MORPHOLOGY OF THE CEREBRAL CONVOLUTIONS. 353 



Let p, Fig. 23, be one of the two points at which terminate the three arcs, along 

 which the two films and the partition are cut by the plane in question, and let 

 p c = p be the radius of the larger film. 



„ rt0 Draw the indefinite lines p m and 



r IG. La. x 



^ -^ D p n in such manner that the angles 



/ ^^---^v. , c p m and m p n shall be each of 



/ /' \ v-'-""'*" " 60°- On p m let us take p c' equal 



/ f/'_ \ \ -.--"' \ to p' — that is to say, the radius of 



/ / .-''"A \ / the smallest film; let us join c c' 



*k"~ \ \ / and prolong the right line until it 



\ Vc meets at d with p n. The three 



\ r\ x • • 



\ I \ points, c, c' and d, will evidently be 



\ / three centres, and p d will be the 



\v^^ s^ radius, r, of the partition, so that if 



from these three centres and with 



these three radii we trace three portions of circumferences terminating on the one 



hand at the point p, and on the other at its symmetrical q, we shall have as the 



figure shows, and still on the hypothesis of angles of 120°, the section of the system 



of the two films and of the partition. Let us seek now to determine the radius 



of this partition in a function of the two others. For this take pf= pc' and 



join c' f, the angle c p c' being 60°, the triangle f pc' will be equilateral, and we 



shall consequently have f c' = p c' = p' ; for the same reason, the angle f c'p 



will be 60°, like the angle c' p d, whence it follows that the right lines f c' and 



p d will be parallel ; we may therefore assume -±- — = ~ — ; by then substituting, in 



f c' f c 



this formula, for p d, f c' and p c their respective values r, p' and p, and observing 

 that f c= p — p', we shall deduce r — ' > ; being identically the value given 



by the first method, thus two laws, apparently independent, conduct to the same 

 conclusion. 



If a third spherical laminar cap joins itself to two others already united, the 

 system will evidently have three partitions, namely, one proceeding from the union 

 of the first two films, and two from the union of each of these films with the third. 

 These three partitions will necessarily terminate at the same arc of junction, and 

 supposing that they still have spherical curvatures, it will result that at three lines 

 of junction of each of them with two of the films the angles will still be of 120° ; it 

 will result, moreover, for reasons already given, that at the arc of junction of the 

 three partitions with each other the angles will be also of 120°. This being pre- 

 mised let us see by what means we can trace the base of a system of this kind, as 

 we have traced, Fig. 23, that of a system of two films. After having described, Fig. 

 24, the bases of the first two films, bases having for centres c and c', and for radii 

 the lengths given which we will again designate p and p', let us take commencing 



