530 PROCEEDINGS OF THE ACADEMY OP 



whether any of these parts have a position remarkable in a mathematical 

 point of view, and which might, therefore, possibly suggest something im- 

 portant in regard to further researches.* 



Cubical contents. The volume of the hyper-ellipsoid is equal to the solidity of 

 a prolate ellipsoid having the same length and thickness. f Hence it appears 

 that a definite quantity of material fit for the composition of an egg might, con- 

 sidered geometrically without regard to other conditions, take the form of 

 either an ellipsoid or hyper-ellipsoid egg ; the length and the thickness being 

 the same in each case. It seems probable that either form might suit the 

 structure of those parts of the bird which anatomists believe to be most directly 

 concerned in giving shape to the egg. I do not certainly know whether the same 

 hen can lay eggs of both forms. Among several hyper-ellipsoid eggs, said to 

 be from the same hen, was found one which most observers would probably 

 consider ellipsoidal. A gentleman who once took much interest in the 

 breeding of fowls states that, whilst engaged in tbis pursuit, he was able from 

 the appearance of the eggs, but not judging alone by the shape and size, to 

 recognize with considerable certainty the eggs of particular birds and of par- 

 ticular breeds. In his opinion, the eggs of the same hen would appear, to 

 ordinary observation, to be of nearly the same size and shape: sometimes, how- 

 ever, an unusually large egg containing two yolks will be produced. My 

 limited observation is, in general, in favor of the supposition of uniformity of 

 size and shape among the eggs of the same individual. I have, besides meas- 

 uring some hen's eggs, carefully inspected the eggs found in several nests of 

 wild birds. 



Standard of comparison for shape. As far as I am aware, no mathematical 

 standard of comparison for the shape of eggs has been fixed. Thus, for ex- 

 ample, if we had an egg intermediate, as the term would generally be ap- 

 plied, between the ideal form above found for the egg of Epiornis, and a true 

 ellipsoid having the same diameters, it would be left to the judgment alone 

 to decide which ideal form should be preferred as a representative of the egg. 



M. St. Hilaire does not give measurements to show the agreement between 

 the ellipsoidal eggs of Epiornis and true ellipsoids. Of some of them, he 

 says their resemblance to each other was so great that one might have readily 

 been mistaken for the other. From this description I doubt whether these 

 e^gs resembled ellipsoids more nearly than the present egg of Epiornis re- 

 sembles the hyper-ellipsoid. J 



RESEMBLANCES BETWEEN MATHEMATICAL, ACOUSTIC, ELECTRIC, 

 OPTICAL AND ORGANIC FIGURES. 



The mathematical laws of the propagation of light are shown to be partic- 

 ular cases of the more general laws of vibratory motion in any elastic medium 

 composed of attracting and repelling molecules. It would, therefore, seem 

 that forms similar to those shown in the polarization of light, and in other 



* I am not informed how far naturalists have considered this subject. Some experiments of my 

 own, made on hen's eggs, in order to ascertain the relation between the size of the yolk and other 

 dimensions of the egg, and also whether the centre of the yolk more nearly coincides with the 

 centre of gravity of the egg or with the centre of the axis, resulted in gaining some preliminary 

 experience in the method of observation, but did not establish any thing certainin regard to the 

 object of research. 



- The rule for computation is. Multiply the square of the thickness by the length, and the pro- 

 duct by -b'lZS. The result is the solidity. 



J Since writing the above I have seen, in the collection of the Smithsonian Institution, the cast 

 of an egg of Epiornis (the egg sent from Madagascar in 1850), but have not had an opportunity rf 

 closely examining it. The date indicates that it is from a cast of the ellipsoidal egg described ty 

 M. St. Hilaire in his first memoir, and which accompanied the egg we have endeavored to imitate 

 in Fig. 4. Without a careful measurement of the cast, it would, in my opinion, be unsafe to con- 

 clude that the egg in question is more nearly ellipsoidal than its fellow is hyper-ellipsoidal. 



Encyclopedia Britannica, Boston ed., art. Optics, p. 546. 



[D 



ec. 



