532 PROCEEDINGS OF THE ACADEMY OF 



An electrical figure having a strong resemblance to an egg may be seen on 

 Plate III. of Lichtenberg's figures.* 



M. Cornay considers electricity to be the radical universal generator. He 

 endeavors to illustrate this idea by comparing positions assumed by electric- 

 ally charged needles to the positions of parts of plants and animals. For 

 this purpose he has numerous engravings. f His description of the circula- 

 tion of the electric fluid, and of the effect of it in producing the nervation of 

 leaves and the spiral arrangement of leaves around the trunk of the plant, 

 reminds us of similar suggestions of Grandus to account for the disposition of 

 the petals of a flower. But M. Cornay's resort to experiment to test his opinions 

 is an important step in the right direction, for which he deserves the thanks 

 of morphologists, although as yet his experiments cannot be considered 

 conclusive proof of the correctness of his views. 



EXPLANATION OF THE PREVIOUS CONSTRUCTIONS CUBATURE 

 OF THE HYPER-ELLIPSOID. t 



Construction of the Hyper-ellipse and Hyperaster. Let (Fig. 3) the axis A B, 

 or length of the egg, =2d, and the greatest double ordinate, or thickness 

 of the egg, = 2 m. We have shown, in our work already referred to, that 



FA = a| s/ a (a m) and FB = a >/ a (a m) : it is now required 

 to find these distances by construction. By the construction given for Fig. 1, 

 D K = m, C D = a, therefore C K = a m. But, by Geometry, C F is a 

 mean proportional between C H and C K, that is, between a and a m. Hence 



CF = >/ a (a m) ; whence FA = CA + CF = a-|- *S a ( a m), and 

 FB = CB CF = a s/ a (a m); which was required. 



We have further shown that the radius vector of the hyper-ellipse is equal 

 to the radius vector of an ellipse referred to the centre, and in which the polar 

 angle is one-half that of the hyper-ellipse. This is the ellipse shown in Fig. 

 2, and hence the construction before given for Fig. 3 is evident. By referring 

 to our work, it will be seen that the hyperaster, Figs. 6 and 7, may also be 

 constructed from an ellipse in a similar manner, taking care that their polar 



* Conimentationes Societatis, 4c, Goettingen, 1778, vol. i. For a curious resemblance to a tree, 

 produced by the action of lightning, see Mr. Charles Tomlinson on Lightning Figures, Edinburgh 

 New Phil. Journal. Vol. xiv. No. 2, Oct. 1861, and vol. xv. No. 1, Jan. 1862. 



f Principes de Physiologie et Elements de Morphogenie Generate, par J. E. Cornay (de Roche- 

 fort), Paris, 1853, pp. 112, 191, 212 215. M. Cornay has labored earnestly and industriously to 

 promote the knowledge of Morphology. Some important propositions which he confidently as- 

 sumes appear to us still to want satislactory proof. Thus, for example, because the shape of an 

 insect agrees with the outline of a cluster of electrified needles, he appears to be satisfied that he 

 has found in the action of electricity, or of some hypothetical fluid, the true cause of the organic 

 form . 



% For certain formulae which will be necessary in this and the following investigations, see 

 Stn lies in Organic Morphology, pp. 32, 33, 40, 41. The curves now to be discussed belong to the 

 general form 



-/ p y. 



p \} e cos k ej ' 



wherein p is the semi-parameter, and e the eccentricity, of an ellipse. For the hyper-ellipse, 



7, = 1, n h In Fig. 5, k 5, n \. In Fig. 7, k 4, n \. The equation p = ?- j- 



Jl ~ COS f'C u 



represents an immovable orbit substituted for an elliptical orbit revolving about its focus, Prop. 

 XL1II.B. I., Newton's Principia, and Wright's Commentary on the Principia, London. 1828, vol.ii. 

 p. 245. Curves of the sort in question may be produced by revolving an ellipse, under various con- 

 ditions, whilst a describing point revolves in the ellipse. Some years since, I exhibited to the 

 Pottsville Scientific Association a mechanical arrangement for producing such figures. Suardis's 

 Geometric Pen is also an interesting instrument for describing curves. The joints of the pen remind 

 us of the joints in the limbs of animals, and furnish a hint as to a mathematical conception of 

 the motion of the limbs. See Adams's Geometrical and Graphical Essays, Loudon, 1S13, p. 151. 



[Dec. 



