1. Equations describing the geotropic orientation of young rats as a function of the inclination of the surface on which creeping take place, under standardized conditions, are found to be of similar form but with different values of the contained constants, when several different, genetically stabilized lines or races are compared. The values of these constants are characteristic for the several races.
2. The biological "reality" of the differences between young rats of two races, as given mathematical form in terms of these parameters and coefficients, can be submitted to radical test by investigating their behavior in inheritance. A simple result favorable to the inquiry would be decisive; a complex, non-clear result would not however be definitely unfavorable to the view that "real" differences in behavior are in question. The actual result is of a kind demonstrating (a) the efficiency of the original formulations, and (b), at the same time, the definite inheritance of certain quantitative aspects of geotropic behavior.
3. On the assumption that orientation on a sloping surface is achieved when, within a threshold difference, the tension-excitations on the two sides of the body (legs) are the same, the angle of oriented progression (θ) can be taken as a direct measure of the total excitation. This is consistent with the equation, accurately obeyed by our initial races, Δ cos θ/Δ sin α = - const., where α is the slope of the surface.
4. The total excitation of tension-receptors must be regarded as involving, over a gross interval of time, (1) the total array of receptors with thresholds below a certain value, a function of the stretching force, and (2) the frequency of change of tension. The latter, largely determined (it is assumed) by the frequency of stepping, should be proportional to the speed of progression. This speed is directly proportional to log sin α. Hence Δθ/Δ log sin α. plotted against sin α, should give a picture of the distribution of effective thresholds among the available tension-receptors in terms of the exciting component of gravity. For the races investigated this distribution can be resolved in each case into three groups.
5. A "variability number" is employed which permits the demonstration that the variability of θ as measured is (1) definitely controlled by α, and is (2) a characteristic number for each of the pure races used.
6. By attaching a weight to rats of one race it is found that Δθ/Δα is modified in a manner concordant with the assumption that the three "groups of sense organs" are in fact discrete.
7. In race K these three groups (I, II, III) are large, in race A, small (i, ii, iii). F1 rats of the cross between these two races show i, ii, III.
8. F1 individuals back-crossed to A give in the progeny two sorts of individuals, in equal numbers: i, ii, III and i, ii, iii.
9. F1 individuals back-crossed to K are expected to give in the progeny four types of individuals, I, II; i, II; I, ii; i, ii. In the numbers available these classes are reasonably clear, and occur with equal frequency.
10. It is pointed out that these considerations imply a mode of definition of a gene somewhat different from that commonly employed by tacit assumption; namely, a definition of the effect in inheritance as a function of some controlling, independent variable.