[Nature of the curves of the cranial vault and their relationship with various brain structures]

A radiometric investigation for various angles of two dry craniums and of the encephalographic or cerebral arteriographic pictures of 250 subjects has revealed the following facts: The architectural lines of the dome of the skull found by orthogonal projection of the profile, from the front, and in vertical projection, are hyperbolic spirals starting from the base of the skull and converging on the sphenoid. These lines join up in the parietal region forming a hyperbole. The frontal spiral is a simple hyperbolic spiral. The temporal spiral is of the lituus type. The axes of these lines converge in a frontal plane on the epiphysis. The axis of the parietal hyperbole on a projection of the profile passes through the epiphysis and is followed by the parietal artery. Central cranio-encephalic formations follow the same spiral path. The contour of the upper edge of the cerebellum is a lituus spiral. The outline of the lower part of the cerebellum is a simple hyperbolic spiral. The right side of the polar origins of a spiral plotted in the plane of the insula coincides with the right side of the opercula. It can always be plotted, in theory, and forms an angle of 22 degrees 30' with the right side of the median frontal spiral. It cuts the axis of the parietal hyperbole at the apex of the insular triange. The bissector of the angle formed by the two right sides of the polar origins bissects the axis of the parietal hyperbole at a point corresponding to the epiphysis. The temporal hyperbolic lituus spiral has its focal point under the anterior, clinoid, at the junction of the segments CII and CIII of the carotid siphon the curve of which follows the convolutions of the temporal spiral. The right side of the polar origins of this curve indicates the mean direction of the posterior cerebral. The contours of the corpus callosum are homothetic with those of the dome of the skull as far as the axis of the parietal hyperbole. The frontal and parietal curves converge according to four types in the main Pacchionian granulations. The sections of the frontal spiral are often marked by bone abnormalities on the internal table. This analytic test is invariably valid whatever the constants of the spirals or the eccentricities of the hyperboles. Combinations between spirals with different constants and hyperboles of various eccentricities amount to very many types which call for separate study.