The above investigation shows:—

• 1. The nature of homogeneity of structure, and the properties which distinguish it from structureless homogeneity. The new definition of a homogeneous structure recently put forward by the author in Groth's Zeitschrift is given.

• 2. A method of realising in a concrete form, and with great generality, the kind of repetition in space which constitutes homogeneity of structure, the models employed for this purpose each consisting of a number of similar plaster hands appropriately arranged in space.

  The total number of types of arrangement, all of which can be represented in this way, is 230, this being the number of typical point systems described by Fedorow and Schönflies, derived by their extension of Sohncke's methods. The various types of homogeneous structure, like the corresponding point-systems, all fall into the 32 classes of crystal symmetry.

• 3. What property common to all homogeneous structures whatever most nearly coyresponds to Thomson and Tait's definition of homogeneity.

• 4. Reasons for regarding as untenable the arguments put forward by Fedorow in support of his recent attempt to select from among the types of homogeneous structure those which are possible for crystals, and to determine the shapes of their ultimate units.

• 5. The possibility of so classifying all conceivable ways of symmetrically partitioning all the types of homogeneous structure as to avoid all reference to the nature of the cell-faces, whether plane or otherwise, and, in other respects also, be perfectly general. Some reasons for undertaking this classification, notwithstanding its complexity, are given, the chief one being the relation of symmetrical partitioning to some stereo-chemical and other experimental facts.

The humite series has formed one of the most interesting problems to mineralogists ever since Scacchi established the three types. I may, perhaps, recall that he found the crystals to be divisible into three classes, all capable of representation by reference to a common parametral plane and three zone-axes at right angles to one another. But the three classes differ in the following respects:--(1) Each has a peculiar set of faces, and, with the exception of the pinakoids and the actual or theoretical prisms, few of the forms coincide in different types. (2) Whilst all the faces on crystals of one class can be easily represented by quite simple indices, such as (111) (123) (103) by a judicious selection of one of its faces as parametral plane, the faces on crystals of the remaining two classes give for the same parameters very high and complicated indices.

Some years ago I found in the bed of the Satlej at Wangtu, in the N.W. Himalayas, about 80 miles, as the crow flies, north-east of Simla, a boulder of the rock described in the following pages, It is composed of biotite, cyanite and cordierite, with apatite and rutile as accessory minerals.

The specimen has a specific gravity of 2.92. Its structure is holocrystalline, and its minerals show no trace of parallelism in their orientation. It is, I think, a product of contact metamorphism.