The relation between heterosis and variabihty discussed by previous speakers i well illustrated by an example in the mouse where the structure of the second thoracic vertebra (vertebra prominens) is very variable; it may have a broad spatulat spinous process (+ + +), a round rod-shaped one (+ +), a mere spike (+), or then may be no osseous spinous process at all (—). As shown in table 20, the thre inbred strains CBA , C 57 BL and A differ much from each other ( means and variances have been calculated by ascribing arbitrary numerical values 3, 2, 1 an 0 to the four classes). In the cross CBA x C 57 BL , the variance in F 1 , F 2 and the backcross is much smaller than in either of the two parent strains. By contrast, i the cross between C 57 BL and A , the F 1 variance is between that of the pare strains, and F 2 is distinctly more variable. The same character thus has a great reduced variance in the first cross, but not in the second. The first cross led striking heterosis in F 1 as judged by the general vigour and the reproductive behaviour of the animals; the second cross showed little or no heterosis. While it is thus plausible to relate reduced variance to heterosis, nothing is known in the mouse as to why certain crosses between inbred strains result in marked heterosis while others do not.