In this paper is given an inference as to the stability relation of kyanite, sillimanite, andalusite, and mullite., The Stability relation is represented in the figure, in which the ranges of conditions corresponding to varius mineral facies are also roughly shown., This diagram was constructed chiefly on the basis of the following facts., In such high-pressre rocks as eclogite, kyanite is commonly found but sillimanite is rare., In ordinary regional metamorphism under comparatively high pressures as shown by h, d or thereabouts in Fig., 1, kyanite is formed at lower temperatures, and sillimanite at higher., In some cases of regional metamorphism where the pressures prevailing are relatively low as shown by s or therebouts in the diagram, andalusite also occurs., In thermal metamorphism under even low pressures s, r or still low in Fig., 1, andalusite is most commonly found, but in some highly metamorphased rocks sillimanite also occures., Under very low pressures mullite is formed, at least at high temperatures., The figure illustrating these facts is consistent with all these and other modes of occurrence of the aluminium-silicate minerals without exception, insofar as the writer is aware., It may be seen from the figure that these minerals are useful as indicators of pressures of their formation., If we can determine quantitativery the stability relation in the future, the estimation of pressure in metamorphic processes may become possible., It is quite usual that andalusite occurs in hornfelses, and kyanite in crystalline shists., The explanation of the absence of kyanite in the ordinary contact metamorphic aureole may be that the inner zone of the aureole was too intensely heated for kyanite to be stable, this mineral being stable only at low temperatures (as is seen in the figure) under moderate pressures, and in the outer zone recrystallization was not so complete as to from kyanite, or other low-temperature minerals, e., g., sericite, clay-minerals, etc., were formed instead of kyanite., In very exceptional cases, however, kyanite occurs as a product of thermal metamorphism., In most cases where the association staurolite-andulusite or kyanite-andalusite occurs, one mineral of each of these pairs shows such features as to indicate earlier formation than the other, and then the association may be regarded as one of non-equilibrium., There seems to be some cases, however, where the association represents a stable one., The stable association of kyanite with andalusite does not conflict with the mineralogical phase rule, for they are not usually the pure compounds of the compositions Al2SiO5, but contain some quantities of other compounds as solid solutions.,