CRYSTALLIZATION. 275 



faces will be developed; nud if one edge, or angle, be truncated, all the 

 correspond iiig edges, or angles, will be truncated. Were it otherwise, 

 there would not be a balance between the surface tensions in the sev- 

 eral faces. But there is another point to be taken into account. The 

 surface energy may become less in two ways — either by reducing the 

 tension per unit surface, or by reducing the total surface. When a 

 li(piid separates from another fluid, as chloroform from a sohition of 

 chloral hydrate on adding an alkali, or a cloud from moist air, the 

 liquid assumes the form which, for a given mass, has the least surface — 

 that is, the drops are spherical. If you cut off the i)roJ('cting corners 

 ami plane away tlie projecting edges of a cube or an octahedron, you 

 bring it nearer to a si)here, and if you suppose the volume to remain 

 constant, you still diminisli the surface. And if the diminution of the 

 total surface is not comi)ensated by the increased energy on the trunca- 

 tions, there will be a tendency for the crystals to grow Avith such 

 truncations. The like will be true in more complicated combinations. 

 There will be a tendency for sucli combinations to foi'm, provided the 

 surface energy of the new faces is not too great as compared with that 

 of the first simple form. 



But it does not always happen that an octahedron of alum develops 

 truncated angles. This leads to another point. To produce a surface 

 in a continuous mass requires a supply of energy, and to generate a 

 surface in the interior of any fluid is Jiot easy. Air maybe super-satu- 

 rated with aijueous vapor, or a solution with a salt, and no cloud or 

 crystals be formed, unless tiiere is some discontinuity in the mass, 

 specks of dust, or something of the kind. In like manner, if we have 

 a surface already, as wlieu a supersaturated solution meets tlie air or 

 the sides of the vessel containing it, and if the energy of either of these 

 surfaces is less than that of a crystal of the salt, some energy will have 

 to be supplied in onler to produce the new surfa(;e, but not so much as 

 if there were no surface there to begin with. Hence, crystals usually 

 form on tlu^ sides of tlie vessel or at the toj) of the liquid. When a solid 

 sei>arates from a solution there is gencMally some energy available from 

 the changi; of state, Avhich su])plies the energy lor the new surface. 

 But at tirst when the mass deposited is very small, the energy 

 available will be correspondingly small, and since the mass varies as 

 the cube of the dianu^ter of the solid, whereas the surface varies as 

 the square of the diameter, tlie flrst separated mass is liable to be 

 squeezed into liquid again by its own surface tension. This explains 

 the usual phenomena of sui)er-saturated solutions. A deposit occurs 

 most easily ou a surface of the same energy as that of the deposit, 

 because the additiomil energy reipiired is only for the increased extent 

 of surface. It ex])lains, too, the tendency of large crystals to grow 

 more rapidly than small ones, because the ratio of the increase of 

 surface to that of voluiiu' diminishes as the crystal grows. 



While speaking of the difficulty of creating a new surface in the in- 



