260 Prof. Challis on the Mathematical Theory 



From the same work I take this further extract : — " La theorie 

 des sensations auditives qui precede a ete confirmee d'une maniere 

 interessante par les observations et les experiences de V. Hensen 

 sur les organes de Fou'ie chez les Crustaces. Ces animaux ont de 

 petits sacs moitie fermes, moitie ouverts a Fexterieur, ou les 

 otolithes nagent librement dans une humeur aqueuse, et qui sont 

 surmontes de petits crins rigides particuliers, relies par leurs 

 extremites aux otolithes, formant une serie ordonnee par ordre 

 de grandeur. . . . On trouve aussi, chez beaucoup de crabes, de 

 petits crins tout-a-fait analogues sur les parties libres du corps, 

 et qui doivent etre considered corame les organes de Fouie. 

 Ce qui le prouvent pour les crins exterieurs c'est en partie Fana- 

 logie de leur construction avec les crins des otolithes, en partie 

 la circonstance qu'ils se relient aux nerfs de la meme maniere, et 

 partent de la meme souche que dans les otolithes. Enfin Hen- 

 sen a trouve que Fouie persistait apres Fextirpation des sacs des 

 otolithes dans le My sis [the Opossum Shrimp], Fanimalne con- 

 servaut que les crins exterieurs des antennes"*. 



Without questioning the action of sonorous undulations upon 

 the organs referred to, I would suggest a doubt as to whether 

 the sensations so produced can in any correct sense of the term 

 be designated as sensations of hearing. 



Recurring to the subject of the human ear, I would remark 

 that the aerial waves emanating from a sounding body must ne- 

 cessarily produce an oscillation to and fro of the head in a vertical 

 plane passing through the source of sound. Upon the princi- 

 ples I have above endeavoured to unfold, it is conceivable that 

 this oscillation, however minute, may produce such an effect 

 on the nerves of the ampullae as in some degree to indicate the 

 direction from which the sound proceeds — a view which many 

 have entertained — although these nerves, as I conceive, do not 

 in any way contribute to the sensation of hearing. 



XXXIV. A new discussion of the Mathematical Theory of Oceanic 

 Tides. By the Rev. Professor Challis, M.A., F.R..S.,F.R.A.S.f 



THE theory of ocean-tides which I gave in the Philosophical 

 Magazine for last January conducted to formulae which, 

 under the assumed limitations, appeared to represent correctly 

 some of the laws of tidal phenomena. But on proceeding to 

 calculate the theoretical amount of tide, I found it to be so 

 very small, that I came to the conclusion that the theory was 

 contradicted by observation and must be abandoned. Also, 



* Theorie Physiologique de Musique, &c, par H. Helmholtz, p. 187. 

 t Communicated by the Author. 



