Robartes copied out and gave to Aherne several mathematical diagrams from the _Speculum_, squares and spheres, cones made up of revolving gyres intersecting each other at various angles, figures sometimes of great complexity. His explanation of these, obtained invariably from the followers of Kusta-ben-Luki, is founded upon a single fundamental thought. The mind, whether expressed in history or in the individual life, has a precise movement, which can be quickened or slackened but cannot be fundamentally altered, and this movement can be expressed by a mathematical form. A plant or an animal has an order of developement peculiar to it, a bamboo will not develop evenly like a willow, nor a willow from joint to joint, and both have branches, that lessen and grow more light as they rise, and no characteristic of the soil can alter these things. A poor soil may indeed check or stop the movement and a rich prolong and quicken it. Mendel has shown that his sweet-peas bred long and short, white and pink varieties in certain mathematical proportions, suggesting a mathematical law governing the transmission of parental characteristics. To the Judwalis, as interpreted by Michael Robartes, all living mind has likewise a fundamental mathematical movement, however adapted in plant, or animal, or man to particular circumstance; and when you have found this movement and calculated its relations, you can foretell the entire future of that mind. A supreme religious act of their faith is to fix the attention on the mathematical form of this movement until the whole past and future of humanity, or of an individual man, shall be present to the intellect as if it were accomplished in a single moment. The intensity of the Beatific Vision when it comes depends upon the intensity of this realisation. It is possible in this way, seeing that death is itself marked upon the mathematical figure, which passes beyond it, to follow the soul into the highest heaven and the deepest hell. This doctrine is, they contend, not fatalistic because the mathematical figure is an expression of the mind’s desire, and the more rapid the developement of the figure the greater the freedom of the soul. The figure while the soul is in the body, or suffering from the consequences of that life, is frequently drawn as a double cone, the narrow end of each cone being in the centre of the broad end of the other. [Illustration: A line drawing of two cones superimposed on each other, with the tip of each cone in the centre of the base of the other.]