Whether the partition be or be not a plane surface, it is obvious that its _line of junction_ with the rest of the system lies in a plane, and is at right angles to the axis of symmetry. The actual curvature of the partition-wall is easily seen in optical section; but in surface view, the line of junction is _projected_ as a plane (Fig. 106), perpendicular to the axis, and this appearance has also helped to lend support and authority to “Sachs’s Rule.” ―――――――――― [Illustration: Fig. 107. Filaments, or chains of cells, in various lower Algae. (A) _Nostoc_; (B) _Anabaena_; (C) _Rivularia_; (D) _Oscillatoria_.] Many spherical cells, such as Protococcus, divide into two equal halves, which are therefore separated by a plane partition. Among the other lower Algae, akin to Protococcus, such as the Nostocs and Oscillatoriae, in which the cells are imbedded in a gelatinous matrix, we find a series of forms such as are represented in Fig. 107. Sometimes the cells are solitary or disunited; sometimes they run in pairs or in rows, separated one from another by flat partitions; and sometimes the conjoined cells are approximately hemispherical, but at other times each half is more than a hemisphere. These various conditions depend, {301} according to what we have already learned, upon the relative magnitudes of the tensions at the surface of the cells and at the boundary between them[344]. In the typical case of an equally divided cell, such as a double and co-equal soap-bubble, where the partition-wall and the outer walls are similar to one another and in contact with similar substances, we can easily determine the form of the system. For, at any point of the boundary of the partition-wall, _O_, the tensions being equal, the angles _QOP_, _ROP_, _QOR_ are all equal, and each is, therefore, an angle of 120°. But _OQ_, _OR_ being tangents, the centres of the two spheres (or circular arcs in the figure) lie on perpendiculars to them; therefore the radii _CO_, _C′O_ meet at an [Illustration: Fig. 108.] angle of 60°, and _COC′_ is an equilateral triangle. That is to say, the centre of each circle lies on the circumference of the other; the partition lies midway between the two centres; and the length (i.e. the diameter) of the partition-wall, _PO_, is 2 sin 60° = 1·732 times the radius, or ·866 times the diameter, of each of the cells. This gives us, then, the _form_ of an aggregate of two equal cells under uniform conditions.