The different species of mica have very nearly the same forms and **interfacial** angles, and they not infrequently occur intergrown together in parallel position.

Although bismuth is readily obtained in fine crystals by artificial means, yet natural crystals are rare and usually indistinct: they belong to the rhombohedral system and a cube-like rhombohedron with **interfacial** angles of 92° 20' is the predominating form.

It crystallizes in rhombohedra belonging to the hexagonal system, having **interfacial** angles of 87° 40'.

If T12 denote the **interfacial** tension, the energy corresponding to unit of area of the interface b Q FIG.

Laplace does not treat systematically the question of **interfacial** tension, but he gives incidentally in terms of his quantity H a relation analogous to (47).

(48) ° and in general the functions 0, or 4), must be regarded as capable of assuming different forms. Under these circumstances there is no limitation upon the values of the **interfacial** tensions for three fluids, which we may denote by T12, T23, T31.

P. 463) deduced relative to the **interfacial** tensions of three bodies.

(52) According to (52), the **interfacial** tension between any two bodies is proportional to the square of the difference of their densities.

The densities a 1, 'a' 2, Q3 being in descending order of magnitude, we may write T 31 = (01 - 02+a, - o"3)'T0 =T 12+ T 23 + 2 (e 1 - (72) (02-0.3)Tc; so that T31 necessarily exceeds the sum of the other two **interfacial** tensions.

The problem is to make the sum of the **interfacial** tensions a minimum, each tension being proportional to the square of the difference of densities of the two contiguous liquids in question.