already seen, the two partition-walls have the relative magnitudes of MP ã₤:ã₤ RS =ã₤0ôñ875ã₤:ã₤1ôñ111; (2) the point D , where RS equals unity, that is to say where the periclinal partition has the same length as a radial one; this occurs when öÝ is rather under 82ô¯ (cf. the points D , Dÿ£¢ãý ); (3) the point E , where RS and MP intersect; that is to say the point at which the two partitions, periclinal and anticlinal, are of the same magnitude; this is the case, according to our diagram, when the angle of arc is just over 62ô§ô¯. We see from this, then, that what we have called an anticlinal partition, as MP , is only likely to occur in a triangular or prismatic cell whose angle of arc lies between 90ô¯ and 62ô§ô¯. In all narrower or more tapering cells, the periclinal partition will be of less area, and will therefore be more and more likely to occur.
The case (F) where the angle öÝ is just 60ô¯ is of some interest. Here, owing to the curvature of the peripheral border, and the consequent fact that the peripheral angles are somewhat greater than the apical angle öÝ, the periclinal partition has a very slight and almost imperceptible advantage over the anticlinal, the relative proportions being about as MPã₤:ã₤RS =ã₤0ôñ73ã₤:ã₤0ôñ72. But if the equilateral triangle be a plane spherical triangle, i.e. a plane triangle bounded by circular arcs, then we see that there is no longer any distinction at all between our two partitions; MP and RS are now identical.
On the same diagram, I have inserted the curve for values of {367} cosecã₤ö¡ã₤ãã₤cotã₤ö¡ =ã₤ OM , that is to say the distances from the centre, along the side of the cell, of the starting-point ( M ) of the anticlinal partition. The point Cÿ£¢ã° represents its position in