Nevertheless the bipartition of the stars into two such distinct classes must be considered as vague and doubtful. Such an _apparent_ bipartition is, indeed, necessary in all statistics as soon as individuals are selected from a given population in such a manner as the parallax stars are selected from the stars in space. Let us consider three attributes, say _A_, _B_ and _C_, of the individuals of a population and suppose that the attribute _C_ is _positively_ correlated to the attributes _A_ and _B_, so that to great or small values of _A_ or _B_ correspond respectively great or small values of _C_. Now if the individuals in the population are statistically selected in such a way that we choose out individuals having great values of the attributes _A_ and small values of the attribute _B_, then we get a statistical series regarding the attribute _C_, which consists of two seemingly distinct normal frequency distributions. It is in like manner, however, that the parallax stars are selected. The reason for this selection is the following. The annual parallax can only be determined for near stars, nearer than, say, 5 siriometers. The direct picking out of these stars is not possible. The astronomers have therefore attacked the problem in the following way. The near stars must, on account of their proximity, be relatively brighter than other stars and secondly possess greater proper motions than those. Therefore parallax observations are essentially limited to (1) bright stars, (2) stars with great proper motions. Hence the selected attributes of the stars are _m_ and μ. But _m_ and μ are both positively correlated to _M_. By the selection of stars with small _m_ and great μ we get a series of stars which regarding the attribute _M_ seem to be divided into two distinct classes. The distribution of the parallax stars gives us no reason to believe that the stars of the types K and M are divided into the two supposed classes. There is on the whole no reason to suppose the existence at all of classes of giant and dwarf stars, not any more than a classification of this kind can be made regarding the height of the men in a population. What may be statistically concluded from the distribution of the absolute magnitudes of the parallax stars is only that the _dispersion_ in _M_ is increased at the transition from blue to yellow or red stars. The filling up of the gap between the “dwarfs” and the “giants” will probably be performed according as our knowledge of the distance of the stars is extended, where, however, not the annual parallax but other methods of measuring the distance must be employed. TABLE 8. _THE ABSOLUTELY FAINTEST STARS._