280 Formation of Compound or Twin Crystals. 



attends the passage of a body from the state of a fluid to that of a 

 solid. 



The three axes indispensable to the construction of a Cube, may 

 be represented by lines connecting the centres of the opposite faces. 

 A sphere being inscribed in this solid, these axes will be three di- 

 ameters at right angles with one another, (Fig. 1.) Spherical mo- 

 lecules influenced by such forces would be arranged on one another 

 as in Fig. 2, being in contact at the extremities of these axes, where 

 the attraction for one another is exerted. 



In the Right Square Prism, because of the inequality of the ver- 

 tical axis to the other two which are equal, the length of the mole- 

 cule is unequal to its breadth, and consequently it is an ellipsoid of 

 revolution,* to which the rectangular axes of the prism are conjugate 

 axes, (Fig. 3.) The action of such molecules on one another would 



* A few remarks may possibly be required in explanation of the solids termed 

 ellipsoids or solid ellipses, and their axes. 



In the plain ellipse AA' BB', the lines AB, A'B' at 

 right angles, are termed conjugate axes, and ab, a'b', con- 

 jugate diameters. The peculiarity of these lines is, that 

 if aline as mn is drawn touching the ellipse at the ex- 

 tremity of one diameter, it will be parallel to the other 

 diameter. When ab = a'b', these lines are called the 

 eqital conjugate diameters. The axes are conjugate di- 

 ameters at right angles with one another. 



The revolution of a plain semi-ellipse, as AB'B, 

 around one axis, describes the surface of a solid which 

 is denominated an ellipsoid of revolution. Suppose the 

 semi-ellipse AB'B to revolve on AB as an axis, all the 

 sections of the described solid, which pass through AB 

 will be ellipses, of the same curvature as the above plain ellipse, their curvature 

 being determined by that of AB'B. Again as every point in the curve AB'B de- 

 scribes a circle in its revolution about AB, the sections parallel to A'B' are circles, 

 and consequently the lateral axes which lie in the section A'B' are equal. The 

 ellipsoid of revolution has therefore its sections in one direction circles. If these 

 sections are ellipses, the figure is still an ellipsoid but not one of revolution, as the 

 simple revolution of a plain ellipse will not describe it. 



The axes in the ellipsoids, are three in number, and as in the plain ellipse, are 

 lines at right angles with one another. The three conjugate diameters may have 

 any position, with this restriction, that if a plane touches the ellipsoid at the ex- 

 tremity of one, it must be parallel to the plane in which the other two diameters 

 are situated. The axes are consequently diameters, but only the rectangular di- 

 ameters, axes. A moment's thought will make it evident that each face of a crys- 

 tal (tangent at the extremity of one axis,) is parallel to the plane in which are sit- 

 uated the lines connecting the centres of the other faces; and these lines are the 

 other axes. 



