allometric growth exponents of the radii of curvature of the semicircular canals. Unexplained by our best estimate of growth exponents was the very high value observed for the posterior vertical semicircular canals.
4. No significant correlation could be found between the residuals of the major dimensions of the posterior vertical semicircular canals and those of body width or depth once the influence of body mass was removed. This finding suggests the rejection of the hypothesis that the allometry of this semicircular canal is simply correlated with overall body expansion in its plane.
5. The discrepancies between our predictions and observations of growth exponents could be explained by a gradual increase of the spring constant of the semicircular canals on the order ofthough they may also be due to other factors neglected in our model, e.g. the allometry of the added mass of the fish.
6. No evidence suggested that the shape of the semicircular canals was altered over the size range of the fish we studied. However, among the fins of the fish and the major body dimensions, only the width and the depth of the fish exhibited growth constants that did not differ significantly from each other.
7. We computed the effective toroidal radii of the non-toroidal-shaped vertical semicircular canals and found that the equivalent toroidal radius of the anterior vertical semicircular canal was consistently greater than that of the posterior vertical semicircular canal. This difference is explicable on the basis of the different moments of inertia of the animal about axes through the center of gravity and parallel to the axes of the semicircular canals.
8. We computed the allometry of the ratios R̄/r2 for all three semicircular canals and found in accordance with the prediction of Jones & Spells that they did not differ significantly from zero.
9. The allometry of the outer tube radii of the several semicircular canals was determined, and, while there was no significant difference in the growth exponents of the tube radii, it was noted that the tube radius of the horizontal semicircular canal was consistently and significantly smaller than that of the vertical semicircular canal. We suggested that this difference might be due to the broader range of frequencies that the fish experienced about its yaw axis.
10. Taken as a whole the data and calculations of this paper generally support the theory that the dimensions of the semicircular canals and the ontogenetic changes in them attune the semicircular canals to the angular frequency spectra that the fish experience about their axes.
On a Generalization of One-Dimensional Kinetics
